Coherent change detection using paired synthetic aperture radar (SAR) images is often performed using a classical coherence estimator that is invariant to the true variances of the populations underlying each paired sample. While attractive, this estimator is biased and requires a significant number of samples to yield good performance. Increasing sample size often results in decreased image resolution. Thus, we propose the use of Berger's coherence estimate because, with the same number of pixels, the estimator effectively doubles the sample support without sacrificing resolution when the underlying population variances are equal or near equal. A potential drawback of this approach is that it is not invariant since its distribution depends on the pixel pair population variances. While Berger's estimator is inherently sensitive to the inequality of population variances, we propose a method of insulating the detector from this acuity. A two-stage change statistic is introduced to combine a noncoherent intensity change statistic given by the sample variance ratio, followed by the alternative Berger estimator, which assumes equal population variances. The first-stage detector identifies pixel pairs that have nonequal variances as changes caused by the displacement of sizeable object. The pixel pairs that are identified to have equal or near-equal variances in the first stage are used as an input to the second stage. The second-stage test uses the alternative Berger coherence estimator to detect subtle changes such as tire tracks and footprints. We show experimentally that the proposed method yields higher contrast SAR change detection images than the classical coherent change detector (state of the art), the alternative coherent change detector, and the intensity change detector. Experimental results are presented to show the effectiveness and robustness of the proposed algorithm for SAR change detection.

Coherent change detection using paired synthetic aperture radar images is performed using a classical coherence estimator applied under an assumption of complex Gaussian data. The magnitudes of the resulting coherence estimates are plotted as an image and used to gauge changes in the observed scene. In this paper, a two-stage change statistic that combines non-coherent and coherent change detection algorithms is proposed. In the first stage, a non-coherent intensity change detector is applied to test for changes caused by the displacement of a sizable object using the sample variance ratio test. The sample pairs that failed the first stage are used as an input to the second stage. The second stage test uses an alternative coherence estimator that assumes equal population variances, to detect subtle changes such as tire tracks and footprints. We show experimentally that the proposed method not only has a superior change detection performance over the classical coherent change detector, but also over either the non-coherent intensity change detector or the alternative coherent change detector, alone. Experimental results are presented to show the effectiveness and robustness of the proposed algorithm for SAR change detection.

As abstract representations of relational data, graphs and networks find wide use in a variety of fields, particularly when working in non-Euclidean spaces. Yet for graphs to be truly useful in in the context of signal processing, one ultimately must have access to flexible and tractable statistical models. One model currently in use is the Chung-Lu random graph model, in which edge probabilities are expressed in terms of a given expected degree sequence. An advantage of this model is that its parameters can be obtained via a simple, standard estimator. Although this estimator is used frequently, its statistical properties have not been fully studied. In this paper, we develop a central limit theory for a simplified version of the Chung-Lu parameter estimator. We then derive approximations for moments of the general estimator using the delta method, and confirm the effectiveness of these approximations through empirical examples.

In many applications, it is convenient to represent data as a graph, and often these datasets will be quite large. This paper presents an architecture for analyzing massive graphs, with a focus on signal processing applications such as modeling, filtering, and signal detection. We describe the architecture, which covers the entire processing chain, from data storage to graph construction to graph analysis and subgraph detection. The data are stored in a new format that allows easy extraction of graphs representing any relationship existing in the data. The principal analysis algorithm is the partial eigendecomposition of the modularity matrix, whose running time is discussed. A large document dataset is analyzed, and we present subgraphs that stand out in the principal eigenspace of the time-varying graphs, including behavior we regard as clutter as well as small, tightly-connected clusters that emerge over time.

n this article we derive an unbiased expression for the expected mean-squared error associated with continuously differentiable estimators of the noncentrality parameter of a chisquare random variable. We then consider the task of denoising squared-magnitude magnetic resonance image data, which are well modeled as independent noncentral chi-square random variables on two degrees of freedom. We consider two broad classes of linearly parameterized shrinkage estimators that can be optimized using our risk estimate, one in the general context of undecimated filterbank transforms, and another in the specific case of the unnormalized Haar wavelet transform. The resultant algorithms are computationally tractable and improve upon most state-of-the-art methods for both simulated and actual magnetic resonance image data.

