Online distributed optimization is particularly useful for solving optimization problems with streaming data collected by multiple agents over a network. When the solutions lie on a Riemannian manifold, such problems become challenging to solve, particularly when efficiency and continuous adaptation are required. This work tackles these challenges and devises a diffusion adaptation strategy for decentralized optimization over general manifolds. A theoretical analysis shows that the proposed algorithm is able to approach network agreement after sufficient iterations, which allows a non-asymptotic convergence result to be derived. We apply the algorithm to the online decentralized principal component analysis problem and Gaussian mixture model inference. Experimental results with both synthetic and real data illustrate its performance.

Modeling the relationships that may connect optimal parameter vectors is essential for the performance of parameter estimation methods in distributed networks. In this paper, we consider a low-rank relationship and introduce matrix factorization to promote this low-rank property. To devise a distributed algorithm that does not require any prior knowledge about the low-rank space, we first formulate local optimization problems at each node, which are subsequently addressed using the Alternating Direction Method of Multipliers (ADMM). Three subproblems naturally arise from ADMM, each resolved in an online manner with low computational costs. Specifically, the first one is solved using stochastic gradient descent (SGD), while the other two are handled using the conjugate gradient descent method to avoid matrix inversion operations. To further enhance performance, a variance reduction algorithm is incorporated into the SGD. Simulation results validate the effectiveness of the proposed algorithm.

Latest advances in multi-agent technology and hardware architecture design have made multivariate or multichannel data, often supported by graphs or networks, ubiquitous in recent scientific and engineering applications. Examples include smart grids management and sensor networks monitoring to cite a few. Multivariate empirical mode decomposition (MEMD), as a fully data-driven technique, has been shown to be effective in the multiscale analysis of non-stationary signals across multiple channels. However, it still lacks the capability to capture the dependency structure of signals over channels when supported by a graph, which limits the relevance of the provided analyses. This work aims to extend MEMD to temporal graph signals. To achieve this, non-uniform projections are processed to preserve smoothness relative to the topology of the graph. A noise-assisted mechanism is also proposed in order to adapt to the randomness of signals on vertices, eliminating mode mixing and misalignment phenomena. To further demonstrate the performance of the proposed graph multivariate empirical mode decomposition (GMEMD), and in particular of its noise-assisted counterpart, we validate its mode alignment property among same-index intrinsic mode functions and its efficacy as a filter bank. Simulations on both synthetic temporal graph signals and real-world electroencephalogram data support the analysis.

Data generated by network-structured applications, such as sensor networks or communication networks, typically reside on complex and irregular structures. These data necessitate specific graph signal processing tools to harness their characteristics. Detecting anomalous events in graph signals is significant in enhancing reliability of systems, where anomalies often activate localized groups of vertices. In this paper, we introduce a novel approach, the Joint Graph Wavelet Canonical Correlation Analysis, for detecting anomalies in graph signals through cooperative filtering while identifying their locations. This approach conducts canonical correlation analysis on graph signals to achieve data fusion within the wavelet domain while accounting for the graph topology. Subsequently, we devise an optimization algorithm specifically tailored for anomaly detection in graph signals. Finally, we illustrate its effectiveness through numerical simulations on synthetic data and by presenting test results from a multi-microphone network.

International audience

Distributed adaptation and learning recently gained considerable attention in solving optimization problems with streaming data collected by multiple agents over a graph. This work focuses on such problems where the solutions lie on a Riemannian manifold. This research topic is of particular interest for many applications, e.g., principal component analysis (PCA). Although several incremental and consensus algorithms have been proposed, there is a lack of methods designed for general Riemannian manifolds with efficient diffusion strategies. In this paper, we devise two Riemannian diffusion adaptation strategies, namely, adaptation-then-combination (ATC) and combination-then-adaptation (CTA), for decentralized Riemannian optimization over graphs. In the adaptation step, a Riemannian stochastic gradient descent method (SGD) is used to estimate the local solution at each node. In the combination step, the local estimates at the different nodes are combined by computing the weighted Fréchet mean over the neighborhood of each node. We apply our algorithms to online distributed PCA and compare them to both non-cooperative and centralized solutions.

Non-parametric detection of change points in streaming time series data that belong to Euclidean spaces has been extensively studied in the literature. Nevertheless, when the data belongs to a Riemannian manifold, existing approaches are no longer applicable as they fail to account for the structure and geometry of the manifold. In this paper, we introduce a non-parametric algorithm for online change point detection in manifold-valued data streams. This algorithm monitors the generalized Karcher mean of the data, computed using stochastic Riemannian optimization. We provide theoretical bounds on the detection and false alarm rate performances of the algorithm, using a new result on the non-asymptotic convergence of the stochastic Riemannian gradient descent. We apply our algorithm to two different Riemannian manifolds. Experimental results with both synthetic and real data illustrate the performance of the proposed method.

Incremental speech enhancement (ISE), with the ability to incrementally adapt to new noise domains, represents a critical yet comparatively under-investigated topic. While the regularization-based method has been proposed to solve the ISE task, it usually suffers from the dilemma wherein the gain of one domain directly entails the loss of another. To solve this issue, we propose an effective paradigm, termed Learning Noise Adapters (LNA), which significantly mitigates the catastrophic domain forgetting phenomenon in the ISE task. In our methodology, we employ a frozen pre-trained model to train and retain a domain-specific adapter for each newly encountered domain, enabling the capture of variations in feature distributions within these domains. Subsequently, our approach involves the development of an unsupervised, training-free noise selector for the inference stage, which is responsible for identifying the domains of test speech samples. A comprehensive experimental validation has substantiated the effectiveness of our approach.

Distributed Acoustic Sensing (DAS) that transforms city-wide fiber-optic cables into a large-scale strain sensing array has shown the potential to revolutionize urban traffic monitoring by providing a fine-grained, scalable, and low-maintenance monitoring solution. However, the real-world application of DAS is hindered by challenges such as noise contamination and interference among closely traveling cars. In response, we introduce a self-supervised U-Net model that can suppress background noise and compress car-induced DAS signals into high-resolution pulses through spatial deconvolution. Our work extends recent research by introducing three key advancements. Firstly, we perform a comprehensive resolution analysis of DAS-recorded traffic signals, laying a theoretical foundation for our approach. Secondly, we incorporate space-domain vehicle wavelets into our U-Net model, enabling consistent high-resolution outputs regardless of vehicle speed variations. Finally, we employ L-2 norm regularization in the loss function, enhancing our model’s sensitivity to weaker signals from vehicles in remote traffic lanes. We evaluate the effectiveness and robustness of our method through field recordings under different traffic conditions and various driving speeds. Our results show that our method can enhance the spatial-temporal resolution and better resolve closely traveling cars. The spatial deconvolution U-Net model also enables the characterization of large-size vehicles to identify axle numbers and estimate the vehicle length. Monitoring large-size vehicles also benefits imaging deep earth by leveraging the surface waves induced by the dynamic vehicle-road interaction.

Detecting change points in streaming time series data is a long standing problem in signal processing. A plethora of methods have been proposed to address it, depending on the hypotheses at hand. Non-parametric approaches are particularly interesting as they do not make any assumption on the distribution of data or on the nature of changes. Nevertheless, leveraging recent advances in deep learning to detect change points in time series data is still challenging. In this paper, we propose a change point detection method using an online approach based on neural networks to directly estimate the density-ratio between current and reference windows of the data stream. A variational continual learning framework is employed to train the neural network in an online manner while retaining information learned from past data. This leads to a statistically-principled fully nonparametric framework to detect change points from streaming data. Experimental results with synthetic and real data illustrate the effectiveness of the proposed approach.

