Kalman filtering is widely used for object tracking applications but often relies on predefined motion models, which limits its adaptability to nonlinear or uncertain trajectories. Formulating a Gaussian Process (GP) as a linear Gaussian state-space model provides a data-driven alternative for efficient sequential inference within a Kalman filtering framework. This paper extends the Integrated GP (iGP) model to introduce three novel variants: the Twice-Integrated GP (iiGP), the Dynamics-Informed Integrated GP (iDGP), and the Dynamics-Informed Twice-Integrated GP (iiDGP). The dynamics-informed models incorporate system dynamics alongside data-driven modelling, enabling more accurate tracking of motion under uncertain environments. The twice-integrated models enforce smoother motion patterns while maintaining the flexibility of GPs as driving noise. These models are implemented in the Stone Soup tracking framework. We discuss the software design, implementation challenges, and present evaluation results on synthetic and insect motion trajectory data. Results highlight the benefits of incorpo-rating dynamical information in GP-based tracking models, as well as the trade-offs between adaptability and robustness.

Existing trackers based on Poisson measurement process often struggle with efficiency and accuracy in large-scale tracking under heavy clutter. To overcome this, we introduce PiVoT, a scalable, robust multi-object tracker capable of efficiently detecting and tracking a large, varying number of objects, along with their shapes, existence probabilities, and measurement rates, even in heavy clutter. PiVoT employs a novel two-stage variational inference routine to achieve inference tractability and closed-form, parallelisable updates. Efficiency is further enhanced by early identification and removal of ineffective birth objects and designing highly simplified, much faster, yet equivalent variational updates. Additionally, PiVoT inherently offers efficient clutter-robust clustering, an innovation that can also enhance existing trackers that depend on supplementary clustering techniques. Experiments demonstrate PiVoT's clear accuracy and efficiency gains over existing methods, while also highlighting its ability to track a thousand closely spaced objects in under a second on a standard laptop without gating.

Lévy state-space models (SSMs) are a class of Bayesian models exhibiting heavy-tailed dynamics, particularly suited to systems with extreme values and abrupt changes. A broad family of Lévy SSMs that admit a linear-Gaussian conditional sub-model can be filtered using the Rao-Blackwellized particle filter (RBPF). In this work, we implement an efficient form of particle MCMC, taking advantage of end-to-end GPU acceleration and the special structure of the Lévy SSM, to permit inference in a practical time frame. We benchmark the performance of our implementation against a comparable CPU implementation, as well as existing comparable software packages, before showcasing our inference methods on a financial time series example, performing efficient joint inference on the SSM parameters alongside a novel Bayesian nonparametric estimate of the driving Lévy measure.

In recent years, state-space models for highly manoeuvrable objects have been proposed based on non-Gaussian, continuous time, jump-based Lévy processes, the so-called Lévy state-space model [1]–[4]. In these models, the standard Brownian motion driving process for continuous time processes is replaced with a heavy-tailed non-Gaussian alternative. This retains all the flexibility of its Gaussian counterpart in terms of possible dynamical model structures and operations with irregular time stamps or heterogeneous data sources. These models aim to operate in areas such as surveillance of irregularly moving drones or people, and tracking wildlife or biological data. Implementation is relatively straightforward since the Kalman filters of the Brownian motion case can be replaced in the nonGaussian case by mixtures of Kalman filters within a marginalised particle filtering framework [5]. While the Stone Soup tracking software environment includes both Kalman filtering and generic particle filtering, it does not currently allow the combination of these tasks within a marginalised particle filtering framework. We discuss the significant challenges involved in incorporating these models and algorithms into Stone Soup, and present initial simulation results for the new software.

This paper presents an adaptive approach to real-time multi-object localisation in addition to Siteswap inference, and performance evaluation metrics for juggling routines, employing a proposed bimodal machine learning-enhanced state-space model implementation. Considering the complex multi-modal characteristics exhibited by objects during performances, the paper introduces a bespoke Interacting Multiple Model (IMM) component for increased Siteswap beat detection accuracy and gravitational acceleration inference, and a scheme for causal Siteswap inference derived through machine learning-enhanced IMM mode outputs. The algorithm effectively models the transitory behaviour of the system, enabling rapid and smooth transitions between the two discrete tracking cases (airborne, and caught) and accurate Siteswap inference under a variety of camera and environmental conditions. The employment of beat tracking algorithms that exploit optimal compromises in time domain onset detection functions and Tempograms, enables effective error correction of Siteswap detections, in addition to providing performance analysis and visualisation utilities. Experimentally, the algorithm is capable of object tracking and Siteswap inference with up to 11 objects for a variety of challenging Siteswaps and conditions, serving as a versatile performance analysis, evaluation, and visualisation utility.

This paper investigates the task of tracking multiple objects in clutter under a distributed multi-sensor network with time-varying connectivity. Designed with the same objective as the centralised variational multi-object tracker, the proposed method achieves optimal decentralised fusion in performance with local processing and communication with only neighboring sensors. A key innovation is the decentralised construction of a locally maximised evidence lower bound, which greatly reduces the information required for communication. Our decentralised natural gradient descent variational multi-object tracker, enhanced with the gradient tracking strategy and natural gradients that adjusts the direction of traditional gradients to the steepest, shows rapid convergence. Our results verify that the proposed method is empirically equivalent to the centralised fusion in tracking accuracy, surpasses suboptimal fusion techniques with comparable costs, and achieves much lower communication overhead than the consensus-based variational multi-object tracker.

In this paper we introduce tracking models based on non-Gaussian continuous time stochastic processes with time-varying skewness. The idea behind this is that the skewness of the dynamical model may be able to model a propensity for an object to undergo manoeuvres of a particular type, for example velocities tending in a particular direction, but that these may change over time. This process is constructed based on a random series representation of conditionally Gaussian Lévy processes, which enables straightforward simulation of the models. We demonstrate the specific example of α-stable processes and find that such processes can capture abrupt changes owing to their heavy-tailed behaviour, and demonstrate the random changes in direction caused by the time-changing skewness of the distribution. We propose methods for joint tracking of both states and skewness for such processes, based on a marginalised particle filter, which are demonstrated to perform well even with limited numbers of particles.

This paper proposes a reversible jump Markov chain Monte Carlo method that provides efficient inference for the general problem of pulse fitting. In particular, it minimises the potential of an adopted parametric model overfitting to the (noisy) data via the inclusion of a peak proximity parameter. This facilitates learning a more representative underlying model and significantly reduces the computational cost. Synthetic and real data are used to demonstrate the efficacy of the introduced Bayesian technique.

A key challenge for multi-target trackers is being able to track both agile and simply moving targets effectively. This is only furthered by the standard difficulties of automated track initiation and deletion. This paper proposes a solution to this, where unknown associations and track management are handled by a Dirichlet process prior, and Gaussian processes model the dynamics of the targets. The promising performance of the proposed tracker is demonstrated on both synthetic and real radar data against a selection of other methods.

In this work we present the variance-gamma driven state-space model (VGSSM) - a linear vector stochastic differential equation driven by the variance-gamma (VG) Lévy process, and propose a novel inference framework in such systems. There are closed form expressions for the first four moments of the marginals of the VG process, allowing for more flexible modelling than Brownian motion (BM), retaining BM as a limiting case. The conditionally Gaussian formulation of the variance-gamma process lends itself well to the use of a marginalised particle filter (MPF) which can include the estimation of model parameters as part of the sampling framework. As an example we present a state-space formulation of Langevin dynamics in the VGSSM for estimation of both the observed and the latent first-order dynamics of a system. We apply this specific Langevin formulation to synthetically generated data to validate the results of the MPF, followed by an application to foreign-exchange tick data to demonstrate the method for trend tracking in data sets that are irregularly sampled in time.

This paper addresses the joint detection and tracking of an unknown and time-varying number of targets in clutter. Here we formulate the tracking task in a variable-dimension state space, under which the reversible jump sequential Markov chain Monte Carlo sampling methods can be utilised to online estimate the target number, their kinematic states, and the association variables. In particular, a fast Rao-Blackwellisation scheme is devised to improve the tracking accuracy and sampling efficiency for linear Gaussian models. Based on the nonhomogeneous Poisson process measurement model, the developed tracker enjoys a partially parallel sampling structure, thereby being able to efficiently tackle the data association under massive measurements and clutter. The simulation results demonstrate that the developed tracker exhibits superior tracking performance in comparison to existing trackers in both accuracy and computational efficiency when tracking multiple targets under heavy clutter.

Multi-target tracking of agile targets can be limited by choice of dynamical models. This is typically overcome by using sophisticated non-Gaussian and/or nonlinear motion models, and complex data association schemes. Here we aim to tackle scenarios when tracking (semi-)autonomous systems, such as drones, which often follow smooth optimised trajectories and undertake rapid manoeuvres when needed. This paper introduces a novel, flexible, multi-target tracking approach based upon a Gaussian process as a dynamical model, coupled with a non-homogeneous Poisson process for the observation model. It applies a particle filtering inference method for state estimation (including data association) and online parameter learning. The promising performance of the proposed technique is demonstrated on both synthetic data and real drone surveillance radar measurements, compared with a selection of more standard approaches.

With the aim of addressing audio signal restoration as a sequential inference problem, we build upon Gabor regression to propose a state-space model for audio time series. Exploiting the structure of our model, we devise a sequential Markov chain Monte Carlo algorithm to explore the sequence of filtering distributions of the synthesis coefficients. The algorithm is then tested on a series of denoising examples. Results suggest that the sequential approach is competitive with batch strategies in terms of perceptual quality and signal-to-noise ratio, while showing potential for real-time applications.

