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

Underdetermined convolutive source separation using two dimensional non-negative factorization techniques

PhD ThesisIn this thesis the underdetermined audio source separation has been considered, that is, estimating the original audio sources from the observed mixture when the number of audio sources is greater than the number of channels. The separation has been carried out using two approaches; the blind audio source separation and the informed audio source separation. The blind audio source separation approach depends on the mixture signal only and it assumes that the separation has been accomplished without any prior information (or as little as possible) about the sources. The informed audio source separation uses the exemplar in addition to the mixture signal to emulate the targeted speech signal to be separated. Both approaches are based on the two dimensional factorization techniques that decompose the signal into two tensors that are convolved in both the temporal and spectral directions. Both approaches are applied on the convolutive mixture and the high-reverberant convolutive mixture which are more realistic than the instantaneous mixture. In this work a novel algorithm based on the nonnegative matrix factor two dimensional deconvolution (NMF2D) with adaptive sparsity has been proposed to separate the audio sources that have been mixed in an underdetermined convolutive mixture. Additionally, a novel Gamma Exponential Process has been proposed for estimating the convolutive parameters and number of components of the NMF2D/ NTF2D, and to initialize the NMF2D parameters. In addition, the effects of different window length have been investigated to determine the best fit model that suit the characteristics of the audio signal. Furthermore, a novel algorithm, namely the fusion K models of full-rank weighted nonnegative tensor factor two dimensional deconvolution (K-wNTF2D) has been proposed. The K-wNTF2D is developed for its ability in modelling both the spectral and temporal changes, and the spatial covariance matrix that addresses the high reverberation problem. Variable sparsity that derived from the Gibbs distribution is optimized under the Itakura-Saito divergence and adapted into the K-wNTF2D model. The tensors of this algorithm have been initialized by a novel initialization method, namely the SVD two-dimensional deconvolution (SVD2D). Finally, two novel informed source separation algorithms, namely, the semi-exemplar based algorithm and the exemplar-based algorithm, have been proposed. These algorithms based on the NMF2D model and the proposed two dimensional nonnegative matrix partial co-factorization (2DNMPCF) model. The idea of incorporating the exemplar is to inform the proposed separation algorithms about the targeted signal to be separated by initializing its parameters and guide the proposed separation algorithms. The adaptive sparsity is derived for both ii of the proposed algorithms. Also, a multistage of the proposed exemplar based algorithm has been proposed in order to further enhance the separation performance. Results have shown that the proposed separation algorithms are very promising, more flexible, and offer an alternative model to the conventional methods

Blind source separation using statistical nonnegative matrix factorization

PhD ThesisBlind Source Separation (BSS) attempts to automatically extract and track a signal of interest in real world scenarios with other signals present. BSS addresses the problem of recovering the original signals from an observed mixture without relying on training knowledge. This research studied three novel approaches for solving the BSS problem based on the extensions of non-negative matrix factorization model and the sparsity regularization methods. 1) A framework of amalgamating pruning and Bayesian regularized cluster nonnegative tensor factorization with Itakura-Saito divergence for separating sources mixed in a stereo channel format: The sparse regularization term was adaptively tuned using a hierarchical Bayesian approach to yield the desired sparse decomposition. The modified Gaussian prior was formulated to express the correlation between different basis vectors. This algorithm automatically detected the optimal number of latent components of the individual source. 2) Factorization for single-channel BSS which decomposes an information-bearing matrix into complex of factor matrices that represent the spectral dictionary and temporal codes: A variational Bayesian approach was developed for computing the sparsity parameters for optimizing the matrix factorization. This approach combined the advantages of both complex matrix factorization (CMF) and variational -sparse analysis. BLIND SOURCE SEPARATION USING STATISTICAL NONNEGATIVE MATRIX FACTORIZATION ii 3) An imitated-stereo mixture model developed by weighting and time-shifting the original single-channel mixture where source signals can be modelled by the AR processes. The proposed mixing mixture is analogous to a stereo signal created by two microphones with one being real and another virtual. The imitated-stereo mixture employed the nonnegative tensor factorization for separating the observed mixture. The separability analysis of the imitated-stereo mixture was derived using Wiener masking. All algorithms were tested with real audio signals. Performance of source separation was assessed by measuring the distortion between original source and the estimated one according to the signal-to-distortion (SDR) ratio. The experimental results demonstrate that the proposed uninformed audio separation algorithms have surpassed among the conventional BSS methods; i.e. IS-cNTF, SNMF and CMF methods, with average SDR improvement in the ranges from 2.6dB to 6.4dB per source.Payap Universit

Contributions to probabilistic non-negative matrix factorization - Maximum marginal likelihood estimation and Markovian temporal models