The ubiquity of integrating detectors in imaging and other applications implies that a variety of real-world data are well modeled as Poisson random variables whose means are in turn proportional to an underlying vector-valued signal of interest. In this article, we first show how the so-called Skellam distribution arises from the fact that Haar wavelet and filterbank transform coefficients corresponding to measurements of this type are distributed as sums and differences of Poisson counts. We then provide two main theorems on Skellam shrinkage, one showing the near-optimality of shrinkage in the Bayesian setting and the other providing for unbiased risk estimation in a frequentist context. These results serve to yield new estimators in the Haar transform domain, including an unbiased risk estimate for shrinkage of Haar-Fisz variance-stabilized data, along with accompanying low-complexity algorithms for inference. We conclude with a simulation study demonstrating the efficacy of our Skellam shrinkage estimators both for the standard univariate wavelet test functions as well as a variety of test images taken from the image processing literature, confirming that they offer some performance improvements over existing alternatives.

Covariance matrix estimates are an essential part of many signal processing algorithms, and are often used to determine a low-dimensional principal subspace via their spectral decomposition. However, for sufficiently high-dimensional matrices exact eigen-analysis is computationally intractable, and in the case of limited data, sample eigenvalues and eigenvectors are known to be poor estimators of their true counterparts. To address these issues, we propose a covariance estimator that is computationally efficient while also performing shrinkage on the sample eigenvalues. Our approach is based on the Nyström method, which uses a data-dependent orthogonal projection to obtain a fast low-rank approximation of a large positive semidefinite matrix. We provide a theoretical analysis of the error properties of our estimator as well as empirical results.

Improving on recent work on joint source-filter analysis of speech waveforms, we explore improvements to an autoregressive model with exogenous inputs represented by flexible basis functions. Following a brief review of the maximum likelihood estimators of the model parameters, the Cramer-Rao bounds are derived to provide evidence for the challenging nature of estimating source and filter characteristics with overlapping spectra. Wavelet expansion of the exogenous inputs is employed, and the selection of an appropriate subset of wavelets is described as an online, signal-adaptive approach. Results from synthesized and real vowel analysis illustrate the promise of iterative wavelet shrinkage using soft and hard thresholding and an alternative regularization method.

In this article we develop Stein-type results for unbiased estimation of the risk associated with parametric estimators of the noncentrality parameter of chi-squared random variables on two degrees of freedom. These results allow for estimator adaptivity, and thus can be used to optimize the parameters of a broad class of typical denoising functions, subject only to weak smoothness assumptions. We show how to apply these results to the problem of enhancing magnitude magnetic resonance images, which are known to be corrupted by Rician noise. As an example, we propose a transform-domain point-wise estimator based on linear expansion of thresholds. Finally, we apply this estimator to synthetic and real image data in conjunction with the undecimated Haar wavelet transform, and conclude that it is able to outperform previous wavelet-based techniques and compares favorably with a more recent approach based on non-local means.

Latent variable models are frequently used to identify structure in dichotomous network data, in part because they give rise to a Bernoulli product likelihood that is both well understood and consistent with the notion of exchangeable random graphs. In this article we propose conservative confidence sets that hold with respect to these underlying Bernoulli parameters as a function of any given partition of network nodes, enabling us to assess estimates of \emph{residual} network structure, that is, structure that cannot be explained by known covariates and thus cannot be easily verified by manual inspection. We demonstrate the proposed methodology by analyzing student friendship networks from the National Longitudinal Survey of Adolescent Health that include race, gender, and school year as covariates. We employ a stochastic expectation-maximization algorithm to fit a logistic regression model that includes these explanatory variables as well as a latent stochastic blockmodel component and additional node-specific effects. Although maximum-likelihood estimates do not appear consistent in this context, we are able to evaluate confidence sets as a function of different blockmodel partitions, which enables us to qualitatively assess the significance of estimated residual network structure relative to a baseline, which models covariates but lacks block structure.