Coordinate ascent variational inference (CAVI) is a popular approximate inference method; however, it relies on a mean-field assumption that can lead to large estimation errors for highly correlated variables. In this paper, we propose a conditionally factorized variational family with an adjustable conditional structure and derive the corresponding coordinate ascent algorithm for optimization. The algorithm is termed Conditionally factorized Variational Bayes (CVB) and implemented with importance sampling. We show that by choosing a finer conditional structure, our algorithm can be guaranteed to achieve a better variational lower bound, thus providing a flexible trade-off between computational cost and inference accuracy. The validity of the method is demonstrated in a simple posterior computation task.

Measurement rates for both targets and clutter have been assumed to be known a priori in most existing tracking systems, whereas practically the rates may be unknown to users or time-varying. This paper therefore fills this gap by developing a Poisson mixture process tracker (PMPT) to capture the temporal characteristics of the rate parameters under a Poisson mixture measurement process. Specifically, the Generalized inverse Gaussian (GIG) distribution is proposed as a prior for Poisson rates, and two novel priors, the time independent GIG prior and the GIG Markov chain prior, are designed. In addition, a scalable inference framework is introduced to enable efficient data association and parallel updating of target states under a sequential Markov chain Monte Carlo (MCMC) scheme with linear complexity in the number of measurements and targets. Results show that our proposed method can provide a robust solution in highly dynamic detection probability environments.

Audio-visual tracking of multiple speakers requires to estimate the state (e.g. velocity and location) of each speaker by leveraging the information of both audio and visual modalities. Estimating the number of speakers and their states jointly remains a challenging problem. We propose an Audio-Visual Possion Multi-Bernoulli Mixture Filter (AV-PMBM) that can not only predict the number of speakers but also give accurate estimation of their states. We also propose a novel sound source localization technique based on DOA information and a deep learning based object detector to provide reliable audio measurements for the AV tracker. To our knowledge, this represents the first attempt using PMBM for multi-speaker tracking with audio visual modalities. Experiments on the AV16.3 dataset demonstrate that AV-PMBM achieves state-of-the-art performance in optimal sub-pattern assignment (OSPA).

We address the problem of autonomous tracking and state estimation for marine vessels, autonomous vehicles, and other dynamic signals under a (structured) sparsity assumption. The aim is to improve the tracking and estimation accuracy with respect to the classical Bayesian filters and smoothers. We formulate the estimation problem as a dynamic generalized group Lasso problem and develop a class of smoothing-and-splitting methods to solve it. The Levenberg-Marquardt iterated extended Kalman smoother-based multiblock alternating direction method of multipliers (LM-IEKS-mADMMs) algorithms are based on the alternating direction method of multipliers (ADMMs) framework. This leads to minimization subproblems with an inherent structure to which three new augmented recursive smoothers are applied. Our methods can deal with large-scale problems without preprocessing for dimensionality reduction. Moreover, the methods allow one to solve nonsmooth nonconvex optimization problems. We then prove that under mild conditions, the proposed methods converge to a stationary point of the optimization problem. By simulated and real-data experiments, including multisensor range measurement problems, marine vessel tracking, autonomous vehicle tracking, and audio signal restoration, we show the practical effectiveness of the proposed methods.

Parameter learning of the state-space model (SSM) plays a significant role in the modelling of time-series data and dynamical systems. However, the closed-form inference of the parameter posterior is often limited by sequential construction and non-linearity of the SSMs, which has led to the development of sampling-based algorithms such as particle Markov chain Monte Carlo (PMCMC). We present a novel algorithm, the particle filter variational inference (PF-VI) algorithm, which achieves closed-form learning of SSM parameters while tractably inferring the non-linear sequential states. We apply the algorithm to a popular non-linear SSM example and compare its performance against two competing PMCMC algorithms.

In this paper we present on-line Bayesian filtering methods for non-linear multivariate time series models corrupted by generalised asymmetric Laplace noise. We derive the optimum kernel for a particle filter applied to multivariate non-linear state-space models with scalar observations, where the observation noise is additive and asymmetric Laplacian. We show that sampling from this multivariate kernel is tractable using commonly available methods for use in particle filters, and that its associated likelihood can be evaluated. A particle filter is implemented for a test case using the developed kernel, and its performance is compared to that of a traditional bootstrap filter. The proposed methods show potential for application to systems with heavy-tailed skew noise.

In this paper we present multidimensional α-stable state-space models for object tracking, expressed in continuous time as Lévy processes. In contrast with the conventional Gaussian models, these heavy-tailed α-stable models are more likely to exhibit extreme noise values, thus showing the capability for modeling of erratic manoeuvring behaviour. Despite the potential benefits, such models are usually highly intractable for inference and therefore have not yet been widely adopted in the tracking field. Here the models are represented in a conditionally Gaussian series form, so that the marginal (Rao-Blackwellised) particle filter can be employed to perform tracking and smoothing very efficiently. As the result, the simulation tracks present some sharp manoeuvres, owing to the heavy-tailed property, and experiments demonstrate improved performance on an intent inference problem from automotive UI with highly perturbed pointing data.

This paper introduces a novel leader-follower model for tracking a group of manoeuvring objects under a probabilistic framework. The proposed model develops on the conventional leader-follower model in which the followers are driven stochastically towards the velocity and position of the leader. Here we consider the dynamic of followers as a mean-reverting process and express it in a continuous-time stochastic differential equation. Instead of using a standard global Cartesian or polar system, an intrinsic coordinate model is utilised for the leader where piecewise constant forces are applied relative to the heading of the leader. Followers then mean revert towards the heading angle and speed of the leader, leading to a more realistic behavioural modelling than the more conventional global coordinate systems. Such a dynamical model is readily incorporated into tracking algorithms using for example the variable rate particle filtering framework which can accurately capture and estimate the manoeuvres of the leader and followers. The simulation results verify its efficacy under challenging group tracking scenarios and future work will explore automatic identification of group structure and leadership from measurements of groups of moving objects.

In this paper we present on-line Bayesian filtering methods for time series models corrupted by asymmetric Laplace noise. An optimum kernel particle filter is designed for the general asymmetric case, and its performance is compared to that of a traditional bootstrap filter and a newly designed Rao-Blackwellised particle filter for the symmetric linear case. The optimum kernel is shown to improve performance and reduce degeneracy in the filter for a non-linear time-series model, and both the Rao-Blackwellised and the optimum kernel filter show significant advantages over a traditional bootstrap particle filter for a linear model.

In group object tracking, the identification of the group leader can be highly beneficial for predicting the intention and future manoeuvres of objects as well as learning the underlying group behaviour traits. This paper presents an online approach for inferring dominant entities in tracked groups from observations. Unlike traditional leader-follower models, here we develop a new rotated leadership model that can capture the dynamic evolution of the interaction patterns in groups over time. Two methods, an online Gibbs sampler and deterministic particle filter, are then designed to infer sequentially the leader in group object tracking scenarios. Synthetic and real pigeon flocking data are used to demonstrate the effectiveness of the proposed techniques in terms of identifying the group leader under complex dynamics.

We propose a particle filter (PF) for tracking time-varying states (e.g., position, velocity) of multiple targets jointly from superpositional data, which depend on the sum of all target signals. Many conventional methods perform thresholding for detection prior to tracking, which severely limits tracking performance at a low signal-to-noise ratio. In contrast, the proposed PF can operate directly on unthresholded sensor signals. Though there also exist methods applicable to unthresholded sensor signals called track-before-detect (TBD), the proposed PF has significant advantages over them. First, it is general without any restrictions on the form of a function that maps each target's states to its signal (e.g., disjoint, binary) or on the statistics of observation noise (e.g., Gaussian). Second, it can track an unknown, time-varying number of targets without knowing their initial states owing to Septier et al.'s state modeling with a birth/death process. The proposed PF includes Salmond et al.'s TBD PF for at most one target as a particular instance up to some implementation details. We present a simulation example in the context of radio-frequency tomography, where the proposed PF significantly outperformed Nannuru et al.'s state-of-the-art method based on random finite sets in terms of the optimal subpattern assignment (OSPA) metric.

The results of a series of theoretical studies are reported, examining the convergence rate for different approximate representations of α-stable distributions. Although they play a key role in modelling random processes with jumps and discontinuities, the use of α-stable distributions in inference often leads to analytically intractable problems. The LePage series, which is a probabilistic representation employed in this work, is used to transform an intractable, infinite-dimensional inference problem into a finite-dimensional (conditionally Gaussian) parametric problem. A major component of our approach is the approximation of the tail of this series by a Gaussian random variable. Standard statistical techniques, such as ExpectationMaximization (EM), Markov chain Monte Carlo, and Particle Filtering, can then be readily applied. In addition to the asymptotic normality of the tail of this series, we establish explicit, nonasymptotic bounds on the approximation error. Their proofs follow classical Fourier-analytic arguments, using Esséen's smoothing lemma. Specifically, we consider the distance between the distributions of: (i) the tail of the series and an appropriate Gaussian; (ii) the full series and the truncated series; and (iii) the full series and the truncated series with an added Gaussian term. In all three cases, sharp bounds are established, and the theoretical results are compared with the actual distances (computed numerically) in specific examples of symmetric αstable distributions. This analysis facilitates the selection of appropriate truncations in practice and offers theoretical guarantees for the accuracy of resulting estimates. One of the main conclusions obtained is that, for the purposes of inference, the use of a truncated series together with an approximately Gaussian error term has superior statistical properties and is likely a preferable choice in practice.