Deconvolution is a widely used strategy to mitigate the blurring and noisy degradation of hyperspectral images (HSI) generated by the acquisition devices. This issue is usually addressed by solving an ill-posed inverse problem. While investigating proper image priors can enhance the deconvolution performance, it is not trivial to handcraft a powerful regularizer and to set the regularization parameters. To address these issues, in this paper we introduce a tuning-free Plug-and-Play (PnP) algorithm for HSI deconvolution. Specifically, we use the alternating direction method of multipliers (ADMM) to decompose the optimization problem into two iterative sub-problems. A flexible blind 3D denoising network (B3DDN) is designed to learn deep priors and to solve the denoising sub-problem with different noise levels. A measure of 3D residual whiteness is then investigated to adjust the penalty parameters when solving the quadratic sub-problems, as well as a stopping criterion. Experimental results on both simulated and real-world data with ground-truth demonstrate the superiority of the proposed method.

Hyperspectral image (HI) and multispectral image (MI) fusion allows us to overcome the hardware limitations of hyperspectral imaging systems inherent to their lower spatial resolution. Nevertheless, existing algorithms usually fail to consider realistic image acquisition conditions. This article presents a general imaging model that considers inter-image variability of data from heterogeneous sources and flexible image priors. The fusion problem is stated as an optimization problem in the maximum a posteriori framework. We introduce an original image fusion method that, on one hand, solves the optimization problem accounting for inter-image variability with an iteratively reweighted scheme and, on the other hand, that leverages lightweight convolutional neural network (CNN)-based networks to learn realistic image priors from data. In addition, we propose a zero-shot strategy to directly learn the image-specific prior of the latent images in an unsupervised manner. The performance of the algorithm is illustrated with real data subject to inter-image variability.

Distributed Acoustic Sensing (DAS) is a novel vibration sensing technology that can be employed to detect vehicles and to analyse traffic flows using existing telecommunication cables. DAS therefore has great potential in future “smart city” developments, such as real-time traffic incident detection. Though previous studies have considered vehicle detection under relatively light traffic conditions, in order for DAS to be a feasible technology in real-world scenarios, detection algorithms need to also perform robustly under a wide range of traffic conditions. In this study we investigate the potential of roadside DAS for the simultaneous detection and characterisation of the velocity of individual vehicles. To improve the temporal resolution and detection accuracy, we propose a self-supervised Deep Learning approach that deconvolves the characteristic car impulse response from the DAS data, which we refer to as a Deconvolution Auto-Encoder (DAE). We show that deconvolution of the DAS data with our DAE leads to better temporal resolution and detection performance than the original (non-deconvolved) data. We subsequently apply our DAE to a 24-hour traffic cycle, demonstrating the feasibility of our proposed method to process large volumes of DAS data, potentially in near-real time.

Fiber-optic distributed acoustic sensing (DAS) is an emerging technology for vibration measurements with numerous applications in seismic signal analysis, including microseismicity detection, ambient noise tomography, earthquake source characterization, and active source seismology. Using laser-pulse techniques, DAS turns (commercial) fiber-optic cables into seismic arrays with a spatial sampling density of the order of meters and a time sampling rate up to one thousand Hertz. The versatility of DAS enables dense instrumentation of traditionally inaccessible domains, such as urban, glaciated, and submarine environments. This in turn opens up novel applications such as traffic density monitoring and maritime vessel tracking. However, these new environments also introduce new challenges in handling various types of recorded noise, impeding the application of traditional data analysis workflows. In order to tackle the challenges posed by noise, new denoising techniques need to be explored that are tailored to DAS. In this work, we propose a Deep Learning approach that leverages the spatial density of DAS measurements to remove spatially incoherent noise with unknown characteristics. This approach is entirely self-supervised, so no noise-free ground truth is required, and it makes no assumptions regarding the noise characteristics other than that it is spatio-temporally incoherent. We apply our approach to both synthetic and real-world DAS data to demonstrate its excellent performance, even when the signals of interest are well below the noise level. Our proposed methods can be readily incorporated into conventional data processing workflows to facilitate subsequent seismological analyses.

In this paper, we propose a novel clustered multitask diffusion RLS (MT-DRLS) algorithm over network to further improve the performance of its counterpart, the multitask diffusion LMS (MT-DLMS) algorithm. Its transient behavior is investigated, in the mean and mean-square error sense. Simulation results illustrate the significant improvement of the MT-DRLS over the MT-DLMS in terms of convergence rate and steady-state error, as well as the accuracy of the theoretical findings.

To overcome inherent hardware limitations of hyperspectral imaging systems with respect to their spatial resolution, fusion-based hyper-spectral image (HSI) super-resolution is attracting increasing attention. This technique aims to fuse a low-resolution (LR) HSI and a conventional high-resolution (HR) RGB image in order to obtain an HR HSI. Recently, deep learning architectures have been used to address the HSI super-resolution problem and have achieved remarkable performance. However, they ignore the degradation model even though this model has a clear physical interpretation and may contribute to improving the performance. We address this problem by proposing a method that, on the one hand, makes use of the linear degradation model in the data-fidelity term of the objective function and, on the other hand, utilizes the output of a convolutional neural network for designing a deep prior regularizer in spectral and spatial gradient domains. Experiments show the performance improvement achieved with this strategy.

The recent evolution of hyperspectral imaging technology and the proliferation of new emerging applications press for the processing of multiple temporal hyperspectral images. In this work, we propose a novel spectral unmixing (SU) strategy using physically motivated parametric endmember (EME) representations to account for temporal spectral variability. By representing the multitemporal mixing process using a state-space formulation, we are able to exploit the Bayesian filtering machinery to estimate the EME variability coefficients. Moreover, by assuming that the temporal variability of the abundances is small over short intervals, an efficient implementation of the expectation–maximization (EM) algorithm is employed to estimate the abundances and the other model parameters. Simulation results indicate that the proposed strategy outperforms state-of-the-art multi-temporal SU (MTSU) algorithms.

In this paper, we propose to jointly solve the hyperspectral super-resolution problem and the unmixing problem of the underlying super-resolution image using a coupled LL1 block-tensor decomposition. We consider a spectral variability phenomenon occurring between the observed low-resolution images. Exact recovery conditions for the image and mixing factors are provided. We propose two algorithms, an unconstrained one and another one subject to nonnegativity constraints, to solve the problems at hand. We showcase performance of the proposed approach on synthetic and real images.

International audience

Hyperspectral image (HSI) super-resolution is commonly used to overcome the hardware limitations of existing hyperspectral imaging systems on spatial resolution. It fuses a low-resolution (LR) HSI and a high-resolution (HR) conventional image of the same scene to obtain an HR HSI. In this work, we propose a method that integrates a physical model and deep prior information. Specifically, a novel, yet effective two-stream fusion network is designed to serve as a regularizer for the fusion problem. This fusion problem is formulated as an optimization problem whose solution can be obtained by solving a Sylvester equation. Furthermore, the regularization parameter is simultaneously estimated to automatically adjust contribution of the physical model and the learned prior to reconstruct the final HR HSI. Experimental results on both simulated and real data demonstrate the superiority of the proposed method over other state-of-the-art methods on both quantitative and qualitative comparisons.

Identifying directed connectivity patterns from nodal measurements is an important problem in network analysis. Recent works proposed to leverage the performance and flexibility of strategies operating in reproducing kernel Hilbert spaces (RKHS) to model nonlinear interactions between network agents. Moreover, several applications require online and efficient solutions, which motivated the consideration of distributed adaptive learning strategies inspired by algorithms such as the kernel least mean square (KLMS). Despite showing good performance, a thorough theoretical understanding of the behavior of such algorithms is still missing. This makes applying them in practice challenging, especially because the set-up of adaptive algorithms involves additional parameters like the step size and a dictionary of kernel functions. In this paper, we present a convergence analysis of the graph-topology-inference KLMS algorithm. Monte Carlo simulations demonstrate the accuracy of the theoretical models.

