Structured Sparsity Models for Multiparty Speech Recovery from Reverberant Recordings

We tackle the multi-party speech recovery problem through modeling the acoustic of the reverberant chambers. Our approach exploits structured sparsity models to perform room modeling and speech recovery. We propose a scheme for characterizing the room acoustic from the unknown competing speech sources relying on localization of the early images of the speakers by sparse approximation of the spatial spectra of the virtual sources in a free-space model. The images are then clustered exploiting the low-rank structure of the spectro-temporal components belonging to each source. This enables us to identify the early support of the room impulse response function and its unique map to the room geometry. To further tackle the ambiguity of the reflection ratios, we propose a novel formulation of the reverberation model and estimate the absorption coefficients through a convex optimization exploiting joint sparsity model formulated upon spatio-spectral sparsity of concurrent speech representation. The acoustic parameters are then incorporated for separating individual speech signals through either structured sparse recovery or inverse filtering the acoustic channels. The experiments conducted on real data recordings demonstrate the effectiveness of the proposed approach for multi-party speech recovery and recognition.Comment: 31 page

Convexity in source separation: Models, geometry, and algorithms

Source separation or demixing is the process of extracting multiple components entangled within a signal. Contemporary signal processing presents a host of difficult source separation problems, from interference cancellation to background subtraction, blind deconvolution, and even dictionary learning. Despite the recent progress in each of these applications, advances in high-throughput sensor technology place demixing algorithms under pressure to accommodate extremely high-dimensional signals, separate an ever larger number of sources, and cope with more sophisticated signal and mixing models. These difficulties are exacerbated by the need for real-time action in automated decision-making systems. Recent advances in convex optimization provide a simple framework for efficiently solving numerous difficult demixing problems. This article provides an overview of the emerging field, explains the theory that governs the underlying procedures, and surveys algorithms that solve them efficiently. We aim to equip practitioners with a toolkit for constructing their own demixing algorithms that work, as well as concrete intuition for why they work

Sparsity and adaptivity for the blind separation of partially correlated sources

Blind source separation (BSS) is a very popular technique to analyze multichannel data. In this context, the data are modeled as the linear combination of sources to be retrieved. For that purpose, standard BSS methods all rely on some discrimination principle, whether it is statistical independence or morphological diversity, to distinguish between the sources. However, dealing with real-world data reveals that such assumptions are rarely valid in practice: the signals of interest are more likely partially correlated, which generally hampers the performances of standard BSS methods. In this article, we introduce a novel sparsity-enforcing BSS method coined Adaptive Morphological Component Analysis (AMCA), which is designed to retrieve sparse and partially correlated sources. More precisely, it makes profit of an adaptive re-weighting scheme to favor/penalize samples based on their level of correlation. Extensive numerical experiments have been carried out which show that the proposed method is robust to the partial correlation of sources while standard BSS techniques fail. The AMCA algorithm is evaluated in the field of astrophysics for the separation of physical components from microwave data.Comment: submitted to IEEE Transactions on signal processin

Joint Tensor Factorization and Outlying Slab Suppression with Applications

We consider factoring low-rank tensors in the presence of outlying slabs. This problem is important in practice, because data collected in many real-world applications, such as speech, fluorescence, and some social network data, fit this paradigm. Prior work tackles this problem by iteratively selecting a fixed number of slabs and fitting, a procedure which may not converge. We formulate this problem from a group-sparsity promoting point of view, and propose an alternating optimization framework to handle the corresponding $\ell_p$ ($0<p\leq 1$) minimization-based low-rank tensor factorization problem. The proposed algorithm features a similar per-iteration complexity as the plain trilinear alternating least squares (TALS) algorithm. Convergence of the proposed algorithm is also easy to analyze under the framework of alternating optimization and its variants. In addition, regularization and constraints can be easily incorporated to make use of \emph{a priori} information on the latent loading factors. Simulations and real data experiments on blind speech separation, fluorescence data analysis, and social network mining are used to showcase the effectiveness of the proposed algorithm

Reverberant Audio Source Separation via Sparse and Low-Rank Modeling

The performance of audio source separation from underdetermined convolutive mixture assuming known mixing filters can be significantly improved by using an analysis sparse prior optimized by a reweighting l1 scheme and a wideband datafidelity term, as demonstrated by a recent article. In this letter, we show that the performance can be improved even more significantly by exploiting a low-rank prior on the source spectrograms.We present a new algorithm to estimate the sources based on i) an analysis sparse prior, ii) a reweighting scheme so as to increase the sparsity, iii) a wideband data-fidelity term in a constrained form, and iv) a low-rank constraint on the source spectrograms. Evaluation on reverberant music mixtures shows that the resulting algorithm improves state-of-the-art methods by more than 2 dB of signal-to-distortion ratio

Underdetermined Separation of Speech Mixture Based on Sparse Bayesian Learning

This paper describes a novel algorithm for underdetermined speech separation problem based on compressed sensing which is an emerging technique for efficient data reconstruction. The proposed algorithm consists of two steps. The unknown mixing matrix is firstly estimated from the speech mixtures in the transform domain by using K-means clustering algorithm. In the second step, the speech sources are recovered based on an autocalibration sparse Bayesian learning algorithm for speech signal. Numerical experiments including the comparison with other sparse representation approaches are provided to show the achieved performance improvement