This paper develops a general detection theory for speech analysis based on time-varying autoregressive models, which themselves generalize the classical linear predictive speech analysis framework. This theory leads to a computationally efficient decision-theoretic procedure that may be applied to detect the presence of vocal tract variation in speech waveform data. A corresponding generalized likelihood ratio test is derived and studied both empirically for short data records, using formant-like synthetic examples, and asymptotically, leading to constant false alarm rate hypothesis tests for changes in vocal tract configuration. Two in-depth case studies then serve to illustrate the practical efficacy of this procedure across different time scales of speech dynamics: first, the detection of formant changes on the scale of tens of milliseconds of data, and second, the identification of glottal opening and closing instants on time scales below ten milliseconds.

This paper describes a series of new results outlining equivalences between certain “rewirings” of filterbank system block diagrams, and the corresponding actions of convolution, modulation, and downsampling operators. This gives rise to a general framework of reverse-order and convolution subband structures in filterbank transforms, which we show to be well suited to the analysis of filterbank coefficients arising from subsampled or multiplexed signals. These results thus provide a means to understand time-localized aliasing and modulation properties of such signals and their subband representations - notions that are notably absent from the global viewpoint afforded by Fourier analysis - as well as signal recovery from sampled sequences based on their filterbank characterizations. The utility of filterbank rewirings is demonstrated by the closed-form analysis of signals subject to degradations such as missing data, spatially or temporally multiplexed data acquisition, or signal-dependent noise, the likes of which are often encountered in practical signal processing applications.

Spectral methods requiring the computation of eigenvalues and eigenvectors of a positive definite matrix are an essential part of signal processing. However, for sufficiently high-dimensional data sets, the eigenvalue problem cannot be solved without approximate methods. We examine a technique for approximate spectral analysis and low-rank matrix reconstruction known as the Nyström method, which recasts the eigendecomposition of large matrices as a subset selection problem. In particular, we focus on the performance of the Nyström method when used to approximate random matrices from the Wishart ensemble. We provide statistical results for the approximation error, as well as an experimental analysis of various subset sampling techniques.

It is well known that the classical linear predictive model for speech fails to take into account the quasi-periodic nature of the glottal flow typical of voiced speech. In this article we describe how to incorporate an estimate of the glottal flow directly into the traditional linear prediction framework, through the use of flexible basis function expansions that admit efficient estimation procedures. As we show, this not only allows for improved estimation of vocal tract transfer function parameters in a manner that is robust to pitch variation, but also precludes the need for nonlinear optimization procedures typically required in glottal waveform estimation. We illustrate our approach with experiments using synthesized and real speech waveforms, and show how it may be used to directly estimate the relative degree of voicing and aspiration present in a given utterance.

Graphs are canonical examples of high-dimensional non-Euclidean data sets, and are emerging as a common data structure in many fields. While there are many algorithms to analyze such data, a signal processing theory for evaluating these techniques akin to detection and estimation in the classical Euclidean setting remains to be developed. In this paper we show the conceptual advantages gained by formulating graph analysis problems in a signal processing framework by way of a practical example: detection of a subgraph embedded in a background graph. We describe an approach based on detection theory and provide empirical results indicating that the test statistic proposed has reasonable power to detect dense subgraphs in large random graphs.

Recent advances in spatio-spectral sampling and panchromatic pixels have contributed to increased spatial resolution and enhanced noise performance. As such, it is necessary to consider the universality of demosaicking design principles-instead of CFA-specific optimization for signal recovery. In this article, we introduce a new universal demosaicking method that draws from the lessons learned in Bayer demosaicking designs, but can be applied to arbitrary array patterns. We recast the data-dependence of Bayer demosaicking as a parsimonious reconstruction of the underlying image signal that is inherently sparse in some representation. Using properties of filterbanks, we generalize this principle to yield a nonlinear recovery method that is consistent with the state-of-the-art Bayer demosaicking methods.

A common technique used to acquire high dynamic range image data is that of exposure bracketing-short exposure times are required to capture bright regions of the image without saturation, whereas long exposure times are needed to capture darker image regions effectively. This article describes how to take into account the statistics of the photon arrival process to derive optimal exposure control for maximizing signal recoverability in high dynamic range imaging.

Many classes of image data span a low dimensional nonlinear space embedded in the natural high dimensional image space. We adopt and generalize a recently proposed dimensionality reduction method for computing approximate regularized Laplacian eigenmaps on large data sets and examine for the first time its application in a variety of image analysis examples. These experiments demonstrate the potential of regularized Laplacian eigenmaps in developing new learning algorithms and improving performance of existing systems.