Multiple endmember spectral mixture analysis (MESMA) is one of the leading approaches to perform spectral unmixing (SU) considering the variability of the endmembers (EMs). It represents each EM in the image using libraries of spectral signatures acquireda priori. However, existing spectral libraries are often small and unable to properly capture the variability of each EM in practical scenes, which compromises the performance of MESMA. In this letter, we propose a library augmentation strategy to increase the diversity of existing spectral libraries, thus improving their ability to represent the materials in real images. First, we leverage the power of deep generative models to learn the statistical distribution of the EMs based on the spectral signatures available in the existing libraries. Afterward, new samples can be drawn from the learned EM distributions and used to augment the spectral libraries, improving the overall quality of the SU process. Experimental results using synthetic and real data attest to the superior performance of the proposed method even under library mismatch conditions.

Convergence of the diffusion RLS (DRLS) algorithm to steady-state has been extensively studied in the literature, whereas no analysis of its transient convergence behavior has been reported yet. In this letter, we conduct a theoretical analysis of the transient behavior of the DRLS algorithm for cyclostationary colored inputs, in the mean and mean-square error sense. The resulting analytical models allows us to thoroughly investigate the convergence behavior of the algorithm over adaptive networks in such complex scenarios. Simulation results support the accuracy and correctness of the theoretical findings.

Detecting changes in network-structured time series data is of utmost importance in critical applications as diverse as detecting denial of service attacks against online service providers or monitoring energy and water supplies. The aim of this paper is to address this challenge when anomalies activate unknown groups of nodes in a network. We devise an online change-point detection algorithm that fully benefits from the recent advances in graph signal processing to exploit the characteristics of the data that lie on irregular supports. Built upon the kernel machinery, it performs density ratio estimation in an online way. The algorithm is scalable in the sense that it is spatially distributed over the nodes to monitor large-scale dynamic networks. The detection and localization performances of the algorithm are illustrated with simulated data.

Modeling relations between local optimum parameter vectors in multitask networks has attracted much attention over the last years. This work considers a distributed optimization problem for parameter vectors with a jointly sparse structure among nodes, that is, the parameter vectors share the same support set. By introducing an ℓ∞,1-norm penalty at each node, and using a proximal gradient method to minimize the regularized cost, we devise a proximal multitask diffusion LMS algorithm which promotes the joint-sparsity to enhance the estimation performance. Analyses are provided to ensure the stability. Simulation results are presented to highlight the performance.

In graph signal processing, there are often settings where the graph topology is not known beforehand and has to be estimated from data. Moreover, some graphs can be dynamic, such as brain activity supported by neurons or brain regions. This paper focuses on estimating in an online and adaptive manner a network structure capturing the non-linear dependencies among streaming graph signals in the form of a possibly directed, adjacency matrix. By projecting data into a higher- or infinite-dimension space, we focus on capturing nonlinear relationships between agents. In order to mitigate the increasing number of data points, we employ kernel dictionaries. Finally, we run a series of tests in order to experimentally illustrate the usefulness of our kernel-based approach on biomedical data, on which we obtain results comparable to state-of-the-art methods.

Hyperspectral image (HSI) deconvolution is an ill-posed problem aiming at recovering sharp images with tens or hundreds of spectral channels from blurred and noisy observations. In order to successfully conduct the deconvolution, proper priors are required to regularize the optimization problem. However, handcrafting a good regularizer may not be trivial and complex regularizers lead to difficulties in solving the optimization problem. In this paper, we use the alternating direction method of multipliers (ADMM) to decompose the optimization problem into iterative subproblems where the prior only appears in a denoising subproblem. Then a 3D denoising convolutional neural network (3DDnCNN) is designed and trained with data for solving this problem. In this way, the hyperspectral image deconvolution is then solved with a framework that integrates the optimization techniques and deep learning. Experimental results demonstrate the superiority of the proposed method with several blurring settings in both quantitative and qualitative comparisons.

We study the problem of distributed estimation over adaptive networks where communication delays exist between nodes. In particular, we investigate the diffusion Least-Mean-Square (LMS) strategy where delayed intermediate estimates (due to the communication channels) are employed during the combination step. One important question is: Do the delays affect the stability condition and performance? To answer this question, we conduct a detailed performance analysis in the mean and in the mean-square-error sense of the diffusion LMS with delayed estimates. Stability conditions, transient and steady-state mean-square-deviation (MSD) expressions are provided. One of the main findings is that diffusion LMS with delays can still converge under the same step-sizes condition of the diffusion LMS without delays. Finally, simulation results illustrate the theoretical findings.

Introducing spatial prior information in hyperspectral imaging (HSI) analysis has led to an overall improvement of the performance of many HSI methods applied for denoising, classification, and unmixing. Extending such methodologies to nonlinear settings is not always straightforward, specially for unmixing problems where the consideration of spatial relationships between neighboring pixels might comprise intricate interactions between their fractional abundances and nonlinear contributions. In this paper, we consider a multiscale regularization strategy for nonlinear spectral unmixing with kernels. The proposed methodology splits the unmixing problem into two sub-problems at two different spatial scales: a coarse scale containing low-dimensional structures, and the original fine scale. The coarse spatial domain is defined using superpixels that result from a multiscale transformation. Spectral unmixing is then formulated as the solution of quadratically constrained optimization problems, which are solved efficiently by exploring their strong duality and a reformulation of their dual cost functions in the form of root-finding problems. Furthermore, we employ a theory-based statistical framework to devise a consistent strategy to estimate all required parameters, including both the regularization parameters of the algorithm and the number of superpixels of the transformation, resulting in a truly blind (from the parameters setting perspective) unmixing method. Experimental results attest the superior performance of the proposed method when comparing with other, state-of-the-art, related strategies.

Sparse hyperspectral unmixing from large spectral libraries has been considered to circumvent the limitations of endmember extraction algorithms in many applications. This strategy often leads to ill-posed inverse problems, which can greatly benefit from spatial regularization strategies. However, existing spatial regularization strategies lead to large-scale nonsmooth optimization problems. Thus, efficiently introducing spatial context in the unmixing problem remains a challenge and a necessity for many real world applications. In this letter, a novel multiscale spatial regularization approach for sparse unmixing is proposed. The method uses a signal-adaptive spatial multiscale decomposition based on segmentation and oversegmentation algorithms to decompose the unmixing problem into two simpler problems: one in an approximation image domain and another in the original domain. Simulation results using both synthetic and real data indicate that the proposed method outperforms the state-of-the-art total variation-based algorithms with a computation time comparable to that of their unregularized counterparts.

This paper proposes a hyperspectral image deconvolution algorithm for the online restoration of hyperspectral images as provided by wiskbroom and pushbroom scanning systems. We introduce a least-mean-squares (LMS)-based framework accounting for the convolution kernel noncausality and including nonquadratic (zero attracting and piecewise constant) regularization terms. This results in the so-called sliding block regularized LMS (SBR-LMS), which maintains a linear complexity compatible with real-time processing in industrial applications. A model for the algorithm mean and mean-squares transient behavior is derived and the stability condition is studied. Experiments are conducted to assess the role of each hyper-parameter. A key feature of the proposed SBR-LMS is that it outperforms standard approaches in low SNR scenarios such as ultra-fast scanning.