Bayesian orthogonal component analysis for sparse representation

This paper addresses the problem of identifying a lower dimensional space where observed data can be sparsely represented. This under-complete dictionary learning task can be formulated as a blind separation problem of sparse sources linearly mixed with an unknown orthogonal mixing matrix. This issue is formulated in a Bayesian framework. First, the unknown sparse sources are modeled as Bernoulli-Gaussian processes. To promote sparsity, a weighted mixture of an atom at zero and a Gaussian distribution is proposed as prior distribution for the unobserved sources. A non-informative prior distribution defined on an appropriate Stiefel manifold is elected for the mixing matrix. The Bayesian inference on the unknown parameters is conducted using a Markov chain Monte Carlo (MCMC) method. A partially collapsed Gibbs sampler is designed to generate samples asymptotically distributed according to the joint posterior distribution of the unknown model parameters and hyperparameters. These samples are then used to approximate the joint maximum a posteriori estimator of the sources and mixing matrix. Simulations conducted on synthetic data are reported to illustrate the performance of the method for recovering sparse representations. An application to sparse coding on under-complete dictionary is finally investigated.Comment: Revised version. Accepted to IEEE Trans. Signal Processin

System approach to robust acoustic echo cancellation through semi-blind source separation based on independent component analysis

We live in a dynamic world full of noises and interferences. The conventional acoustic echo cancellation (AEC) framework based on the least mean square (LMS) algorithm by itself lacks the ability to handle many secondary signals that interfere with the adaptive filtering process, e.g., local speech and background noise. In this dissertation, we build a foundation for what we refer to as the system approach to signal enhancement as we focus on the AEC problem. We first propose the residual echo enhancement (REE) technique that utilizes the error recovery nonlinearity (ERN) to "enhances" the filter estimation error prior to the filter adaptation. The single-channel AEC problem can be viewed as a special case of semi-blind source separation (SBSS) where one of the source signals is partially known, i.e., the far-end microphone signal that generates the near-end acoustic echo. SBSS optimized via independent component analysis (ICA) leads to the system combination of the LMS algorithm with the ERN that allows for continuous and stable adaptation even during double talk. Second, we extend the system perspective to the decorrelation problem for AEC, where we show that the REE procedure can be applied effectively in a multi-channel AEC (MCAEC) setting to indirectly assist the recovery of lost AEC performance due to inter-channel correlation, known generally as the "non-uniqueness" problem. We develop a novel, computationally efficient technique of frequency-domain resampling (FDR) that effectively alleviates the non-uniqueness problem directly while introducing minimal distortion to signal quality and statistics. We also apply the system approach to the multi-delay filter (MDF) that suffers from the inter-block correlation problem. Finally, we generalize the MCAEC problem in the SBSS framework and discuss many issues related to the implementation of an SBSS system. We propose a constrained batch-online implementation of SBSS that stabilizes the convergence behavior even in the worst case scenario of a single far-end talker along with the non-uniqueness condition on the far-end mixing system. The proposed techniques are developed from a pragmatic standpoint, motivated by real-world problems in acoustic and audio signal processing. Generalization of the orthogonality principle to the system level of an AEC problem allows us to relate AEC to source separation that seeks to maximize the independence, hence implicitly the orthogonality, not only between the error signal and the far-end signal, but rather, among all signals involved. The system approach, for which the REE paradigm is just one realization, enables the encompassing of many traditional signal enhancement techniques in analytically consistent yet practically effective manner for solving the enhancement problem in a very noisy and disruptive acoustic mixing environment.PhDCommittee Chair: Biing-Hwang Juang; Committee Member: Brani Vidakovic; Committee Member: David V. Anderson; Committee Member: Jeff S. Shamma; Committee Member: Xiaoli M

Tensor Decompositions for Signal Processing Applications From Two-way to Multiway Component Analysis

The widespread use of multi-sensor technology and the emergence of big datasets has highlighted the limitations of standard flat-view matrix models and the necessity to move towards more versatile data analysis tools. We show that higher-order tensors (i.e., multiway arrays) enable such a fundamental paradigm shift towards models that are essentially polynomial and whose uniqueness, unlike the matrix methods, is guaranteed under verymild and natural conditions. Benefiting fromthe power ofmultilinear algebra as theirmathematical backbone, data analysis techniques using tensor decompositions are shown to have great flexibility in the choice of constraints that match data properties, and to find more general latent components in the data than matrix-based methods. A comprehensive introduction to tensor decompositions is provided from a signal processing perspective, starting from the algebraic foundations, via basic Canonical Polyadic and Tucker models, through to advanced cause-effect and multi-view data analysis schemes. We show that tensor decompositions enable natural generalizations of some commonly used signal processing paradigms, such as canonical correlation and subspace techniques, signal separation, linear regression, feature extraction and classification. We also cover computational aspects, and point out how ideas from compressed sensing and scientific computing may be used for addressing the otherwise unmanageable storage and manipulation problems associated with big datasets. The concepts are supported by illustrative real world case studies illuminating the benefits of the tensor framework, as efficient and promising tools for modern signal processing, data analysis and machine learning applications; these benefits also extend to vector/matrix data through tensorization. Keywords: ICA, NMF, CPD, Tucker decomposition, HOSVD, tensor networks, Tensor Train