In this paper, we introduce a generic Bayesian framework for inferring the intent of a tracked object, as early as possible, based on the available partial sensory observations. It treats the prediction problem, i.e. not estimating the object state such as position, within an object tracking formulation. This leads to a low-complexity implementation of the inference routine with minimal training requirements. The proposed approach utilises suitable stochastic, namely linear Gaussian, models to capture long term dependencies in the object trajectory as dictated by intent. Numerical examples are shown to demonstrate the efficacy of this framework.

In this paper we focus on Bayesian blind and semi-blind adaptive signal processing based on a broadband MIMO FIR model (e.g., for blind source separation (BSS) and blind system identification (BSI)). Specifically, we study in this paper a framework allowing us to systematically incorporate various types of prior knowledge: (1) source signal statistics, (2) deterministic knowledge on the mixing system, and (3) stochastic knowledge on the mixing system. In order to exploit all possible types of source signal statistics (1), our considerations are based on TRINICON, a previously introduced generic framework for broadband blind (and semi-blind) adaptive MIMO signal processing. The motivation for this paper is threefold: (a) the extension of TRINICON to Bayesian point estimation to address (3) in addition to (1), and (b) more specifically to unify system-based blind adaptive MIMO signal processing with the tracking of time-varying scenarios, and finally (c) to show how the Bayesian TRINICON-based tracking can be formulated as a sequence estimation approach on arbitrary partly smooth manifolds. As we will see in this paper, the Bayesian approach to incorporate stochastic priors and the manifold learning approach to exploit deterministic system knowledge (2) complement one another very efficiently in the context of TRINICON.

This paper presents a survey of the ideas behind the particle filtering, or sequential Monte Carlo, method, from at least 1930 up to the present day. The particle filter, which is now 25 years old, has been an immensely successful and widely used suite of methods for filtering and smoothing in state space models, and it is still under research today. The key ideas that led to the development in 1993 of the original particle filter, the bootstrap filter, were Monte Carlo integration, Importance Sampling, Bayesian updating, Probabilistic State Space models, and Sampling-Importance-Resampling. We survey these methods within their historical context and then provide a general framework for description of most current variants on the particle filtering methodology, based upon updating the joint smoothing distribution of the states. This framework aids in the understanding of the various elements of a particle filter, including resampling. prediction and weighting. We further summarise recent developments and look to the future of the methodology.

In this paper we present Bayesian methods for tracking scenarios in which an intrinsic coordinate model is considered and inertial measurements plus occasional position fixes are available. The methods are first tested using synthetic data, giving a comprehensive evaluation as to their performance. Further evaluation on real data also reveals our approaches can be favourable alternatives to existing inertial tracking/navigation models.

This letter presents an alternative, more consistent, construction for bridging distributions, which enables inferring the destination of a tracked object from the available partial sensory observations. Two algorithms are then introduced to sequentially estimate the probability of all possible endpoints within a generic Bayesian framework. They capture the influence of intended destination on the object's motion via suitably adapted stochastic models. Whilst the bridging approach has low training requirements, the proposed formulation can lead to more efficient predictors, e.g. around 65% less computations for certain models. Synthetic and real data is used to illustrate the effectiveness of the introduced algorithms.

The objective of this paper is twofold. First, it presents a brief overview of existing driver and passenger identification or recognition approaches, which rely on smartphone data. This includes listing the typically available sensory measurements and highlighting a few key practical considerations for automotive settings. Second, a simple identification method that utilizes the smartphone inertial measurements and, possibly, doors signal is proposed. It is based on analyzing the user behavior during entry, namely, the direction of turning, and extracting relevant salient features, which are distinctive depending on the side of entry to the vehicle. This is followed by applying a suitable classifier and decision criterion. Experimental data is shown to demonstrate the usefulness and effectiveness of the introduced probabilistic, low-complexity, identification technique.

Predictive touch is an HMI technology that relies on inferring, early in the pointing gesture, the interface item a driver or passenger intends to select on an in-vehicle display [1, 2]. It simplifies and expedites the selection task, thereby reducing the associated interaction effort. This paper presents two studies on drivers using predictive touch and focuses on evaluating the best means to facilitate selecting the intended on-display item. This includes immediate midair selection with the system autonomously auto-selecting the predicted interface component, hover/dwell and drivers pressing a button on the steering wheel to execute the selection action. These were arrived at in an expert workshop study with twelve participants. The results of the subsequent evaluation study with twenty four participants demonstrate, using quantitative and qualitative measures, that immediate mid-air selection is a promising assistive scheme, where drivers need not touch a physical surface to select interface components, thus touch-free control.

This paper introduces a Bayesian framework for estimating the probability of a driver or passenger(s) returning to the vehicle, from the available partial (noisy) track of his/her location. The latter can be provided by a smartphone navigational service and/or other dedicated user to vehicle positioning solution, for instance RF-based. The proposed approach treats the addressed intent prediction problem, i.e. not tracking the object's state (e.g. the driver/passenger position, velocity, etc.) or predicting its next few values, within an object tracking formulation, leading to a Kalman-filter-based implementation of the inference routine. Hence, it is dubbed meta-tracker in lieu of a conventional “sensor-level” tracking algorithm and relies on utilising bridging distributions to encapsulate the long term dependencies in the trajectory followed by the driver or passenger as dictated by the intended endpoint, if any. Two example trajectories are shown to demonstrate the effectiveness of this flexible framework.

In this paper we address the challenging task of tracking a fast-moving bicycle, in the indoor velodrome environment, using inertial sensors and infrequent position measurements. Since the inertial sensors are physically in the intrinsic frame of the bike, we adopt an intrinsic frame dynamic model for the motion, based on curvilinear dynamical models for manoeuvring objects. We show that the combination of inertial measurements with the intrinsic dynamic model leads to linear equations, which may be incorporated effectively into particle filtering schemes. Position measurements are provided through timing measurements on the track from a camera-based system and these are fused with the inertial measurements using a particle filter weighting scheme. The proposed methods are evaluated on synthesised cycling datasets based on real motion trajectories, showing their potential accuracy, and then real data experiments are reported.

The Non-homogeneous Poisson process is a point process with time-varying intensity across its domain, the use of which arises in numerous areas in signal processing and machine learning. However, applications are largely limited by the intractable likelihood function and the high computational cost of existing inference schemes. We present a sequential inference framework that utilises generative Poisson data and sequential Markov Chain Monte Carlo (SMCMC) algorithm to enable online inference in various applications. The proposed model is compared to competing methods on synthetic datasets and tested with real-world financial data.

This paper investigates the on-line analysis of high-frequency financial order book data using Bayesian modelling techniques. Order book data involves evolving queues of orders at different prices, and here we propose that the order book shape is proportional to a gamma or inverse-gamma density function. Inference for these models is implemented on-line using particle filters and evaluated on a high-frequency EURUSD foreign exchange limit order book. The two possible order book shapes are tested using particle filter marginal likelihood estimates and in addition, heat maps are constructed based on the inference results to reveal the imbalance of order distributions between the two sides of an order book, thereby offering valuable insights into the movements of future prices.

We report the results of several theoretical studies into the convergence rate for certain random series representations of α -stable random variables, which are motivated by and find application in modelling heavy-tailed noise in time series analysis, inference, and stochastic processes. The use of α -stable noise distributions generally leads to analytically intractable inference problems. The particular version of the Poisson series representation invoked here implies that the resulting distributions are “conditionally Gaussian,” for which inference is relatively straightforward, although an infinite series is still involved. Our approach is to approximate the residual (or “tail”) part of the series from some point, c > 0, say, to ∞, as a Gaussian random variable. Empirically, this approximation has been found to be very accurate for large c. We study the rate of convergence, as c → ∞, of this Gaussian approximation. This allows the selection of appropriate truncation parameters, so that a desired level of accuracy for the approximate model can be achieved. Explicit, nonasymptotic bounds are obtained for the Kolmogorov distance between the relevant distribution functions, through the application of probability-theoretic tools. The theoretical results obtained are found to be in very close agreement with numerical results obtained in earlier work.

In several application areas, such as human computer interaction, surveillance and defence, determining the intent of a tracked object enables systems to aid the user/operator and facilitate effective, possibly automated, decision making. In this paper, we propose a probabilistic inference approach that permits the prediction, well in advance, of the intended destination of a tracked object and its future trajectory. Within the framework introduced here, the observed partial track of the object is modeled as being part of a Markov bridge terminating at its destination, since the target path, albeit random, must end at the intended endpoint. This captures the underlying long term dependencies in the trajectory, as dictated by the object intent. By determining the likelihood of the partial track being drawn from a particular constructed bridge, the probability of each of a number of possible destinations is evaluated. These bridges can also be employed to produce refined estimates of the latent system state (e.g., object position, velocity, etc.), predict its future values (up until reaching the designated endpoint) and estimate the time of arrival. This is shown to lead to a low complexity Kalman-filter-based implementation of the inference routine, where any linear Gaussian motion model, including the destination reverting ones, can be applied. Free hand pointing gestures data collected in an instrumented vehicle and synthetic trajectories of a vessel heading toward multiple possible harbors are utilized to demonstrate the effectiveness of the proposed approach.

This paper describes a study on modelling the Received Signal Strength Indicator (RSSI) measured by the smartphone of a vehicle user. The present transmissions are emitted by dedicated radio frequency sources, such as Bluetooth Low Energy (BLE) beacons, mounted to the vehicle to determine the driver/passenger(s) proximity or relative position(s). Based on empirical data, a model of the measurements noise, which utilises skewed distributions, is proposed to capture inconsistencies in reception and the impact of occlusions on the RSSI profile in an automotive setting, for example occlusions in car parks. Experimental data is used to demonstrate the suitability of the introduced model.