We study the problem of parametric modeling of network-structured signals with graph filters. To benefit from the properties of several graph shift operators simultaneously, and to enhance interpretability, we investigate combinations of parallel graph filters with different shift operators. Due to their extra degrees of freedom, these models might suffer from over-fitting. We address this problem through a weighted ℓ2-norm regularization formulation to perform model selection by encouraging group sparsity. What makes this formulation interesting is that it is actually a smooth convex optimization problem. Experiments on real-world data structured by undirected and directed graphs show the effectiveness of this method.

This letter proposes a general regularization framework for inference over multitask networks. The optimization approach relies on minimizing a global cost consisting of the aggregate sum of individual costs regularized by a term that allows to incorporate global information about the graph structure and the individual parameter vectors into the solution of the inference problem. An adaptive strategy, which responds to streaming data and employs stochastic approximations in place of actual gradient vectors, is devised and studied. Methods allowing the distributed implementation of the regularization step are also discussed. This letter shows how to blend real-time adaptation with graph filtering and a generalized regularization framework to result in a graph diffusion strategy for distributed learning over multitask networks.

The performance of iterative algorithms aimed at solving a regularized least squares problem typically depends on the value of some regularization parameter. Tuning the regularization parameter value is a fundamental step necessary to control the strength of the regularization and hence ensure a good performance. We address the problem of finding the optimal regularization parameter in such iterative algorithms. We propose to adaptively adjust the regularization parameter throughout the iterations of the algorithm by minimizing an estimate of the current risk, typically the Weighted Stein unbiased risk estimate (WSURE). We then prove that, for the case of the Tikhonov regularization, the proposed ADAptive Parameter Tuning (ADA-PT) strategy provides a stationary point consistent with the risk minimizer. We illustrate the efficiency of ADA-PT on two image deconvolution problems: one with the Tikhonov regularization and one with the weighted ℓ-1 analysis wavelet regularization.

International audience

Most works on graph signal processing assume static graph signals, which is a limitation even in comparison to traditional DSP techniques where signals are modeled as sequences that evolve over time. For broader applicability, it is necessary to develop techniques that are able to process dynamic or streaming data. Many earlier works on adaptive networks have addressed problems related to this challenge by developing effective strategies that are particularly well-suited to data streaming into graphs. We are thus faced with two paradigms: one where signals are modeled as static and sitting on the graph nodes, and another where signals are modeled as dynamic and streaming into the graph nodes. The objective of this work is to blend these concepts and propose diffusion strategies for adaptively learning from streaming graph signals.

This paper presents a kernel-based nonlinear mixing model for hyperspectral data, where the nonlinear function belongs to a Hilbert space of vector valued functions. The proposed model extends the existing ones by accounting for band-dependent and neighboring nonlinear contributions. The key idea is to work under the assumption that nonlinear contributions are dominant in some parts of the spectrum, while they are less pronounced in other parts. In addition to this, we motivate the need for taking into account nonlinear contributions originating from the ground covers of neighboring pixels by practical considerations, precisely the adjacency effect. The relevance of the proposed model is that the nonlinear function is associated with a matrix valued kernel that allows to jointly model a wide range of nonlinearities and includes prior information regarding band dependences. Furthermore, the choice of the nonlinear function input allows to incorporate neighboring effects. The optimization problem is strictly convex and the corresponding iterative algorithm is based on the alternating direction method of multipliers. Finally, experiments conducted using synthetic and real data demonstrate the effectiveness of the proposed approach.

Kernel-based nonlinear mixing models have been applied to unmix spectral information of hyperspectral images when the type of mixing occurring in the scene is too complex or unknown. Such methods, however, usually require the inversion of matrices of sizes equal to the number of spectral bands. Reducing the computational load of these methods remains a challenge in large-scale applications. This paper proposes a centralized band selection (BS) method for supervised unmixing in the reproducing kernel Hilbert space. It is based upon the coherence criterion, which sets the largest value allowed for correlations between the basis kernel functions characterizing the selected bands in the unmixing model. We show that the proposed BS approach is equivalent to solving a maximum clique problem, i.e., searching for the biggest complete subgraph in a graph. Furthermore, we devise a strategy for selecting the coherence threshold and the Gaussian kernel bandwidth using coherence bounds for linearly independent bases. Simulation results illustrate the efficiency of the proposed method.

This communication proposes an unsupervised neighbor dependent nonlinear unmixing algorithm for hyperspectral data. The proposed mixing scheme models the reflectance vector of a pixel as the sum of a linear combination of the endmem-bers plus a nonlinear function acting on neighboring spectra. The nonlinear function belongs to a reproducing kernel Hilbert space. The observations themselves are considered as the endmember candidates, and the group lasso regulariza-tion is used to enable selecting the purest pixels among the candidates. Experiments on synthetic data demonstrate the effectiveness of the proposed approach.

Considering groups of variables, rather than variables individually, can be beneficial for estimation accuracy if structural relationships between variables exist (e.g., spatial, hierarchical or related to the physics of the problem). Group-sparsity inducing estimators are typical examples that benefit from such type of prior knowledge. Building on this principle, we show that the diffusion LMS algorithm for distributed inference over networks can be extended to deal with structured criteria built upon groups of variables, leading to a flexible framework that can encode various structures in the parameters to estimate. We also propose an unsupervised online strategy to differentially promote or inhibit collaborations between nodes depending on the group of variables at hand.

Diffusion LMS is an efficient strategy for solving distributed optimization problems with cooperating agents. In some applications, the optimum parameter vectors may not be the same for all agents. Moreover, agents usually exchange information through noisy communication links. In this work, we analyze the theoretical performance of the single-task diffusion LMS when it is run, intentionally or unintentionally, in a multitask environment in the presence of noisy links. To reduce the impact of these nuisance factors, we introduce an improved strategy that allows the agents to promote or reduce exchanges of information with their neighbors.

Hyperspectral data unmixing has attracted considerable attention in recent years. Hyperspectral data may however suffer from varying levels of signal-to-noise ratio over spectral bands. In this paper, we investigate a robust approach for nonlinear hyperspectral data unmixing. Each observed pixel is modeled as a linear mixing of endmember spectra with nonlinear fluctuations embedded in a reproducing kernel Hilbert space. Welsch M-estimator is considered for reducing the sensitivity of the unmixing process. Experimental results, with both synthetic and real data, illustrate the effectiveness of the proposed scheme.

Zero-attracting least-mean-square (ZA-LMS) algorithm has been widely used for online sparse system identification. It combines the LMS framework and l1-norm regularization to promote sparsity, and relies on subgradient iterations. Despite the significant interest in ZA-LMS, few works analyzed its transient behavior. The main difficulty lies in the nonlinearity of the update rule. In this study, a detailed analysis in the mean and mean-square sense is carried out in order to examine the behavior of the algorithm. Simulation results illustrate the accuracy of the model and highlight its performance through comparisons with an existing model.

Linear mixture models are commonly used to represent a hyperspectral data cube as linear combinations of endmember spectra. However, determining the number of endmembers for images embedded in noise is a crucial task. This paper proposes a fully automatic approach for estimating the number of endmembers in hyperspectral images. The estimation is based on recent results of random matrix theory related to the so-called spiked population model. More precisely, we study the gap between successive eigenvalues of the sample covariance matrix constructed from high-dimensional noisy samples. The resulting estimation strategy is fully automatic and robust to correlated noise owing to the consideration of a noise-whitening step. This strategy is validated on both synthetic and real images. The experimental results are very promising and show the accuracy of this algorithm with respect to state-of-the-art algorithms.