When working with network datasets, the theoretical framework of detection theory for Euclidean vector spaces no longer applies. Nevertheless, it is desirable to determine the detectability of small, anomalous graphs embedded into background networks with known statistical properties. Casting the problem of subgraph detection in a signal processing context, this article provides a framework and empirical results that elucidate a detection theory" for graph-valued data. Its focus is the detection of anomalies in unweighted, undirected graphs through L1 properties of the eigenvectors of the graph’s so-called modularity matrix. This metric is observed to have relatively low variance for certain categories of randomly-generated graphs, and to reveal the presence of an anomalous subgraph with reasonable reliability when the anomaly is not well-correlated with stronger portions of the background graph. An analysis of subgraphs in real network datasets confirms the efficacy of this approach."

It is well known that the performance of adaptive beamformers may degrade in the presence of steering errors. In this context, diagonal loading is one of the most popular methods used for robust beamforming, and can be derived from an l2norm constraint. Equivalently, this method assumes a white Gaussian prior on the beamforming vector, similar to ridge regression in statistical point of view. By changing the loading level, which can be treated as confidence of this prior distribution, a trade-off between robustness and adaptivity is obtained. In this article, we generalize this approach via Ipnorms. We find that under different settings, it is not optimal to set p = 2 compared with other p ¿ with the loading level chosen in such a way that the prior variance is maintained. We derive an iterative form to calculate the beamformer, as well as an iterative online implementation. Convergence is observed in empirical simulations and discussed under certain conditions.

In this paper we propose a nonparametric hypothesis test for stationarity based on local Fourier analysis. We employ a test statistic that measures the variation of time-localized estimates of the power spectral density of an observed random process. For the case of a white Gaussian noise process, we characterize the asymptotic distribution of this statistic under the null hypothesis of stationarity, and use it to directly set test thresholds corresponding to constant false alarm rates. For other cases, we introduce a simple procedure to simulate from the null distribution of interest. After validating the procedure on synthetic examples, we demonstrate one potential use for the test as a method of obtaining a signal-adaptive means of local Fourier analysis and corresponding signal enhancement scheme.

Owing to the stochastic nature of discrete processes such as photon counts in imaging, a variety of real-world data are well modeled as Poisson random variables whose means are in turn proportional to an underlying vector-valued signal of interest. Certain wavelet and filterbank transform coefficients corresponding to measurements of this type are distributed as sums and differences of Poisson counts, taking in the simplest case the so-called Skellam distribution. We show that a Skellam mean estimator provides a Poisson intensity estimation method based on shrinkage of filterbank coefficients, and a means of estimating the risk of any Skellam mean estimator is derived in closed form under a frequentist model.

This paper addresses selecting between candidate pronunciations for out-of-vocabulary words in speech processing tasks. We introduce a simple, unsupervised method that outperforms the conventional supervised method of forced alignment with a reference. The success of this method is independently demonstrated using three metrics from large-scale speech tasks: word error rates for large vocabulary continuous speech recognition, decision error tradeoff curves for spoken term detection, and phone error rates compared to a handcrafted pronunciation lexicon. The experiments were conducted using state-of-the-art recognition, indexing, and retrieval systems. The results were compared across many terms, hundreds of hours of speech, and well known data sets.

In this article we address the issue of denoising photon-limited image data by deriving new and efficient multivariate Bayesian estimators that approximate the conditional expectation of Haar wavelet and filterbank transform coefficients of Poisson data - coefficients that take the so-called Skellam distribution. We show that in this setting, the posterior mean under a Bayesian model forms the solution to a linear differential equation, owing in part to the recursive property of the Skellam distribution. We then propose a practical approach to solve - approximately - this differential equation, and arrive at a near mean-square-optimal Skellam mean estimator that is both computationally efficient and amenable to an empirical Bayes approach. We then derive three approaches to shrinkage based on smoothing the marginal likelihood of the data, and demonstrate their superior performance relative to state-of-the-art approaches for both natural test images and examples from computed tomography scans.