We propose a deterministic recursive algorithm for approximate Bayesian filtering. The proposed filter uses a function referred to as the approximate Gaussian flow transformation that transforms a Gaussian prior random variable into an approximate posterior random variable. Given a Gaussian filter prediction distribution, the succeeding filter prediction is approximated as Gaussian by applying sigma point moment-matching to the composition of the Gaussian flow transformation and the state transition function. This requires linearising the measurement model at each sigma point, solving the linearised models analytically, and introducing the measurement information gradually to improve the linearisation points progressively. Computer simulations show that the proposed method can provide higher accuracy and better posterior covariance matrix approximation than some state-of-the art computationally light approximative filters when the measurement model function is nonlinear but differentiable and the noises are additive and Gaussian. We also present a highly nonlinear scenario where the proposed filter occasionally diverges. In the accuracy-computational complexity axis the proposed algorithm is between Kalman filter extensions and Monte Carlo methods.

This paper proposes a probabilistic intent inference approach that is significantly more computationally efficient than other existing bridging-distributions-based predictors. It sequentially determines the probabilities of all possible destinations of a tracked object, whose motion is modelled by a Markov chain with the distribution of its terminal state equal to that of a nominal endpoint. This encapsulates the long term dependencies in the object trajectory as dictated by intent. Simulations using real data show that the notable reductions in computations achieved by the introduced bridging-based predictor does not impact the quality of the overall inference results.

In this paper we introduce a novel class of efficient multichannel adaptive filtering algorithms for sparse FIR systems. By suitably integrating ideas from compressed sensing and adaptive filter theory, this class of algorithms allows to significantly reduce the actual number of adaptive coefficients in an efficient way. These algorithms, termed compressive-domain adaptive filters, can be interpreted as a novel type of transform-domain techniques. They can also be seen as adaptive approach in an efficiently self-learning manifold based on the prior knowledge of sparseness of the system. An important property of this concept is that it does not place additional restrictions on the input signal characteristics. Based on the well-known RLS algorithm as a reference, the simulation results confirm that the proposed algorithm converges at acceptable rates, even for strongly colored signals such as speech and audio.

In this paper we extend to the multidimensional case the modified Poisson series representation of linear stochastic processes driven by α-stable innovations. The latter has been recently introduced in the literature and it involves a Gaussian approximation of the residuals of the series, via the exact characterization of their moments. This allows for Bayesian techniques for parameter or state inference that would not be available otherwise, due to the lack of a closed-form likelihood function for the α-stable distribution. Simulation results are presented to validate the introduced extension and the quality of the approximation of the distribution. Finally, we show an example of generation from the process.

In the community of remote sensing, nonlinear mixture models have recently received particular attention in hyperspectral image processing. In this paper, we present a novel nonlinear spectral unmixing method following the recent multilinear mixing model of Heylen and Scheunders, which includes an infinite number of terms related to interactions between different endmembers. The proposed unmixing method is unsupervised in the sense that the endmembers are estimated jointly with the abundances and other parameters of interest, i.e., the transition probability of undergoing further interactions. Nonnegativity and sum-to-one constraints are imposed on abundances while only nonnegativity is considered for endmembers. The resulting unmixing problem is formulated as a constrained nonlinear optimization problem, which is solved by a block coordinate descent strategy, consisting of updating the end-members, abundances, and transition probability iteratively. The proposed method is evaluated and compared with existing linear and nonlinear unmixing methods for both synthetic and real hyperspectral data sets acquired by the airborne visible/infrared imaging spectrometer sensor. The advantage of using nonlinear unmixing as opposed to linear unmixing is clearly shown in these examples.

In this paper, we first give an overview of the predictive display concept, which aims to minimise the demand associated with interacting with in-vehicle displays, such as touchscreens, via free hand pointing gestures. It determines the item the user intends to select, early in the pointing gesture, and accordingly simplifies-expedites the target acquisition. A study to evaluate the impact of using a predictive touchscreen in a car is then presented. The mid-air selection pointing facilitation scheme is applied, such that the user does not have to physically touch the interactive surface. Instead, the predictive display auto-selects the predicted interface icon on behalf of the user, once the required level of inference certainty is achieved. The study results, which are based on data collected from 20 participants under various driving-road conditions, demonstrate that a predictive display can significantly reduce the workload, effort and durations of completing on-screen selection tasks in vehicles.

Examining the dynamic aspects of functional networks in the brain is imperative in order to obtain a thorough description and to gain a better insight into its several features. Present methods of analysing brain data in task-conditions mainly include concatenation followed by temporal correlation. We employ Markov Chain Monte Carlo methods, namely Metropolis within Gibbs sampling, on a stochastic model to infer dynamic functional connectivity in such conditions. By using a Bayesian probabilistic framework, distributional estimates of the linkage strengths are obtained as opposed to point estimates, and the uncertainty of the existence of such links is accounted for. The methodology is applied to fMRI data from a finger opposition paradigm with task and fixation conditions, investigating the dynamics of the well characterised somato-motor network while using the visual network as a control case.

In many teleconferencing applications using modern laptop and net-book devices it is common to encounter annoying keyboard typing noise. In this paper we propose an acoustic keystroke transient canceler for speech communication terminals as a novel broadband adaptive filter application in such a hands-free scenario. We present this approach in the context of the Google Chromebook Pixel device which is equipped with a special audio reference channel providing various new signal processing possibilities. Our novel semi-blind/semi-supervised approach exploiting this new degree of freedom, combined with the system-based broadband estimation and a novel adaptation control yields a high-quality speech enhancement even under challenging acoustic conditions.

This letter proposes a robust fast multiband image fusion method to merge a high-spatial low-spectral resolution image and a low-spatial high-spectral resolution image. Following the method recently developed by Wei et al., the generalized Sylvester matrix equation associated with the multiband image fusion problem is solved in a more robust and efficient way by exploiting the Woodbury formula, avoiding any permutation operation in the frequency domain as well as the blurring kernel invertibility assumption required in their method. Thanks to this improvement, the proposed algorithm requires fewer computational operations and is also more robust with respect to the blurring kernel compared with the one developed by Wei et al. The proposed new algorithm is tested with different priors considered by Wei et al. Our conclusion is that the proposed fusion algorithm is more robust than the one by Wei et al. with a reduced computational cost.

Fundamental frequency estimation, known as pitch estimation in speech signals is of interest both to the research community and to industry. Meanwhile, the particle filter is known to be a powerful Bayesian inference method to track dynamic parameters in nonlinear state-space models. In this paper, we propose a speech model under a time-varying source-filter speech model, and use variable rate particle filters (VRPF) to develop methods for estimation of pitch periods in speech signals. A Rao-Blackwellised variable rate particle filter (RBVRPF) is also implemented. The proposed VRPF and RBVRPF are compared with a state-of-the-art pitch estimation algorithm, the YIN algorithm. Simulation results show that more accurate estimation of pitch can be obtained by VRPF and RBVRPF even under strong background noise conditions.

Using interactive displays, such as a touchscreen, in vehicles typically requires dedicating a considerable amount of visual as well as cognitive capacity and undertaking a hand pointing gesture to select the intended item on the interface. This can act as a distractor from the primary task of driving and consequently can have serious safety implications. Due to road and driving conditions, the user input can also be highly perturbed resulting in erroneous selections compromising the system usability. In this paper, we propose intent-aware displays that utilize a pointing gesture tracker in conjunction with suitable Bayesian destination inference algorithms to determine the item the user intends to select, which can be achieved with high confidence remarkably early in the pointing gesture. This can drastically reduce the time and effort required to successfully complete an in-vehicle selection task. In the proposed probabilistic inference framework, the likelihood of all the nominal destinations is sequentially calculated by modeling the hand pointing gesture movements as a destination-reverting process. This leads to a Kalman filter-type implementation of the prediction routine that requires minimal parameter training and has low computational burden; it is also amenable to parallelization. The substantial gains obtained using an intent-aware display are demonstrated using data collected in an instrumented vehicle driven under various road conditions.

This paper presents a multiband image fusion algorithm based on unsupervised spectral unmixing for combining a high-spatial-low-spectral-resolution image and a low-spatial-high-spectral-resolution image. The widely used linear observation model (with additive Gaussian noise) is combined with the linear spectral mixture model to form the likelihoods of the observations. The nonnegativity and sum-to-one constraints resulting from the intrinsic physical properties of the abundances are introduced as prior information to regularize this ill-posed problem. The joint fusion and unmixing problem is then formulated as maximizing the joint posterior distribution with respect to the endmember signatures and abundance maps. This optimization problem is attacked with an alternating optimization strategy. The two resulting subproblems are convex and are solved efficiently using the alternating direction method of multipliers. Experiments are conducted for both synthetic and semi-real data. Simulation results show that the proposed unmixing-based fusion scheme improves both the abundance and endmember estimation compared with the state-of-the-art joint fusion and unmixing algorithms.

With the proliferation of the touchscreen technology, interactive displays are becoming an integrated part of the modern vehicle environment. However, due to road and driving conditions, the user input on such displays can be perturbed resulting in erroneous selections. This paper describes an evaluative study of the usability and input performance of in-vehicle touchscreens. The analysis is based on data collected in instrumented cars driven under various road/driving conditions. We assess the frequency of failed selection attempts, distances by which users miss the intended on-screen target and the durations of undertaken free hand pointing gestures to accomplish the selection tasks. It is shown that the road/driving conditions can notably undermine the usability of an interactive display when the user input is perturbed, e.g. due to the experienced vibrations and lateral accelerations in the vehicle. The distance between the location of an erroneous on-screen selection and the intended endpoint on the display, is closely related to the level of present in-vehicle noise. The conducted study can advise graphical user interfaces design for the vehicle environment where the user free hand pointing gestures can be subject to varying levels of perturbations.