Mixing phenomena in hyperspectral images depend on a variety of factors, such as the resolution of observation devices, the properties of materials, and how these materials interact with incident light in the scene. Different parametric and nonparametric models have been considered to address hyperspectral unmixing problems. The simplest one is the linear mixing model. Nevertheless, it has been recognized that the mixing phenomena can also be nonlinear. The corresponding nonlinear analysis techniques are necessarily more challenging and complex than those employed for linear unmixing. Within this context, it makes sense to detect the nonlinearly mixed pixels in an image prior to its analysis, and then employ the simplest possible unmixing technique to analyze each pixel. In this paper, we propose a technique for detecting nonlinearly mixed pixels. The detection approach is based on the comparison of the reconstruction errors using both a Gaussian process regression model and a linear regression model. The two errors are combined into a detection statistics for which a probability density function can be reasonably approximated. We also propose an iterative endmember extraction algorithm to be employed in combination with the detection algorithm. The proposed detect-then-unmix strategy, which consists of extracting endmembers, detecting nonlinearly mixed pixels and unmixing, is tested with synthetic and real images.

This paper introduces a graph Laplacian regularization in the hyperspectral unmixing formulation. The proposed regularization relies upon the construction of a graph representation of the hyperspectral image. Each node in the graph represents a pixel's spectrum, and edges connect similar pixels. The proposed graph framework promotes smoothness in the estimated abundance maps and collaborative estimation between homogeneous areas of the image. The resulting convex optimization problem is solved using the Alternating Direction Method of Multipliers (ADMM). A special attention is given to the computational complexity of the algorithm, and Graph-cut methods are proposed in order to reduce the computational burden. Finally, simulations conducted on synthetic and real data illustrate the effectiveness of the graph Laplacian regularization with respect to other classical regularizations for hyperspectral unmixing.

Complex kernel-based adaptive algorithms have been recently introduced for complex-valued nonlinear system identification. These algorithms are built upon the same framework as complex linear adaptive filtering techniques and Wirtinger's calculus in complex reproducing kernel Hilbert spaces. In this paper, we study the convergence behavior of the augmented complex Gaussian KLMS algorithm. Simulation results illustrate the accuracy of the analysis.

In this work, a diffusion-type algorithm is proposed to solve multitask estimation problems where each cluster of nodes is interested in estimating its own optimum parameter vector in a distributed manner. The approach relies on minimizing a global mean-square error criterion regularized by a term that promotes piecewise constant transitions in the parameter vector entries estimated by neighboring clusters. We provide some results on the mean and mean-square-error convergence. Simulations are conducted to illustrate the effectiveness of the strategy.

This paper presents a stochastic behavior analysis of a kernel-based stochastic restricted-gradient descent method. The restricted gradient gives a steepest ascent direction within the so-called dictionary subspace. The analysis provides the transient and steady state performance in the mean squared error criterion. It also includes stability conditions in the mean and mean-square sense. The present study is based on the analysis of the kernel normalized least mean square (KNLMS) algorithm initially proposed by Chen et al. Simulation results validate the analysis.

The kernel least-mean-square (KLMS) algorithm is an appealing tool for online identification of nonlinear systems due to its simplicity and robustness. In addition to choosing a reproducing kernel and setting filter parameters, designing a KLMS adaptive filter requires to select a so-called dictionary in order to get a finite-order model. This dictionary has a significant impact on performance, and requires careful consideration. Theoretical analysis of KLMS as a function of dictionary setting has rarely, if ever, been addressed in the literature. In an analysis previously published by the authors, the dictionary elements were assumed to be governed by the same probability density function of the input data. In this paper, we modify this study by considering the dictionary as part of the filter parameters to be set. This theoretical analysis paves the way for future investigations on KLMS dictionary design.

Incorporating spatial information into hyperspectral unmixing procedures has been shown to have positive effects, due to the inherent spatial-spectral duality in hyperspectral scenes. Current research works that consider spatial information are mainly focused on the linear mixing model. In this paper, we investigate a variational approach to incorporating spatial correlation into a nonlinear unmixing procedure. A nonlinear algorithm operating in reproducing kernel Hilbert spaces, associated with an ℓ1local variation norm as the spatial regularizer, is derived. Experimental results, with both synthetic and real data, illustrate the effectiveness of the proposed scheme.

Recent research works on distributed adaptive networks have intensively studied the case where the nodes estimate a common parameter vector collaboratively. However, there are many applications that are multitask-oriented in the sense that there are multiple parameter vectors that need to be inferred simultaneously. In this paper, we employ diffusion strategies to develop distributed algorithms that address clustered multitask problems by minimizing an appropriate mean-square error criterion with ℓ2-regularization. Some results on the mean-square stability and convergence of the algorithm are also provided. Simulations are conducted to illustrate the theoretical findings.

This paper investigates the use of Gaussian processes to detect non-linearly mixed pixels in hyperspectral images. The proposed technique is independent of nonlinear mixing mechanism, and therefore is not restricted to any prescribed nonlinear mixing model. The observed reflectances are estimated using both the least squares method and a Gaussian process. The fitting errors of the two approaches are combined in a test statistics for which it is possible to estimate a detection threshold given a required probability of false alarm. The proposed detector is compared to a robust nonlinearity detector recently proposed using synthetic data and is shown to provide a better detection performance. The new detector is also tested on a real hyperspectral image.

The Non-Negative Least-Mean-Square (NNLMS) algorithm and its variants have been proposed for online estimation under non-negativity constraints. The transient behavior of the NNLMS, Normalized NNLMS, Exponential NNLMS and Sign-Sign NNLMS algorithms have been studied in the literature. In this letter, we derive closed-form expressions for the steady-state excess mean-square error (EMSE) for the four algorithms. Simulation results illustrate the accuracy of the theoretical results. This work complements the understanding of the behavior of these algorithms.

Integrating spatial information into hyperspectral unmixing procedures has been shown to have a positive effect on the estimation of fractional abundances due to the inherent spatial-spectral duality in hyperspectral scenes. However, current research works that take spatial information into account are mainly focused on the linear mixing model. In this paper, we investigate how to incorporate spatial correlation into a nonlinear abundance estimation process. A nonlinear unmixing algorithm operating in reproducing kernel Hilbert spaces, coupled with a l1-type spatial regularization, is derived. Experiment results, with both synthetic and real hyperspectral images, illustrate the effectiveness of the proposed scheme.

This paper addresses the problem of blind and fully constrained unmixing of hyperspectral images. Unmixing is performed without the use of any dictionary, and assumes that the number of constituent materials in the scene and their spectral signatures are unknown. The estimated abundances satisfy the desired sum-to-one and nonnegativity constraints. Two models with increasing complexity are developed to achieve this challenging task, depending on how noise interacts with hyperspectral data. The first one leads to a convex optimization problem and is solved with the alternating direction method of multipliers. The second one accounts for signal-dependent noise and is addressed with a reweighted least squares algorithm. Experiments on synthetic and real data demonstrate the effectiveness of our approach.

In recent years, nonlinear unmixing of hyperspectral data has become an attractive topic in hyperspectral image analysis, because nonlinear models appear as more appropriate to represent photon interactions in real scenes. For this challenging problem, nonlinear methods operating in reproducing kernel Hilbert spaces have shown particular advantages. In this paper, we derive an efficient nonlinear unmixing algorithm based on a recently proposed linear mixture/ nonlinear fluctuation model. A multi-kernel learning support vector regressor is established to determine material abundances and nonlinear fluctuations. Moreover, a low complexity locally-spatial regularizer is incorporated to enhance the unmixing performance. Experiments with synthetic and real data illustrate the effectiveness of the proposed method.

Nonlinear adaptive filtering with kernels has become a topic of high interest over the last decade. A characteristics of kernel-based techniques is that they deal with kernel expansions whose number of terms is equal to the number of input data, making them unsuitable for online applications. Kernel-based adaptive filtering algorithms generally rely on a two-stage process at each iteration: a model order control stage that limits the increase in the number of terms by including only valuable kernels into the so-called dictionary, and a filter parameter update stage. It is surprising to note that most existing strategies for dictionary update can only incorporate new elements into the dictionary. This unfortunately means that they cannot discard obsolete kernel functions, within the context of a time-varying environment in particular. Recently, to remedy this drawback, it has been proposed to associate an ℓ1-norm regularization criterion with the mean-square error criterion. The aim of this paper is to provide theoretical results on the convergence of this approach.

