Computational Methods For Structured Sparse Component Analysis of Convolutive Speech Mixtures

We cast the under-determined convolutive speech separation as sparse approximation of the spatial spectra of the mixing sources. In this framework we compare and contrast the major practical algorithms for structured sparse recovery of speech signal. Specific attention is paid to characterization of the measurement matrix. We first propose how it can be identified using the Image model of multi-path effect where the acoustic parameters are estimated by localizing a speaker and its images in a free space model. We further study the circumstances in which the coherence of the projections induced by microphone array design tend to affect the recovery performance

An adaptive stereo basis method for convolutive blind audio source separation

NOTICE: this is the author’s version of a work that was accepted for publication in Neurocomputing. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in PUBLICATION, [71, 10-12, June 2008] DOI:neucom.2007.08.02

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

Hybrid model and structured sparsity for under-determined convolutive audio source separation

International audienceWe consider the problem of extracting the source signals from an under-determined convolutive mixture, assuming known filters. We start from its formulation as a minimization of a convex functional, combining a classical $\ell_2$ discrepancy term between the observed mixture and the one reconstructed from the estimated sources, and a sparse regularization term of source coefficients in a time-frequency domain. We then introduce a first kind of structure, using a hybrid model. Finally, we embed the previously introduced Windowed-Group-Lasso operator into the iterative thresholding/shrinkage algorithm, in order to take into account some structures inside each layers of time-frequency representations. Intensive numerical studies confirm the benefits of such an approach

Improved Convolutive and Under-Determined Blind Audio Source Separation with MRF Smoothing

Convolutive and under-determined blind audio source separation from noisy recordings is a challenging problem. Several computational strategies have been proposed to address this problem. This study is concerned with several modifications to the expectation-minimization-based algorithm, which iteratively estimates the mixing and source parameters. This strategy assumes that any entry in each source spectrogram is modeled using superimposed Gaussian components, which are mutually and individually independent across frequency and time bins. In our approach, we resolve this issue by considering a locally smooth temporal and frequency structure in the power source spectrograms. Local smoothness is enforced by incorporating a Gibbs prior in the complete data likelihood function, which models the interactions between neighboring spectrogram bins using a Markov random field. Simulations using audio files derived from stereo audio source separation evaluation campaign 2008 demonstrate high efficiency with the proposed improvement

Dictionary Learning for Sparse Representations With Applications to Blind Source Separation.

During the past decade, sparse representation has attracted much attention in the signal processing community. It aims to represent a signal as a linear combination of a small number of elementary signals called atoms. These atoms constitute a dictionary so that a signal can be expressed by the multiplication of the dictionary and a sparse coefficients vector. This leads to two main challenges that are studied in the literature, i.e. sparse coding (find the coding coefficients based on a given dictionary) and dictionary design (find an appropriate dictionary to fit the data). Dictionary design is the focus of this thesis. Traditionally, the signals can be decomposed by the predefined mathematical transform, such as discrete cosine transform (DCT), which forms the so-called analytical approach. In recent years, learning-based methods have been introduced to adapt the dictionary from a set of training data, leading to the technique of dictionary learning. Although this may involve a higher computational complexity, learned dictionaries have the potential to offer improved performance as compared with predefined dictionaries. Dictionary learning algorithm is often achieved by iteratively executing two operations: sparse approximation and dictionary update. We focus on the dictionary update step, where the dictionary is optimized with a given sparsity pattern. A novel framework is proposed to generalize benchmark mechanisms such as the method of optimal directions (MOD) and K-SVD where an arbitrary set of codewords and the corresponding sparse coefficients are simultaneously updated, hence the term simultaneous codeword optimization (SimCO). Moreover, its extended formulation ‘regularized SimCO’ mitigates the major bottleneck of dictionary update caused by the singular points. First and second order optimization procedures are designed to solve the primitive and regularized SimCO. In addition, a tree-structured multi-level representation of dictionary based on clustering is used to speed up the optimization process in the sparse coding stage. This novel dictionary learning algorithm is also applied for solving the underdetermined blind speech separation problem, leading to a multi-stage method, where the separation problem is reformulated as a sparse coding problem, with the dictionary being learned by an adaptive algorithm. Using mutual coherence and sparsity index, the performance of a variety of dictionaries for underdetermined speech separation is compared and analyzed, such as the dictionaries learned from speech mixtures and ground truth speech sources, as well as those predefined by mathematical transforms. Finally, we propose a new method for joint dictionary learning and source separation. Different from the multistage method, the proposed method can simultaneously estimate the mixing matrix, the dictionary and the sources in an alternating and blind manner. The advantages of all the proposed methods are demonstrated over the state-of-the-art methods using extensive numerical tests

Estimating number of speakers via density-based clustering and classification decision

It is crucial to robustly estimate the number of speakers (NoS) from the recorded audio mixtures in a reverberant environment. Some popular time-frequency (TF) methods approach this NoS estimation problem by assuming that only one of the speech components is active at each TF slot. However, this condition is violated in many scenarios where the speeches are convolved with long length of room impulse response coefficients, which causes degenerated performance of NoS estimation. To tackle this problem, a density-based clustering strategy is proposed to estimate NoS based on a local dominance assumption of speeches. Our method consists of several steps from clustering to classification of speakers with the consideration of robustness. First, the leading eigenvectors are extracted from the local covariance matrices of mixture TF components and ranked by the combination of local density and minimum distance to other leading eigenvectors with higher density. Second, a gap-based method is employed to determine the cluster centers from the ranked leading eigenvectors at each frequency bin. Third, a criterion based on averaged volume of cluster centers is proposed to select reliable clustering results at some frequency bins for the classification decision of NoS. The experiment results demonstrate that the proposed algorithm is superior to the existing methods in various reverberation cases with noise-free condition or noise condition