We propose a novel probabilistic inference approach that permits predicting, well in advance, the intended destination of a pointing gesture aimed at selecting an icon on an in-vehicle interactive display. It models the partial 3D pointing track as a Markov bridge terminating at a nominal destination. The solution introduced leads to a low-complexity Kalman-filter-type implementation and is applicable in other areas in which early detection of the destination of a tracked object is beneficial. Data collected in an instrumented vehicle illustrate that the proposed technique can infer the intent notably early in the pointing gesture. This can drastically reduce the pointing task time and visual-cognitive-manual attention required.

Recent empirical research has discovered that linkages among fMRI signals of the brain in resting-state have meaningful temporal variations. Most current studies of brain networks assume that these linkages are constant. We propose a model and an accompanying algorithm to infer and track changes in these interaction strengths, thus providing a more comprehensive way to study brain dynamics. The stochastic model employed is akin to one used for neuronal states (DCM) and a Rao-Blackwellized filtering algorithm is set up for tracking purposes. Our results show that time-varying interactions among brain regions can be successfully found which have the potential of providing great clinical value.

In this paper a problem in transient noise suppression for audio streams in laptop and netbook devices is addressed. One or more microphones record voice signals which are corrupted with ambient noise and also transient noise from keyboard and mouse clicks. In the current work, a synchronous reference microphone is embedded in the keyboard which allows for measurement of the key click noise, substantially unaffected by the voice signal and ambient noise. An algorithm is here presented for incorporation of the keybed microphone as a reference signal in a signal restoration process for the voice part. The problem is substantially complicated by the presence of nonlinear vibarations (we postulate) in the hinge and casework of the laptop, which renders a simple linear suppressor ineffective in some cases. Moreover, the transfer functions between key clicks and voice microphone depend strongly upon which key is being clicked. A very low-latency solution is proposed in which short-time transform data is processed sequentially in short frames and a robust statistical model is formulated and estimated using Bayesian inference procedures. Results with real recordings show a significant reduction of typing artefacts at the expense of small amounts of voice distortion.

This paper presents an O(n4) time method for filtering and sampling of a time-varying n × n system matrix Atin a restricted class of time-varying linear systems of the form Xt= AtXt-1+ Ct+ εt, via a matrix-variate normal formulation. This allows larger systems within this class to be inferred via Gibbs sampling in reasonable time than is possible with methods that rely on vectorization of the system matrix, followed by standard Kalman filtering, which run in O(n6) time. It is shown how to apply the method to vector autoregression problems with time-varying system matrices (TVP-VAR problems). Noisy observations of the underlying system state are also accommodated in a straightforward way.

In this paper we present a Bayesian method for parameter estimation in linear Jump-Langevin systems, i.e. systems driven by a linear, mean-reverting jump-diffusion trend process. Such models have been applied successfully to trend following in finance, in order to develop momentum-based trading strategies. Parameter estimation is based around a reversible-jump MCMC method for jump-time inference. Parameter estimation is demonstrated on both synthetic and financial time series, and estimated parameters are compared with ad hoc parameter estimates used in earlier work.

Interactive displays are becoming an integrated part of the modern vehicle environment. Their use typically entails dedicating a considerable amount of attention and undertaking a pointing gesture to select an interface item/icon displayed on a touchscreen. This can have serious safety implications for the driver. The pointing gesture can also be highly perturbed due to the road and driving conditions, resulting in erroneous selections. In this paper, we propose a probabilistic intent prediction approach that facilitates establishing the targeted icon on the interface early in the pointing gesture. It employs a 3D vision sensory device to continuously track the pointing hand/finger in conjunction with suitable Bayesian prediction algorithms. The introduced technique can significantly reduce the pointing task completion time, the necessary associated visual, cognitive and movement efforts as well as enhance the selection accuracy. The substantial furnished gains and the pointing gesture characteristics are demonstrated using data collected in an instrumented vehicle.

In this paper we study parameter estimation for α-stable distribution parameters. The proposed approach uses a Poisson series representation (PSR) for skewed α-stable random variables, which provides a conditionally Gaussian framework. Therefore, a straightforward implementation of Bayesian parameter estimation using Markov chain Monte Carlo (MCMC) methods is feasible. To extend the series representation to practical application, we provide a novel approximation of the series residual terms, which exactly characterises the mean and variance of the approximation and maintains its structure. Simulations illustrate the proposed framework applied to skewed α-stable data, estimating the distribution parameter values.

The goal of this paper is to build a detector of event-related potentials (ERP) in single-trial EEG data. This problem can be reformulated as a parameter estimation problem, where the parameter of interest is the time of occurrence of the ERP. This type of detector has clinical applications (study of schizophrenia, fatigue), or applications in brain-computer-interfaces. However, the poor signal-to-noise ratio (SNR) and lack of understanding of the noise generating process make this a challenging task. In this paper, we take a Bayesian approach, samples are drawn from the posterior of the parameter of interest using Markov chain Monte Carlo (MCMC). Different noise covariances from Gaussian processes are tested. We show that it is possible to pick up the ERP signal in spite of the poor SNR with an appropriate choice of noise covariance structure.

Electromagnetic source localization is a technique that enables the study of neural dynamical activities on a millisecond timescale using Magnetoencephalography (MEG) or Electroencephalography (EEG) data. It aims to reveal neural activities in the brain cortical region which cannot be seen with imaging methods that operate on a slower timescale such as fMRI. In this paper, we model the problem under a Bayesian multi-target tracking framework. A multi-target detection and particle filtering algorithm is developed to estimate the dipolar source dynamics, and a minimum norm (MN) based estimation method is incorporated to construct the birth-death move for the dynamical number of dipolar sources. The algorithm is tested using both simulated and experimental data1. The results demonstrate that the proposed algorithm performs better than that in previous works in terms of both localization accuracy and computational cost.

We consider the smoothing problem for a class of conditionally linear Gaussian state-space (CLGSS) models, referred to as mixed linear/nonlinear models. In contrast to the better studied hierarchical CLGSS models, these allow for an intricate cross dependence between the linear and the nonlinear parts of the state vector. We derive a Rao-Blackwellized particle smoother (RBPS) for this model class by exploiting its tractable substructure. The smoother is of the forward filtering/backward simulation type. A key feature of the proposed method is that, unlike existing RBPS for this model class, the linear part of the state vector is marginalized out in both the forward direction and in the backward direction.

In this paper we study parameter estimation for time series with asymmetric α-stable innovations. The proposed methods use a Poisson sum series representation (PSSR) for the asymmetric α-stable noise to express the process in a conditionally Gaussian framework. That allows us to implement Bayesian parameter estimation using Markov chain Monte Carlo (MCMC) methods. We further enhance the series representation by introducing a novel approximation of the series residual terms in which we are able to characterise the mean and variance of the approximation. Simulations illustrate the proposed framework applied to linear time series, estimating the model parameter values and model order P for an autoregressive (AR(P)) model driven by asymmetric α-stable innovations.

Particle filter-based acoustic source tracking algorithms track (online and in real-time) the position of a sound source-a person speaking in a room-based on the current data from a distributed microphone array as well as the previously recorded data. This paper develops a multi-target tracking (MTT) methodology to allow for an unknown and time-varying number of speakers in a fully probabilistic manner and in doing so does not resort to independent modules for new target proposal or target number estimation as in previous works. The approach uses the concept of an existence grid to propose possible regions of activity before tracking is carried out with a variable dimension particle filter-which also explicitly supports the concept of a null particle, containing no target states, when no speakers are active. Examples demonstrate typical tracking performance in a number of different scenarios with simultaneously active speech sources.

In this paper, models and algorithms are presented for transcription of pitch and timings in polyphonic music extracts, focusing on the algorithm details of the sequential Markov chain Monte Carlo (MCMC) inference techniques used. The data are decomposed frame-wise into the frequency domain, where a Poisson point process model is used to write a polyphonic pitch likelihood function. A dynamical model is then used to link notes between frames. Inference in the model is carried out via Bayesian filtering using a sequential MCMC algorithm. The filtering procedure is sub-optimal, using some novel assumptions to render the task computationally tractable for large numbers of notes. Initial results with guitar music, both laboratory test data and commercial extracts, show promising performance.

In this paper we present Poisson sum series representations for α-stable (αS) random variables and α-stable processes, in particular concentrating on continuous-time autoregressive (CAR) models driven by α-stable Levy processes. Our representations aim to provide a conditionally Gaussian framework, which will allow parameter estimation using Rao-Blackwellised versions of state of the art Bayesian computational methods such as particle filters and Markov chain Monte Carlo (MCMC). To overcome the issues due to truncation of the series, novel residual approximations are developed. Simulations demonstrate the potential of these Poisson sum representations for inference in otherwise intractable α-stable models.

We present a method for the removal of noise including non-Gaussian impulses from a signal. Impulse noise is removed jointly a homogenous Gaussian noise floor using a Gabor regression model. The problem is formulated in a joint Bayesian framework and we use a Gibbs MCMC sampler to estimate parameters. We show how to deal with variable magnitude impulses using a shifted inverse gamma distribution for their variance. Our results show improved signal to noise ratios and perceived audio quality by explicitly modelling impulses with a discrete switching process and a new heavy-tailed amplitude model.