Granger causality considers the question of whether two time series exert causal influences on each other. Causality testing usually relies on prediction, i.e., if the prediction error of the first time series is reduced by taking measurements from the second one into account, then the latter is said to have a causal influence on the former. In this paper, a nonparametric framework based on functional estimation is proposed. Nonlinear prediction is performed via the Bayesian paradigm, using Gaussian processes. Some experiments illustrate the efficiency of the approach.

The autoregressive (AR) model is a well-known technique to analyze time series. The Yule-Walker equations provide a straightforward connection between the AR model parameters and the covariance function of the process. In this paper, we propose a nonlinear extension of the AR model using kernel machines. To this end, we explore the Yule-Walker equations in the feature space, and show that the model parameters can be estimated using the concept of expected kernels. Finally, in order to predict once the model identified, we solve a pre-image problem by getting back from the feature space to the input space. We also give new insights into the convexity of the pre-image problem. The relevance of the proposed method is evaluated on several time series.

Spectral model is simple and efficient for modeling the rain attenuation which occurs in satellite communication channels. The prediction of this attenuation series is a vital step for adaptive coding or adaptive power control, which can improve the efficiency of a communication system. In simulation tasks, the discretized spectral model is usually used for generating the attenuation sequence. Due to this reason, in this paper we derive the conditional probability distribution of the predicted attenuation based on the discretized spectral model. This predictor can be used as a bound for others linear or nonlinear predictor of this model.

In hyperspectral image analysis, pixels are mixtures of spectral components associated to pure materials. Although the linear mixture model is the mostly studied case, nonlinear techniques have been proposed to overcome its limitations. In this paper, a manifold learning approach is used as a dimensionality-reduction step to deal with non-linearities beforehand, or is integrated directly in the endmember extraction and abundance estimation steps using geodesic distances. Simulation results show that these methods improve the precision of estimation in severely nonlinear cases.

In hyperspectral imaging, spectral unmixing is one of the most challenging and fundamental problems. It consists of breaking down the spectrum of a mixed pixel into a set of pure spectra, called endmembers, and their contributions, called abundances. Many endmember extraction techniques have been proposed in literature, based on either a statistical or a geometrical formulation. However, most, if not all, of these techniques for estimating abundances use a least-squares solution. In this paper, we show that abundances can be estimated using a geometric formulation. To this end, we express abundances with the barycentric coordinates in the simplex defined by endmembers. We propose to write them in terms of a ratio of volumes or a ratio of distances, which are quantities that are often computed to identify endmembers. This property allows us to easily incorporate abundance estimation within conventional endmember extraction techniques, without incurring additional computational complexity. We use this key property with various endmember extraction techniques, such as N-Findr, vertex component analysis, simplex growing algorithm, and iterated constrained endmembers. The relevance of the method is illustrated with experimental results on real hyperspectral images.

In mobile sensor networks, it is important to manage the mobility of the nodes in order to improve the performances of the network. This paper addresses the problem of single target tracking in controlled mobility sensor networks. The proposed method consists of estimating the current position of a single target. Estimated positions are then used to predict the following location of the target. Once an area of interest is defined, the proposed approach consists of moving the mobile nodes in order to cover it in an optimal way. It thus defines a strategy for choosing the set of new sensors locations. Each node is then assigned one position within the set in the way to minimize the total traveled distance by the nodes. While the estimation and the prediction phases are performed using the interval theory, relocating nodes employs the ant colony optimization algorithm. Simulations results corroborate the efficiency of the proposed method compared to the target tracking methods considered for networks with static nodes.

Abstract The key impediments to a successful wireless sensor network (WSN) application are the energy and the longevity constraints of sensor nodes. Therefore, two signal processing oriented cluster management strategies, the proactive and the reactive cluster management, are proposed to efficiently deal with these constraints. The former strategy is designed for heterogeneous WSNs, where sensors are organized in a static clustering architecture. A non‐myopic cluster activation rule is realized to reduce the number of hand‐off operations between clusters, while maintaining desired estimation accuracy. The proactive strategy minimizes the hardware expenditure and the total energy consumption. On the other hand, the main concern of the reactive strategy is to maximize the network longevity of homogeneous WSNs. A Dijkstra‐like algorithm is proposed to dynamically form active cluster based on the relation between the predictive target distribution and the candidate sensors, considering both the energy efficiency and the data relevance. By evenly distributing the energy expenditure over the whole network, the objective of maximizing the network longevity is achieved. The simulations evaluate and compare the two proposed strategies in terms of tracking accuracy, energy consumption and execution time. Copyright © 2010 John Wiley & Sons, Ltd.

This paper proposes an unsupervised method for real time detection of abnormal events in the context of audio surveillance. Based on training a One-Class Support Vector Machine (OC-SVM) to model the distribution of the normality (ambience), we propose to construct sets of decision functions. This modification allows controlling the trade-off between false-alarm and miss probabilities without modifying the trained OC-SVM that best capture the ambience boundaries, or its hyperparameters. Then we present an adaptive online scheme of temporal integration of the decision function output in order to increase performance and robustness. We also introduce a framework to generate databases based on real signals for the evaluation of audio surveillance systems. Finally, we present the performances obtained on the generated database.

While an exact stationarization of a process with a given spectrum magnitude can be obtained via a complete randomization of the spectrum phase ("surrogates" technique), we pro pose here a softened version in which the degree of stationarization can be controlled by a perturbation of the actual phase. A basic theory for such "transitional surrogates" is first discussed, with emphasis on two effective constructions based on either white Gaussian noise or random walks. Some typical examples are considered for illustration, and performance evaluations are provided for supporting the usefulness of the approach in the context of stationarity testing.

This article deals with a regularized version of the split gradient method (SGM), leading to multiplicative algorithms. The proposed algorithm is available for the optimization of any divergence depending on two data fields under positivity constraint. The SGM-based algorithm is derived to solve the nonnegative matrix factorization (NMF) problem. An example with a Frobenius norm on both the data consistency and the penalty term is developed and applied to hyperspectral data unmixing.

Like its linear counterpart, the Kernel Least Mean Square (KLMS) algorithm is also becoming popular in nonlinear adaptive filtering due to its simplicity and robustness. The "kernelization" of the linear adaptive filters modifies the statistics of the input signals, which now depends on the parameters of the used kernel. A Gaussian KLMS has two design parameters; the step size and the kernel bandwidth. Thus, new analytical models are required to predict the kernel-based algorithm behavior as a function of the design parameters. This pa per studies the stochastic behavior of the Gaussian KLMS algorithm for white Gaussian input signals. The resulting model accurately predicts the algorithm behavior and can be used for choosing the algorithm parameters in order to achieve a prescribed performance.

This work presents the problem of target tracking and relay localization in wireless sensor networks (WSN) based on quantized proximity sensors. Thus, we use the quantized variational filtering (QVF) in order to estimate jointly the target position and the relay location. Recently, variational filtering has been proved to be suitable to the communication constraints of WSN. However, this problem has been proposed only for binary sensor networks neglecting the information relevance of sensor measurements and the transmission energy consumption. At each sampling instant, the adaptive scheme provides the estimates of the target position and the relay location by using the QVF algorithm. The efficiency of the proposed method is validated by simulation results in target tracking for wireless sensor networks.