In this paper we develop hypothesis tests for speech waveform nonstationarity based on time-varying autoregressive models, and demonstrate their efficacy in speech analysis tasks at both segmental and sub-segmental scales. Key to the successful synthesis of these ideas is our employment of a generalized likelihood ratio testing framework tailored to autoregressive coefficient evolutions suitable for speech. After evaluating our framework on speech-like synthetic signals, we present preliminary results for two distinct analysis tasks using speech waveform data. At the segmental level, we develop an adaptive short-time segmentation scheme and evaluate it on whispered speech recordings, while at the sub-segmental level, we address the problem of detecting the glottal flow closed phase. Results show that our hypothesis testing framework can reliably detect changes in the vocal tract parameters across multiple scales, thereby underscoring its broad applicability to speech analysis. Index Terms: TVAR models, hypothesis testing, GLRT, adaptive speech segmentation, glottal flow analysis

We present a sequence of empirical methods to determine the number of sources in musical signals when only one channel is available. Rather than building evidence through a statistical model-based approach, we instead develop a carefully tuned and tested two-stage system that is able to function effectively even in extremely underdetermined conditions. A first, more general procedure accurately determines the number of sources that are not closely harmonically related, while the second stage subsequently detects the presence of any remaining sources. The main advantages of this approach lie in its avoidance of the restrictive assumptions that can accompany more complex models in underdetermined cases, and in its use of robust heuristics to identify and exploit as much source-specific information as possible. These features make it possible to address even the most difficult cases in which sources are closely harmonically related, or even share the same fundamental frequency. We report an overall accuracy of nearly 80% on average, using both random and harmonically related mixtures of one to six sources taken from two widely available musical instrument databases-a notable result that demonstrates both the efficiency and the robustness of our proposed procedure.

The ubiquity of digital color image content continues to raise consumer technological awareness and expectations, and places a greater demand than ever on algorithms that support color image acquisition for mobile devices. In this paper we consider the key signal processing challenges to advancing the digital camera pipeline for mobile multimedia, with a particular focus on advances that have the potential to enhance image quality and reduce overall cost and power consumption. We first examine key technical challenges to pipeline design presented by demands such as shrinking device footprints, increasing throughput, and enhancing color fidelity. We then describe a recently introduced analytical framework based on spatio-spectral sampling for color image acquisition, and discuss its potential implications for quality and cost improvements. We then describe a number of resolution-distortion trade-offs, in particular noise processes and crosstalk, and show via simulation how a spatio-spectral acquisition framework helps to pinpoint aspects of pipeline design that can enhance computational efficiency and performance simultaneously.

In this paper we present a new adaptive short-time Fourier analysis-synthesis scheme and demonstrate its efficacy in speech enhancement. While a number of adaptive analyses have previously been proposed to overcome the limitations of fixed-resolution schemes, we propose here a modified overlap-add procedure that enables efficient resynthesis. Our adaptation scheme extends earlier work using local measures of time-frequency concentration, and is applicable to power spectral density estimation for the case of noisy speech. We provide evidence of increased gains in signal-to-noise ratios for synthetic signals as well as empirical evidence of reduced musical noise based on expert listening tests for voiced and phonetically balanced utterances observed in noise, relative to a standard baseline speech enhancement system whose time-frequency resolution is fixed.

In digital imaging applications, data are typically obtained via a spatial subsampling procedure implemented as a color filter array-a physical construction whereby only a single color value is measured at each pixel location. Owing to the growing ubiquity of color imaging and display devices, much recent work has focused on the implications of such arrays for subsequent digital processing, including in particular the canonical demosaicking task of reconstructing a full color image from spatially subsampled and incomplete color data acquired under a particular choice of array pattern. In contrast to the majority of the demosaicking literature, we consider here the problem of color filter array design and its implications for spatial reconstruction quality. We pose this problem formally as one of simultaneously maximizing the spectral radii of luminance and chrominance channels subject to perfect reconstruction, and-after proving sub-optimality of a wide class of existing array patterns-provide a constructive method for its solution that yields robust, new panchromatic designs implementable as subtractive colors. Empirical evaluations on multiple color image test sets support our theoretical results, and indicate the potential of these patterns to increase spatial resolution for fixed sensor size, and to contribute to improved reconstruction fidelity as well as significantly reduced hardware complexity.

