Methods for learning adaptive dictionary in underdetermined speech separation

Underdetermined speech separation is a challenging problem that has been studied extensively in recent years. A promising method to this problem is based on the so-called sparse signal representation. Using this technique, we have recently developed a multi-stage algorithm, where the source signals are recovered using a pre-defined dictionary obtained by e.g. the discrete cosine transform (DCT). In this paper, instead of using the pre-defined dictionary, we present three methods for learning adaptive dictionaries for the reconstruction of source signals, and compare their performance with several state-of-the-art speech separation methods. © 2011 IEEE

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

Audio Source Separation Using Sparse Representations

This is the author's final version of the article, first published as A. Nesbit, M. G. Jafari, E. Vincent and M. D. Plumbley. Audio Source Separation Using Sparse Representations. In W. Wang (Ed), Machine Audition: Principles, Algorithms and Systems. Chapter 10, pp. 246-264. IGI Global, 2011. ISBN 978-1-61520-919-4. DOI: 10.4018/978-1-61520-919-4.ch010file: NesbitJafariVincentP11-audio.pdf:n\NesbitJafariVincentP11-audio.pdf:PDF owner: markp timestamp: 2011.02.04file: NesbitJafariVincentP11-audio.pdf:n\NesbitJafariVincentP11-audio.pdf:PDF owner: markp timestamp: 2011.02.04The authors address the problem of audio source separation, namely, the recovery of audio signals from recordings of mixtures of those signals. The sparse component analysis framework is a powerful method for achieving this. Sparse orthogonal transforms, in which only few transform coefficients differ significantly from zero, are developed; once the signal has been transformed, energy is apportioned from each transform coefficient to each estimated source, and, finally, the signal is reconstructed using the inverse transform. The overriding aim of this chapter is to demonstrate how this framework, as exemplified here by two different decomposition methods which adapt to the signal to represent it sparsely, can be used to solve different problems in different mixing scenarios. To address the instantaneous (neither delays nor echoes) and underdetermined (more sources than mixtures) mixing model, a lapped orthogonal transform is adapted to the signal by selecting a basis from a library of predetermined bases. This method is highly related to the windowing methods used in the MPEG audio coding framework. In considering the anechoic (delays but no echoes) and determined (equal number of sources and mixtures) mixing case, a greedy adaptive transform is used based on orthogonal basis functions that are learned from the observed data, instead of being selected from a predetermined library of bases. This is found to encode the signal characteristics, by introducing a feedback system between the bases and the observed data. Experiments on mixtures of speech and music signals demonstrate that these methods give good signal approximations and separation performance, and indicate promising directions for future research

Matrix of Polynomials Model based Polynomial Dictionary Learning Method for Acoustic Impulse Response Modeling

We study the problem of dictionary learning for signals that can be represented as polynomials or polynomial matrices, such as convolutive signals with time delays or acoustic impulse responses. Recently, we developed a method for polynomial dictionary learning based on the fact that a polynomial matrix can be expressed as a polynomial with matrix coefficients, where the coefficient of the polynomial at each time lag is a scalar matrix. However, a polynomial matrix can be also equally represented as a matrix with polynomial elements. In this paper, we develop an alternative method for learning a polynomial dictionary and a sparse representation method for polynomial signal reconstruction based on this model. The proposed methods can be used directly to operate on the polynomial matrix without having to access its coefficients matrices. We demonstrate the performance of the proposed method for acoustic impulse response modeling.Comment: 5 pages, 2 figure

Fast Dictionary Learning for Sparse Representations of Speech Signals

© 2011 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. Published version: IEEE Journal of Selected Topics in Signal Processing 5(5): 1025-1031, Sep 2011. DOI: 10.1109/JSTSP.2011.2157892

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