Due to the limited energy supplies of nodes in wireless sensor networks (WSN), optimizing their design under energy constraints, reducing their communication costs are of paramount importance. To this goal and in order to efficiently solve the problem of target tracking in WSN with quantized measurements, we propose to jointly estimate the target position and select the optimal communication path between the cluster head (CH) and the slave sensors. Firstly, we select the optimal communication path between the candidate sensor and the CH. Then, we estimate the target position using Quantized Variational Filtering (QVF) algorithm. The optimal communication path is selected as well as the highest signal-to-noise ratio (SNR) at the CH. The efficiency of the proposed method is validated by extensive simulations in target tracking for wireless sensor networks.

In this article, we propose an original approach for self-localization in mobile sensor networks. The proposed approach is developed for low-anchors density networks. Based on intervals theory, the presented method is an online technique yielding a bounded-cumulative error. The estimation of the positions of mobile sensors is performed using multi-hop observation model added to an a priori mobility model. One of the contributions of this paper is that it uses the measurements of all types of sensors, including those that do not have GPS, denoted non-anchor nodes. Compared to the existing localization techniques, this method leads to a higher accuracy with a low computational cost.

This paper addresses multiple target tracking (MTT) in wireless sensor networks (WSN) where the nonlinear observed system is assumed to progress according to a probabilistic state space model. In this paper, we propose to improve the use of the quantized variational filtering (QVF) by optimally quantizing the data collected by the sensors and estimating the channel attenuation between sensors. Our proposed technique is intended to jointly estimate the multiple target positions by using the Hybrid QVF and Sequential Monte Carlo-based approach to data association (SMCDA) algorithm, optimize the number of quantization bits per observation and estimate the fading channel coefficient. The adaptive quantization is achieved by maximizing the predicted Fisher information and the fading channel coefficient is estimated by maximizing the a posteriori distribution. The simulation results show that the adaptive quantization algorithm, outperforms both the centralized quantized particle filter (QPF) and the VF algorithm based on binary sensors (BVF).

An operational framework is developed for testing stationarity relatively to an observation scale. The proposed method makes use of a family of stationary surrogates for defining the null hypothesis of stationarity. As a further contribution to the field, we demonstrate the strict-sense stationarity of surrogate signals and we exploit this property to derive the asymptotic distributions of their spectrogram and power spectral density. A statistical hypothesis testing framework is then proposed to check signal stationarity. Finally, some results are shown on a typical model of signals that can be thought of as stationary or nonstationary, depending on the observation scale used.

In this paper, we study the problem of decomposing spectra in hyperspectral data into the sum of pure spectra, or endmembers. We propose to jointly extract the endmembers and estimate the corresponding fractions, or abundances. For this purpose, we show that these abundances can be easily computed using volume of simplices, from the same information used in the classical N-Findr algorithm. This results into a simple scheme for unmixing hyperspectral data, with low computational complexity. Experimental results show the efficiency of the proposed method.

We consider the problem of quantized target tracking in wireless sensor networks (WSN) where the observed system is assumed to evolve according to a probabilistic state space model. We propose to improve the use of the quantized variational filtering (QVF) by jointly estimating the target position and selecting the best sensors that participate in data association. In fact, the QVF has been shown to be adapted to the communication constraints of sensor networks. Its efficiency relies on the fact that the online update of the filtering distribution and its compression are executed simultaneously. Firstly, we select the best sensor that provides satisfied data of the target and balances the energy level among all sensors and minimum node density in a local cluster. Then, we estimate the target position using the QVF algorithm. The best candidate sensors are obtained by maximizing the mutual information function under energy constraints. The efficiency of the proposed method is validated by simulation results in target tracking for wireless sensor networks.

The prime motivation of our work is to balance the inherent trade-off between the resource consumption and the accuracy of the target tracking in wireless sensor networks. Toward this objective, the study goes through three phases. First, a cluster-based scheme is exploited. At every sampling instant, only one cluster of sensors that located in the proximity of the target is activated, whereas the other sensors are inactive. To activate the most appropriate cluster, we propose a nonmyopic rule, which is based on not only the target state prediction but also its future tendency. Second, the variational filtering algorithm is capable of precise tracking even in the highly nonlinear case. Furthermore, since the measurement incorporation and the approximation of the filtering distribution are jointly performed by variational calculus, an effective and lossless compression is achieved. The intercluster information exchange is thus reduced to one single Gaussian statistic, dramatically cutting down the resource consumption. Third, a binary proximity observation model is employed by the activated slave sensors to reduce the energy consumption and to minimize the intracluster communication. Finally, the effectiveness of the proposed approach is evaluated and compared with the state-of-the-art algorithms in terms of tracking accuracy, internode communication, and computation complexity.

In this paper, we propose a distributed learning strategy in wireless sensor networks. Taking advantage of recent developments on kernel-based machine learning, we consider a new sparsification criterion for online learning. As opposed to previously derived criteria, it is based on the estimated error and is therefore is well suited for tracking the evolution of systems over time. We also derive a gradient descent algorithm, and we demonstrate its relevance to estimate the dynamic evolution of temperature in a given region.

In this paper, a data-driven extension of the variational algorithm is proposed. Based on a few selected sensors, target tracking is performed distributively without any information about the observation model. Tracking under such conditions is possible if one exploits the information collected from extra inter-sensor RSSI measurements. The target tracking problem is formulated as a kernel matrix completion problem. A probabilistic kernel regression is then proposed that yields a Gaussian likelihood function. The likelihood is used to derive an efficient and accelerated version of the variational filter without resorting to Monte Carlo integration. The proposed data-driven algorithm is, by construction, robust to observation model deviations and adapted to non-stationary environments.

Resource limitations in wireless sensor networks have put stringent constraints on distributed signal processing. In this paper, we propose a cluster-based decentralized variational filtering algorithm with minimum resource allocation for simultaneous sensor localization and target tracking. At each sampling instant, only one cluster of sensors is activated according to the prediction of the target state. Slave sensors employ a binary proximity observation model to reduce energy consumption and minimize communication cost. Based on the binary measurements between sensors and the target, activated sensors and target location estimates are interdependently improved. By adopting the variational method, the inter-cluster information exchange is reduced to one single Gaussian statistic, further minimizing resource consumption in the network. Since the measurement incorporation and the approximation of the filtering distribution are jointly performed by variational calculus, an effective and lossless compression is achieved compared to the classical particle filtering. Effectiveness of the proposed approach is evaluated in terms of tracking accuracy and localization precision.

Over the past few years, wireless sensor networks received tremendous attention for monitoring physical phenomena, such as the temperature field in a given region. Applying conventional kernel regression methods for functional learning such as support vector machines is inappropriate for sensor networks, since the order of the resulting model and its computational complexity scales badly with the number of available sensors, which tends to be large. In order to circumvent this drawback, we propose in this paper a reduced-order model approach. To this end, we take advantage of recent developments in sparse representation literature, and show the natural link between reducing the model order and the topology of the deployed sensors. To learn this model, we derive a gradient descent scheme and show its efficiency for wireless sensor networks. We illustrate the proposed approach through simulations involving the estimation of a spatial temperature distribution.

In this contribution, we propose an original algorithm for self-localization in mobile ad-hoc networks. The proposed technique, based on interval analysis, is suited to the limited computational and memory resources of mobile nodes. The incertitude about the estimated position of each node is propagated in an interval form. The propagation is based on a state space model and formulated by a constraints satisfaction problem. Observations errors as well as anchor nodes imperfections are taken into account in a simple and computational-consistent way. A simple Waltz algorithm is then applied in order to contract the solution, yielding a guaranteed and robust online estimation of the mobile node position. Simulation results on mobile node group trajectories corroborate the efficiency of the proposed technique and show that it compares favorably to particle filtering methods.