In this paper, we propose a method for restoring the missing or corrupted observations of nonstationary sinusoidal signals which are often encountered in music and speech applications. To model nonstationary signals, we use a time-varying sinusoidal model which is obtained by extending the static sinusoidal model into a dynamic sinusoidal model. In this model, the in-phase and quadrature components of the sinusoids are modeled as first-order Gauss-Markov processes. The inference scheme for the model parameters and missing observations is formulated in a Bayesian framework and is based on a Markov chain Monte Carlo method known as Gibbs sampler. We focus on the parameter estimation in the dynamic sinusoidal model since this constitutes the core of model-based interpolation. In the simulations, we first investigate the applicability of the model and then demonstrate the inference scheme by applying it to the restoration of lost audio packets on a packet-based network. The results show that the proposed method is a reasonable inference scheme for estimating unknown signal parameters and interpolating gaps consisting of missing/corrupted signal segments.

Particle Filter-based Acoustic Source Localization algorithms attempt to track the position of a sound source - one or more people speaking in a room - based on the current data from a microphone array as well as all previous data up to that point. This paper first discusses some of the inherent behavioral traits of the steered beamformer localization function. Using conclusions drawn from that study, a multitarget methodology for acoustic source tracking based on the Track Before Detect (TBD) framework is introduced. The algorithm also implicitly evaluates source activity using a variable appended to the state vector. Using the TBD methodology avoids the need to identify a set of source measurements and also allows for a vast increase in the number of particles used for a comparitive computational load which results in increased tracking stability in challenging recording environments. An evaluation of tracking performance is given using a set of real speech recordings with two simultaneously active speech sources.

We introduce a framework for probabilistic generative models of time–frequency coefficients of audio signals, using a matrix factorization parametrization to jointly model spectral characteristics such as harmonicity and temporal activations and excitations. The models represent the observed data as the superposition of statistically independent sources, and we consider variance-based models used in source separation and intensity-based models for non-negative matrix factorization. We derive a generalized expectation-maximization algorithm for inferring the parameters of the model and then adapt this algorithm for the task of polyphonic transcription of music using labeled training data. The performance of the system is compared to that of existing discriminative and model-based approaches on a dataset of solo piano music.

This paper proposes a frequency-based approach for background noise suppression with consideration for human psychoacoustics. The approach utilizes a perceptual cost function analysis based on temporal masking thresholds. By optimizing the cost function, the concept eliminates background noises that mask the original signals, while maintaining the minimum perceptual distortion of the original signals. The perceptual cost function can also be implemented within a Gibbs sampling framework, which better models the uncertainty within the original signal. These approaches improve existing noise reduction techniques, enhancing perceived audio quality (PEAQ), Mean Opinion Score (MOS), and signal to noise ratio (SNR).

We describe the underlying probabilistic generative signal model of non-negative matrix factorisation (NMF) and propose a realistic conjugate priors on the matrices to be estimated. A conjugate Gamma chain prior enables modelling the spectral smoothness of natural sounds in general, and other prior knowledge about the spectra of the sounds can be used without resorting to too restrictive techniques where some of the parameters are fixed. The resulting algorithm, while retaining the attractive features of standard NMF such as fast convergence and easy implementation, outperforms existing NMF strategies in a single channel audio source separation and detection task.

We describe in this paper an audio denoising technique based on sparse linear regression with structured priors. The noisy signal is decomposed as a linear combination of atoms belonging to two modified discrete cosine transform (MDCT) bases, plus a residual part containing the noise. One MDCT basis has a long time resolution, and thus high frequency resolution, and is aimed at modeling tonal parts of the signal, while the other MDCT basis has short time resolution and is aimed at modeling transient parts (such as attacks of notes). The problem is formulated within a Bayesian setting. Conditional upon an indicator variable which is either 0 or 1, one expansion coefficient is set to zero or given a hierarchical prior. Structured priors are employed for the indicator variables; using two types of Markov chains, persistency along the time axis is favored for expansion coefficients of the tonal layer, while persistency along the frequency axis is favored for the expansion coefficients of the transient layer. Inference about the denoised signal and model parameters is performed using a Gibbs sampler, a standard Markov chain Monte Carlo (MCMC) sampling technique. We present results for denoising of a short glockenspiel excerpt and a long polyphonic music excerpt. Our approach is compared with unstructured sparse regression and with structured sparse regression in a single resolution MDCT basis (no transient layer). The results show that better denoising is obtained, both from signal-to-noise ratio measurements and from subjective criteria, when both a transient and tonal layer are used, in conjunction with our proposed structured prior framework.

A model for vehicle motion on a road network Is developed using an enumeration of feasible routes. Combined with a generic stochastic model of distance travelled, a predicted pdf of vehicle position is derived as a mixture. This approach allows prior information on vehicle intent and behaviour to be included via the mixture weights. Illustrative examples are given using a second-order linear-Gaussian model for vehicle road speed. The value of road map data is shown via a tracking example with poor quality measurements and a substantial period prior to sensor activation. The tracking algorithm is implemented using a standard particle filter. In particular, the scheme has potential for revealing the likely paths taken by the vehicle.

This paper presents a framework for the modelling of temporal characteristics of musical signals and an approximate, sequential Monte Carlo inference scheme which yields estimates of tempo and rhythmic pattern from onset-time data. These two features are quantified through the construction of a probabilistic dynamical model of a hidden 'bar-pointer' and a Poisson observation model. The capabilities of the system are demonstrated by tracking the tempo of a 2 against 3 polyrhythm and detecting a switch in rhythm in a MIDI performance.

In this paper, we present an online approach for joint initiation/termination and tracking for multiple targets with multiple sensors using sequential Monte Carlo (SMC) methods. There are several main contributions in the paper. The first contribution is the extension of the deterministic initiation and termination method proposed by the authors' previous publications to a full SMC context in which track initiation/termination are executed with sampling methods. In effect, the dimensions of the particles are variable. In addition, we also integrate a Markov random field (MRF) motion model with the framework to enable efficient and accurate tracking for interacting targets and to avoid potential track coalescence problems. With the employment of multiple sensors, a centralized tracking strategy is adopted, where the observations from all active sensors are fused together for target initiation/termination and tracking and a set of global tracks is maintained. Intra- and inter-sensor clusters are constructed, comprised of closely spaced observations either in time for single sensors or from distinct sensors at a single time, that can increase the reliability when proposing new tracks for initiation. Computer simulations demonstrate that the proposed approach is robust in joint initiation/termination and tracking of multiple manoeuvring targets even when the environment is hostile with high-clutter rates and low target detection probabilities. The integration of the MRF framework into the proposed methods improves robustness in handling close target interactions when the observation noise is high.

It is now over a decade since the pioneering contribution of Gordon (1993), which is commonly regarded as the first instance of modern sequential Monte Carlo (SMC) approaches. Initially focussed on applications to tracking and vision, these techniques are now very widespread and have had a significant impact in virtually all areas of signal and image processing concerned with Bayesian dynamical models. This paper is intended to serve both as an introduction to SMC algorithms for nonspecialists and as a reference to recent contributions in domains where the techniques are still under significant development, including smoothing, estimation of fixed parameters and use of SMC methods beyond the standard filtering contexts.

Standard algorithms in tracking and other state-space models assume identical and synchronous sampling rates for the state and measurement processes. However, real trajectories of objects are typically characterized by prolonged smooth sections, with sharp, but infrequent, changes. Thus, a more parsimonious representation of a target trajectory may be obtained by direct modeling of maneuver times in the state process, independently from the observation times. This is achieved by assuming the state arrival times to follow a random process, typically specified as Markovian, so that state points may be allocated along the trajectory according to the degree of variation observed. The resulting variable dimension state inference problem is solved by developing an efficient variable rate particle filtering algorithm to recursively update the posterior distribution of the state sequence as new data becomes available. The methodology is quite general and can be applied across many models where dynamic model uncertainty occurs on-line. Specific models are proposed for the dynamics of a moving object under internal forcing, expressed in terms of the intrinsic dynamics of the object. The performance of the algorithms with these dynamical models is demonstrated on several challenging maneuvering target tracking problems in clutter.

This letter explores the potential of Bayesian signal processing for improved modeling of microarray images and enhanced estimation of gene expression ratios. Building upon our earlier work, we describe a novel elliptical spot shape model, with a Bayesian model-fitting method. The analysis of gene replicates at the image-modeling level is also briefly discussed. Prior knowledge from neighboring spots is encompassed in the framework of a Markov random field, potentially enhancing the accuracy and reliability of ratio estimates. The techniques may be particularly beneficial for irregular, overlapping, damaged, saturated, or weakly expressed spots.