This paper presents a new approach to demosaicing of spatially sampled image data observed through a color filter array, in which properties of Smith-Barnwell filterbanks are employed to exploit the correlation of color components in order to reconstruct a subsampled image. The method is shown to be amenable to wavelet-domain denoising prior to demosaicing, and a general framework for applying existing image denoising algorithms to color filter array data is also described. Results indicate that the proposed method performs on a par with the state of the art for far lower computational cost, and provides a versatile, effective, and low-complexity solution to the problem of interpolating color filter array data observed in noise.

This paper addresses the important and ubiquitous problem of sampling from a product of Gaussian mixtures. An exact solution is often computationally infeasible, thus motivating the development of efficient sampling schemes. However, naive Markov chain Monte Carlo algorithms perform poorly in cases where the product mixture is highly multi-modal. In this paper we follow the trend of recent work utilizing multi-scale sampling methods, and propose two new multi-scale Markov chain Monte Carlo algorithms based on simulated and parallel tempering. Empirical results indicate that for the same computational budget, this class of methods can improve performance in cases with widely separated modes.

In digital imaging applications, data are typically obtained via a spatial subsampling procedure implemented as a color filter array - a physical construction whereby only a single color representative is measured at each pixel location. Owing to the growing ubiquity of color imaging and display devices, much recent work has focused on the interplay between color filter array design and subsequent digital processing, including in particular the canonical spatio-chromatic reconstruction task known as demosaicking. Here we consider the problem of improved color filter array design, leading to enhanced image fidelity. We first analyze the limitations of the well-known Bayer pattern, currently most popular in industry. We then propose a framework for designing rectangular color filter arrays amenable to efficient and completely linear reconstruction, and provide examples of new patterns that enable improvements in reconstruction quality.

In digital image display devices, data are typically presented via a spatial subsampling procedure implemented as a color filter array, a physical construction whereby each light emitting element controls the intensity level of only a single color. In this paper, we examine the problem of color filter array design with respect to spatial resolution and human vision; in doing so we quantify the fundamental limitations of existing designs by explicitly considering the spectral wavelength representation induced by the choice of array pattern, and propose a framework for designing and analyzing alternative patterns that minimize aliasing. An empirical evaluations on standard color test image confirms our theoretical results, and indicates the potential of these patterns to significantly increase spatial resolution while at the same time improving color image fidelity.

This paper addresses modeling and inference for localized calcium release events observed in cardiac muscle tissue known as sparks, a recently discovered and little-understood phenomenon thought to be central to cardiac pathophysiology and hence of much scientific interest. In contrast to earlier algorithms proposed for studying sparks observed via confocal line-scan data, we consider here a model for the spatiotemporal spark process in unpaced cardiac myocytes observed in vitro via fluorescence video microscopy. In particular, we focus on parametric modeling of the spark process, leading naturally to a framework for joint localization and estimation of spark events and their parameters in space and time, along with the ability to quantify the uncertainty of our resulting inference. We show that for simulated sparks derived from real micropatterned cardiac myocyte data, and for which ground truth is known, our method significantly outperforms a video-adapted version of the most popular spark localization method currently in use in the cardiac biophysics community. Importantly, the framework we propose extends naturally to other other applications of video microscopy, and also allows for subsequent refinement of both the models and fitting procedures described here.

Vocal tract resonances play a central role in the perception and analysis of speech. Here we consider the canonical task of estimating such resonances from an observed acoustic waveform, and formulate it as a statistical model-based tracking problem. In this vein, Deng and colleagues recently showed that a robust linearization of the formant-to-cepstrum map enables the effective use of a Kalman filtering framework. We extend this model both to account for the uncertainty of speech presence by way of a censored likelihood formulation, as well as to explicitly model formant cross-correlation via a vector autoregression, and in doing so retain a conditionally linear and Gaussian framework amenable to efficient estimation schemes. We provide evaluations using a recently introduced public database of formant trajectories, for which results indicate improvements from twenty to over 30 % per formant in terms of root mean square error, relative to a contemporary benchmark formant analysis tool. Index Terms: formant tracking, speech analysis, Kalman filtering, vocal tract resonances, system identification

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 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.

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.

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.