Kernel-target alignment is commonly used to predict the behavior of any given reproducing kernel in a classification context, without training any kernel machine. However, a poor position of the data in feature space can drastically reduce the value of the alignment. This implies that, in a kernel selection setting, the best kernel in a given collection may be associated with a low value of alignment. In this paper, we present a new algorithm for maximizing the alignment by data translation in feature space. The aim is to reduce the biais introduced by the translation non-invariance of this criterion. Experimental results on multi-dimensional benchmarks show the effectiveness of our approach.

Kernel-target alignment is commonly used to predict the behavior of any given reproducing kernel in a classification context, without training any kernel machine. In this paper, we present a gradient ascent algorithm for maximizing the alignment over linear transform of the input space. Our method is compared to the minimization of the radius-margin bound. Experimental results on multi-dimensional benchmarks show the effectiveness of our approach.

This paper provides new insights into on-line nonlinear sparse approximation of functions based on the coherence criterion. We revisit previous work, and propose tighter bounds on the approximation error based on the coherence criterion. Moreover, we study the connections between the coherence criterion and both the approximate linear dependence criterion and the principal component analysis. Finally, we derive a kernel normalized LMS algorithm based on the coherence criterion, which has linear computational complexity on the model order. Initial experimental results are presented on the performance of the algorithm.

In this contribution, we propose an efficient collaborative strategy for online change detection, in a distributed sensor network. The collaborative strategy ensures the efficiency and the robustness of the data processing, while limiting the required communication bandwidth. The observed systems are assumed to have each a finite set of states, including the abrupt change behavior. For each discrete state, an observed system is assumed to evolve according to a linear state-space model. An efficient Rao-Blackwellized collaborative particle filter (RB-CPF) is proposed to estimate the a posteriori probability of the discrete states of the observed systems. The Rao-Blackwellization procedure combines a sequential Monte Carlo filter with a bank of distributed Kalman filters. Only sufficient statistics are communicated between smart nodes. The spatio-temporal selection of the leader node and its collaborators is based on a trade-off between error propagation, communication constraints and information content complementarity of distributed data.

In this paper, we propose a method for selecting time-frequency distributions appropriate for given learning tasks. It is based on a criterion that has recently emerged from the machine learning literature: the kernel-target alignment. This criterion makes possible to find the optimal representation for a given classification problem without designing the classifier itself. Some possible applications of our framework are discussed. The first one provides a computationally attractive way of adjusting the free parameters of a distribution to improve classification performance. The second one is related to the selection, from a set of candidates, of the distribution that best facilitates a classification task. The last one addresses the problem of optimally combining several distributions

We take a new approach in nonlinear Wiener filtering. This approach is based on the theory of reproducing kernel Hilbert spaces (RKHS). By means of the well-known "kernel trick", the arithmetic operations are carried out in the initial space. We show that the solution is given by solving a linear system which may be ill-conditioned. To find a solution for such a problem, we resorted to a kernel principal component analysis (KPCA) method to perform dimensionality reduction in RKHS. A new reduced-rank Wiener filter based on KPCA is thus elaborated. It is applied on magnetoencephalographic (MEG) data for cardiac artifacts extraction.

We present an approach for extending the scope of standard covariant signal representations by means of implicit nonlinear mappings applied to signals via Mercer kernels. One of the advantages of using such kernels is that we do not need to exhibit the underlying nonlinear maps to be able to compute signal representations. This gives increased computational efficiency. Finally, conditions on kernels to preserve covariance properties are finally discussed.

Linear discriminant analysis (LDA) is a standard statistical tool for data analysis. Recently, a method called generalized discriminant analysis (GDA) has been developed to deal with nonlinear discriminant analysis using kernel functions. Difficulties for the GDA method can arise in the form of both computational complexity and storage requirements. We present a sequential algorithm for GDA avoiding these problems when one deals with large numbers of datapoints.

We propose an extension of the adaptive diffusion technique for time-frequency representations proposed by P. Goncalves and E. Payot (see Proc. IEEE Digital Sig. Process. Workshop, 1998). Instead of processing time-frequency representations and keeping the covariance with respect to time and frequency shifts untouched, our adaptive filtering technique processes time-scale representations of the affine class while preserving the covariance properties of such representations. In order to obtain representations with improved readability, we aim at removing cumbersome interference terms while not blurring the signal terms. We show that the association of a conductance function to our diffusion scheme can make significant improvement toward reaching this goal. Indeed, a conductance function provides a way to adapt locally the amount of smoothing to the representation. Note that the adaptivity of this affine technique is not based on any waveform dictionary, such as matching pursuit algorithms.

Support vector machines (SVMs) are the most well known nonlinear classifiers based on the Mercer kernel trick. They generally lead to very sparse solutions that ensure good generalization performance. Recently, S. Mika et al. (see Advances in Neural Networks for Signal Processing, p.41-8, 1999) proposed a new nonlinear technique based on the kernel trick and the Fisher criterion: the nonlinear kernel Fisher discriminant (KFD). Experiments show that KFD is competitive with SVM classifiers. Nevertheless, it can be shown that there exist distributions such that even though the two classes are linearly separable, the Fisher linear discriminant has an error probability close to 1. We propose an alternative strategy based on Mercer kernels that consists in picking the optimum nonlinear receiver in the sense of the best second-order criterion. We also present a strategy for controlling the complexity of the resulting classifier. Finally, we compare this new method with SVM and KFD.

Statistical detection theories lead to the fundamental result that the optimum test consists in comparing any strictly monotone function of the likelihood ratio with a threshold value. In many applications, implementing such a test may be impossible. Therefore, we are often led to consider a simpler procedure for designing detectors. In particular, we can use alternative design criteria such as second-order measures of quality. A necessary and sufficient condition is given for such criteria to guarantee the best solution in the sense of classical detection theories. This result is illustrated by discussing the relevance of well-known criteria.

Near-field microscopy has been developed to characterize optical properties of materials below the diffraction limit. It consists of scanning a probe, which can be of atomic dimensions, a few nanometers above a material surface, and detecting electromagnetic interaction. The resulting near-field optical images are conventionally analyzed by means of Fourier-based methods although these data are nonstationary. This observation suggests that time frequency analysis is potentially a powerful tool for extracting attributes such as local resolution of near-field optical microscopes. We use bilinear time-frequency distributions and their optimized version by the AOK procedure to analyze experimental near-field optical and magneto-optical raw images. We show that this approach allows local characterization of optical resolution and separation of relevant optical information from artifacts caused by the scanning probe recording process.

It was shown that information conveyed by the discrete Wigner distribution is highly redundant, linear relations connecting its time-frequency components. This means that every component of the discrete Wigner distribution can be expressed as a linear combination of the elements of a basis. This set of generators consists of particular time-frequency components of the distribution. However, up to now, this basis and the associated linear map that allows to entirely generate the representation have still not been characterized. This problem is addressed in the case of real-valued signals. Results are illustrated by means of computer simulations. Finally, some extensions are pointed out.

Detectors design requires substantial knowledge of the observation statistical properties, conditionally to the competing hypotheses H/sub 0/ and H/sub 1/. However, many applications involve complex phenomena, in which few a priori information is available. Several methods of designing time-frequency-based (TF) receivers from labeled training data have been proposed. Unfortunately, the resulting detectors have large biases, particularly when the number of training samples is small compared to the data dimension. The method presented is based on the structural risk minimization principle developed by Vapnik (1982), and consists in locally adjusting the resolution of TF-based detectors to the information carried by each TF location. This operation, controlled by a measure of H/sub 0/ and H/sub 1/ separability, allows one to advantageously reduce the receivers complexity and solutions bias. The resulting reduced-bias TF-based detectors can yield a substantial improvement in detection performance.