International audience

In this paper we present methods for estimating the parameters of a class of non-Gaussian continuous-time stochastic process, the continuous-time auto regressive moving average (CARMA) model driven by symmetric alpha-stable (SalphaS) Levy processes. In this challenging framework we are not able to evaluate the likelihood function directly, and instead we use a distretized approximation to the likelihood. The parameters are then estimated from this approximating model using a Bayesian Monte Carlo scheme, and employing a Kalman filter to marginalize and sample the trajectory of the state process. An efficient exploration of the parameter space is achieved through a novel reparameterization in terms of an equivalent mechanical system. Simulations demonstrate the potential of the methods

In this letter, we propose an approach for sparse linear regression in unions of bases inspired by Bayesian variable selection. Conditionally upon an indicator variable that is 0 or 1, one expansion coefficient of the signal corresponding to one atom of the dictionary is either set to zero or given a Student t prior. A Gibbs sampler (a standard Markov chain Monte Carlo technique) is used to sample from the posterior distribution of the indicator variables, the expansion coefficients (corresponding to nonzero indicator variables), the hyperparameters of the Student t priors, and the variance of the residual signal. The structure of the dictionary, assumed to be a union of bases, allows for alternate sampling of the indicator variables and the expansion coefficients from each basis and avoids any large matrix inversion. Our method is applied to the denoising problem of a piano sequence, using a dual-resolution union of two modified discrete cosine transform bases

We present a Bayesian approach for blind separation of linear instantaneous mixtures of sources having a sparse representation in a given basis. The distributions of the coefficients of the sources in the basis are modeled by a Student t distribution, which can be expressed as a scale mixture of Gaussians, and a Gibbs sampler is derived to estimate the sources, the mixing matrix, the input noise variance and also the hyperparameters of the Student t distributions. The method allows for separation of underdetermined (more sources than sensors) noisy mixtures. Results are presented with audio signals using a modified discrete cosine transform basis and compared with a finite mixture of Gaussians prior approach. These results show the improved sound quality obtained with the Student t prior and the better robustness to mixing matrices close to singularity of the Markov chain Monte Carlo approach

In this paper, we propose an extension of the soft-gating approach for measurement-to-target assignment for multitarget tracking. Given the latest observation and a set of multitarget particles, the proposed method combines efficient m-best 2D data assignment and sampling methods to compute a feasible measurement-to-target assignment with an associated probability for each particle. The particles containing the multitarget states and the association vectors can then be used to recursively estimate the posterior distribution of the targets using sequential Monte Carlo methods. Computer simulations demonstrate the robustness and effectiveness of the proposed method for data association and multitarget tracking.

We present a method to address the (inherently ill-posed) problem of missing data interpolation over repeated short gaps in audio signals. By formulating the problem in terms of a Gabor regression model, we show that it is possible to leverage information from the surrounding time-frequency plane in order to obtain an interpolation in keeping with the qualities of the signal under consideration. As an exploratory investigation of this technique's potential, we consider two example restoration scenarios in which over one third of the data values in total are missing.

We discuss modifications to tracking models, and sequential Monte Carlo algorithms for their estimation from sequential and batch data. New models for tracking are proposed which involve a dynamical model on both the hidden state value and its arrival times. In this way we aim to have a more flexible and parsimonious representation of time-varying state characteristics which is more amenable to estimation using Bayesian filtering. In order to perform inference in this scenario, new particle filters and smoothers are proposed for cases where the state process arrives at unknown times that are generally different from the observation arrival times.

The paper proposes a Bayesian method for polyphonic music description. The method first divides an input audio signal into a series of sections called snapshots, and then estimates parameters such as fundamental frequencies and amplitudes of the notes contained in each snapshot. The parameter estimation process is based on a frequency domain modelling and Gibbs sampling. Experimental results obtained from audio signals of test note patterns are encouraging; the accuracy is better than 80% for the estimation of fundamental frequencies in terms of semitones and instrument names when the number of simultaneous notes is two.

We present a novel approach to audio signal enhancement based on psychoacoustic principles. Specifically, we describe a short-time spectral amplitude estimator whose form comprises a weighted sum of the minimum mean-square error solution and the observed spectral value, where the weighting factor is given by the ratio of the masked threshold and this observed value. We then explore the connection between our approach and the idea of so-called balanced loss functions in statistics, showing the former to be an instance of the latter with a very special choice of weighting factor. Lastly, we present results indicating the relative merits of our approach in both objective and subjective terms, as compared to standard minimum mean-square error estimation under the assumed model.

We propose a method for sequential Bayesian kernel regression. As is the case for the popular Relevance Vector Machine (RVM) [10, 11], the method automatically identifies the number and locations of the kernels. Our algorithm overcomes some of the computational difficulties related to batch methods for kernel regression. It is non-iterative, and requires only a single pass over the data. It is thus applicable to truly sequen- tial data sets and batch data sets alike. The algorithm is based on a generalisation of Importance Sampling, which allows the design of in- tuitively simple and efficient proposal distributions for the model param- eters. Comparative results on two standard data sets show our algorithm to compare favourably with existing batch estimation strategies.

In this paper, we introduce an hybrid time-frequency/support vector machine algorithm for the detection of abrupt spectral changes. A stationarity index is derived from support vector novelty detection theory by using sub-images extracted from the time-frequency plane as feature vectors. Simulations show the efficiency of this new algorithm for audio signal segmentation, compared to another nonparametric detector.

In this paper, we propose a slow time-varying partial correlation (STV-PARCOR) model for dynamical models with slowly varying parameters. Based on it, we develop an online joint parameter and signal estimation algorithm under the sequential Monte Carlo framework. It is believed that the proposed model and algorithm will improve on the standard Monte Carlo filter as it is known that the standard filter becomes highly degenerate for models with slowly varying parameters. The suggested algorithm is tested with real speech data and the results are compared with those generated using existing approaches.

Estimating the pitch of musical signals is complicated by the presence of partials in addition to the fundamental frequency. In this paper, we propose developments to an earlier Bayesian model which describes each component signal in terms of fundamental frequency, partials (‘harmonics’), and amplitude. This basic model is modified for greater realism to include non-white residual spectrum, time-varying amplitudes and partials ‘detuned’ from the natural linear relationship. The unknown parameters of the new model are simulated using a reversible jump MCMC algorithm, leading to a highly accurate pitch estimator. The models and algorithms can be applied for feature extraction, polyphonic music transcription, source separation and restoration of musical sources.

It is becoming increasingly important to develop novel signal processing and statistical analysis techniques to extract information from biotechnology. This task is complicated by large datasets, intricate physical systems, and the sheer diversity of information that is available. In many systems, classical non-parametric signal processing techniques have been applied with some success. However, where sufficient information is available to construct accurate models, substantial gains can sometimes be derived from a model-based approach. The Bayesian paradigm provides an elegant and mathematically rigorous framework for the objective incorporation of information. In this paper, we develop a Bayesian model for DNA sequencing, with an emphasis on generally relevant Bayesian model selection issues.

The Bayesian paradigm provides a natural and effective means of exploit- ing prior knowledge concerning the time-frequency structure of sound signals such as speech and music—something which has often been over- looked in traditional audio signal processing approaches. Here, after con- structing a Bayesian model and prior distributions capable of taking into account the time-frequency characteristics of typical audio waveforms, we apply Markov chain Monte Carlo methods in order to sample from the resultant posterior distribution of interest. We present speech enhance- ment results which compare favourably in objective terms with standard time-varying filtering techniques (and in several cases yield superior per- formance, both objectively and subjectively); moreover, in contrast to such methods, our results are obtained without an assumption of prior knowledge of the noise power.

This paper applies time-varying autoregressive (TVAR) models with stochastically evolving parameters to the problem of speech modeling and enhancement. The stochastic evolution models for the TVAR parameters are Markovian diffusion processes. The main aim of the paper is to perform on-line estimation of the clean speech and model parameters and to determine the adequacy of the chosen statistical models. Efficient particle methods are developed to solve the optimal filtering and fixed-lag smoothing problems. The algorithms combine sequential importance sampling (SIS), a selection step and Markov chain Monte Carlo (MCMC) methods. They employ several variance reduction strategies to make the best use of the statistical structure of the model. It is also shown how model adequacy may be determined by combining the particle filter with frequentist methods. The modeling and enhancement performance of the models and estimation algorithms are evaluated in simulation studies on both synthetic and real speech data sets.

We develop methods for Monte Carlo filtering and smoothing for estimating an unobserved state given a non-linearly distorted signal. Due to the lengthy nature of real signals, we suggest processing the data in blocks and a block-based smoother algorithm is developed for this purpose. In particular, we describe algorithms for de-quantisation and declipping in detail. Both algorithms are tested with real audio data which is either heavily quantised or clipped and the results are shown.

We consider the problem of estimating continuous-time autoregressive (CAR) processes from discrete-time noisy observations. This can be done within a Bayesian framework using Markov chain Monte Carlo (MCMC) methods. Existing methods include the standard random walk Metropolis algorithm. On the other hand, least-squares (LS) algorithms exist where derivatives are approximated by differences and parameter estimation is done in a least-squares manner. In this paper, we incorporate the LS estimation into the MCMC framework to develop a new MCMC algorithm. This new algorithm is combined with the standard Metropolis algorithm and is found to improve performance compared to the standard MCMC algorithm. Simulation results are presented to support our findings.

Methods for determining the letters of our genetic code, known as DNA sequencing, currently depend on clever use of electrophoresis to generate data sets indicative of the underlying sequence. Typically the subsequent off-line data processing is carried out less intelligently using a combination of heuristic methods with little mathematical rigour. In this paper, we present a new robust model which is able to accurately predict the effect of the many biological processes which are involved, and moreover, which is usable on-line. Off-line methods have been hampered by the need for processing in as little time as possible after the data is generated; performing the processing on-line has enabled a more advanced algorithm to be used with associated improved performance. The algorithm is framed within a Bayesian probabilistic framework, thereby allowing representation of the random nature of the generative process, and relies on new advances in the burgeoning field of sequential Monte Carlo methods to perform the required highly non-linear filtering and model selection operations.

We develop methods for performing filtering and smoothing in nonlinear non-Gaussian dynamical models. The methods rely on a particle cloud representation of the filtering distribution which evolves through time using importance sampling and resampling ideas. In particular, novel techniques are presented for generation of random realisations from the joint smoothing distribution and for MAP estimation of the state sequence. Realisations of the smoothing distribution are generated in a forward-backward procedure, while the MAP estimation procedure can be performed in a single forward pass of the Viterbi algorithm applied to a discretised version of the state space. An application to spectral estimation for time-varying autoregressions is described.

We have previously shown how to perform inference about symmetric stable processes using Monte Carlo EM (MCEM) and Markov chain Monte Carlo (MCMC) techniques. Simulation based methods such as these are an excellent tool for inference with stable law distributions, since they do not require any direct evaluation of the stable density function, which is unavailable analytically in the general case. We review the existing methods for inference with MCMC and propose new methods based on the slice sampler, a very simple sampling algorithm which draws points from a uniform distribution over the area under the required density function. There is some evidence in the literature that the slice sampler has better convergence properties than the independence Metropolis samplers and rejection samplers previously proposed. We investigate this in the context of alpha-stable noise distributions.

DNA sequencing may be considered as a two stage process: the generation of noisy data indicative of DNA sequence by using advanced chemical techniques; and the interpretation of that data. We present an algorithm for interpretation, or "base calling", which accurately models the underlying process, and is able to incorporate most of the prior information we possess in a mathematically tractable and minimally ad-hoc manner. Our algorithm is framed within a fully Bayesian probabilistic framework, thereby allowing representation of the random nature of the generative process, using a Reversible Jump Metropolis Hastings algorithm (1970) and the Gibbs sampler to traverse the variable dimension parameter space. The techniques used to construct our algorithm are feasible for use in such applications, due to their inherent computational requirements.

We present a statistical model-based approach to signal enhancement in the case of additive broadband noise. Because broadband noise is localised in neither time nor frequency, its removal is one of the most pervasive and difficult signal enhancement tasks. In order to improve perceived signal quality, we take advantage of human perception and define a best estimate of the original signal in terms of a cost function incorporating perceptual optimality criteria. We derive the resultant signal estimator and implement it in a short-time spectral attenuation framework.

We present methods for fixed-lag smoothing using sequential importance sampling on a discrete non-linear, non-Gaussian state space system with unknown parameters. Our particular application is in the field of digital communication systems. Each input data point is taken from a finite set of symbols. We represent the transmission media as a fixed filter with a finite impulse response (FIR), hence a discrete state-space system is formed. Conventional Markov chain Monte Carlo techniques such as the Gibbs sampler are unsuitable for this task because they can only perform processing on a batch of data. Data arrives sequentially, so it would seem sensible to process it in this way. In addition, many communication systems are interactive, so there is a maximum level of latency that can be tolerated before a symbol is decoded. We demonstrate this method by simulation and compare its performance to existing techniques.

In this paper we address the problem of the separation and recovery of convolutively mixed autoregressive processes in a Bayesian framework. Solving this problem requires the ability to solve integration and/or optimization problems of complicated posterior distributions. We thus propose efficient stochastic algorithms based on Markov chain Monte Carlo (MCMC) methods. We present three algorithms. The first one is a classical Gibbs sampler that generates samples from the posterior distribution. The two other algorithms are stochastic optimization algorithms that allow to optimize either the marginal distribution of the sources, or the marginal distribution of the parameters of the sources and mixing filters, conditional upon the observation. Simulations are presented.

Markov chain Monte Carlo (MCMC) methods are powerful simulation-based techniques for sampling from high-dimensional and/or non-standard probability distributions. These methods have recently become very popular in the statistical and signal processing communities as they allow highly complex inference problems in defection and estimation to be addressed. However, MCMC is not currently well adapted to the problem of marginal maximum a posteriori (MMAP) estimation. In this paper, we present a simple and novel MCMC strategy called state-augmentation for marginal estimation (SAME), that allows MMAP estimates to be obtained for Bayesian models. The methodology is very general and we illustrate the simplicity and utility of the approach by examples in MAP parameter estimation for hidden Markov models (HMMs) and for missing data interpolation in autoregressive time series.

Markov chain Monte Carlo (MCMC) samplers have been a very powerful methodology for estimating signal parameters. With the introduction of the reversible jump MCMC sampler, which is a Metropolis-Hastings method adapted to general state spaces, the potential of the MCMC methods has risen to a new level. Consequently, the MCMC methods currently play a major role in many research activities. In this paper we propose a reversible jump MCMC sampler based on predictive densities obtained by integrating out unwanted parameters. The proposal densities are approximations of the posterior distributions of the remaining parameters obtained by sampling importance resampling (SIR). We apply the method to the problem of signal detection and parameter estimation of signals. To illustrate the proposed procedure, we present an example of sinusoids embedded in noise.

We use reversible jump Markov chain Monte Carlo (MCMC) methods to address the problem of model order uncertainty in autoregressive (AR) time series within a Bayesian framework. Efficient model jumping is achieved by proposing model space moves from the the full conditional density for the AR parameters, which is obtained analytically. This is compared with an alternative method, for which the moves are cheaper to compute, in which proposals are made only for new parameters in each move. Results are presented for both synthetic and audio time series.

Modeling and reconstruction methods are presented for noise reduction of autocorrelated signals in non-Gaussian, impulsive noise environments. A Bayesian probabilistic framework is adopted and Markov chain Monte Carlo methods are developed for detection and correction of impulses. Individual noise sources are modeled as Gaussian with unknown scale (variance), allowing for robustness to "heavy-tailed" impulse distributions, while the underlying signal is modeled as autoregressive (AR). Results are presented for both artificial and real data from voice and music recordings, and comparisons are made with existing techniques. The new techniques are found to give improved detection and elimination of impulses in adverse noise conditions at the expense of some extra computational complexity.

In this paper methods are developed for enhancement and analysis of autoregressive moving average (ARMA) signals observed in additive noise which can be represented as mixtures of heavy-tailed non-Gaussian sources and a Gaussian background component. Such models find application in systems such as atmospheric communications channels or early sound recordings which are prone to intermittent impulse noise. Markov chain Monte Carlo (MCMC) simulation techniques are applied to the joint problem of signal extraction, model parameter estimation and detection of impulses within a fully Bayesian framework. The algorithms require only simple linear iterations for all of the unknowns, including the MA parameters, which is in contrast with existing MCMC methods for analysis of noise-free ARMA models. The methods are illustrated using synthetic data and noise-degraded sound recordings.

We present a stochastic simulation technique for subset selection in time series models, based on the use of indicator variables with the Gibbs sampler within a hierarchical Bayesian framework. As an example, the method is applied to the selection of subset linear AR models, in which only significant lags are included. Joint sampling of the indicators and parameters is found to speed convergence. We discuss the possibility of model mixing where the model is not well determined by the data, and the extension of the approach to include non-linear model terms.

This paper presents methods for detection and reconstruction of 'missing' data in image sequences which can be modelled using 3-dimensional autoregressive (3D-AR) models. The interpolation of missing data is important in many areas of image processing, including the restoration of degraded motion pictures, reconstruction of drop-outs in digital video and automatic 're-touching' of old photographs. Here a probabilistic Bayesian framework is adopted. The method assumes no prior knowledge of the motion field or 3D-AR model parameters as these are estimated jointly with the missing image pixels. Incorporating a degradation model into the framework allows detection to proceed jointly with interpolation.

The separation of independent sources from mixed observed data is a fundamental and challenging problem. In many practical situations, observations may be modelled as linear mixtures of a number of source signals, i.e. a linear multi-input multi-output system. A typical example is speech recordings made in an acoustic environment in the presence of background noise and/or competing speakers. Other examples include EEG signals, passive sonar applications and cross-talk in data communications. We propose iterative algorithms to solve the n/spl times/n linear time invariant system under two different constraints. Some existing solutions for 2/spl times/2 systems are reviewed and compared.

Statistical model-based methods are presented for the reconstruction of autocorrelated signals in impulsive plus continuous noise environments. Signals are modelled as autoregressive and noise sources as discrete and continuous mixtures of Gaussians, allowing for robustness in highly impulsive and non-Gaussian environments. Markov Chain Monte Carlo methods are used for reconstruction of the corrupted waveforms within a Bayesian probabilistic framework and results are presented for contaminated voice and audio signals.

In this paper we derive the a posteriori probability for the location of bursts of noise additively superimposed on a Gaussian AR process. The theory is developed to give a sequentially based restoration algorithm suitable for real-time applications. The algorithm is particularly appropriate for digital audio restoration, where clicks and scratches may be modelled as additive bursts of noise. Experiments are carried out on both real audio data and synthetic AR processes and significant improvements are demonstrated over existing restoration techniques.>

A new algorithm is presented for the identification and restoration of time-varying pitch defects in audio signals. The problem is commonly encountered as 'wow' in gramophone disc and magnetic tape recordings where motor speed variations or eccentricity in the recording process are significant. The algorithm operates in two stages, the first of which tracks tonal components in musical signals to generate a single pitch variation curve, and the second stage which performs restoration as a time-varying resampling operation. Results are presented from both artificially degraded sources and real sources.>

We discuss the extraction of two signals from a monophonic gramophone record, and observe that the impulsive noise is significantly different in the two. This, coupled with the redundancy of the desired parts of the signals, has great advantages in the processes of impulsive noise detection and removal. It is simple to obtain two suitable signals by using a stereo replay cartridge, and we develop detection and interpolation algorithms that use such a pair of signals. We present the results of computer simulations and informal listening tests on archive material. In both cases the two-channel method is found to be an improvement over a similar single-channel algorithm, with little change in computational cost.>

The a posteriori probability for the location of bursts of noise additively superimposed on a Gaussian autoregressive (AR) process is derived. The maximum a posteriori (MAP) solution for noise burst position is obtained by using a simple search procedure, yielding the noise burst location corresponding to minimum probability of error. This procedure finds application in digital audio processing, where clicks and scratches may be modeled as additive bursts of noise. The method permits accurate detection of these degradations and their subsequent replacement (interpolation). Experiments were carried out on both real audio data and synthetic AR processes, and comparisons are made with previous techniques.>