Non-negative matrix factorization (NMF) has become a popular dimensionality reductiontechnique, and has found applications in many different fields, such as audio signal processing,hyperspectral imaging, or recommender systems. In its simplest form, NMF aims at finding anapproximation of a non-negative data matrix (i.e., with non-negative entries) as the product of twonon-negative matrices, called the factors. One of these two matrices can be interpreted as adictionary of characteristic patterns of the data, and the other one as activation coefficients ofthese patterns. This low-rank approximation is traditionally retrieved by optimizing a measure of fitbetween the data matrix and its approximation. As it turns out, for many choices of measures of fit,the problem can be shown to be equivalent to the joint maximum likelihood estimation of thefactors under a certain statistical model describing the data. This leads us to an alternativeparadigm for NMF, where the learning task revolves around probabilistic models whoseobservation density is parametrized by the product of non-negative factors. This general framework, coined probabilistic NMF, encompasses many well-known latent variable models ofthe literature, such as models for count data. In this thesis, we consider specific probabilistic NMFmodels in which a prior distribution is assumed on the activation coefficients, but the dictionary remains a deterministic variable. The objective is then to maximize the marginal likelihood in thesesemi-Bayesian NMF models, i.e., the integrated joint likelihood over the activation coefficients.This amounts to learning the dictionary only; the activation coefficients may be inferred in asecond step if necessary. We proceed to study in greater depth the properties of this estimation process. In particular, two scenarios are considered. In the first one, we assume the independence of the activation coefficients sample-wise. Previous experimental work showed that dictionarieslearned with this approach exhibited a tendency to automatically regularize the number of components, a favorable property which was left unexplained. In the second one, we lift thisstandard assumption, and consider instead Markov structures to add statistical correlation to themodel, in order to better analyze temporal data

Segmentation of Infant Brain Using Nonnegative Matrix Factorization

This study develops an atlas-based automated framework for segmenting infants\u27 brains from magnetic resonance imaging (MRI). For the accurate segmentation of different structures of an infant\u27s brain at the isointense age (6-12 months), our framework integrates features of diffusion tensor imaging (DTI) (e.g., the fractional anisotropy (FA)). A brain diffusion tensor (DT) image and its region map are considered samples of a Markov-Gibbs random field (MGRF) that jointly models visual appearance, shape, and spatial homogeneity of a goal structure. The visual appearance is modeled with an empirical distribution of the probability of the DTI features, fused by their nonnegative matrix factorization (NMF) and allocation to data clusters. Projecting an initial high-dimensional feature space onto a low-dimensional space of the significant fused features with the NMF allows for better separation of the goal structure and its background. The cluster centers in the latter space are determined at the training stage by the K-means clustering. In order to adapt to large infant brain inhomogeneities and segment the brain images more accurately, appearance descriptors of both the first-order and second-order are taken into account in the fused NMF feature space. Additionally, a second-order MGRF model is used to describe the appearance based on the voxel intensities and their pairwise spatial dependencies. An adaptive shape prior that is spatially variant is constructed from a training set of co-aligned images, forming an atlas database. Moreover, the spatial homogeneity of the shape is described with a spatially uniform 3D MGRF of the second-order for region labels. In vivo experiments on nine infant datasets showed promising results in terms of the accuracy, which was computed using three metrics: the 95-percentile modified Hausdorff distance (MHD), the Dice similarity coefficient (DSC), and the absolute volume difference (AVD). Both the quantitative and visual assessments confirm that integrating the proposed NMF-fused DTI feature and intensity MGRF models of visual appearance, the adaptive shape prior, and the shape homogeneity MGRF model is promising in segmenting the infant brain DTI

From representation learning to thematic classification - Application to hierarchical analysis of hyperspectral images

Numerous frameworks have been developed in order to analyze the increasing amount of available image data. Among those methods, supervised classification has received considerable attention leading to the development of state-of-the-art classification methods. These methods aim at inferring the class of each observation given a specific class nomenclature by exploiting a set of labeled observations. Thanks to extensive research efforts of the community, classification methods have become very efficient. Nevertheless, the results of a classification remains a highlevel interpretation of the scene since it only gives a single class to summarize all information in a given pixel. Contrary to classification methods, representation learning methods are model-based approaches designed especially to handle high-dimensional data and extract meaningful latent variables. By using physic-based models, these methods allow the user to extract very meaningful variables and get a very detailed interpretation of the considered image. The main objective of this thesis is to develop a unified framework for classification and representation learning. These two methods provide complementary approaches allowing to address the problem using a hierarchical modeling approach. The representation learning approach is used to build a low-level model of the data whereas classification is used to incorporate supervised information and may be seen as a high-level interpretation of the data. Two different paradigms, namely Bayesian models and optimization approaches, are explored to set up this hierarchical model. The proposed models are then tested in the specific context of hyperspectral imaging where the representation learning task is specified as a spectral unmixing proble

An investigation of the utility of monaural sound source separation via nonnegative matrix factorization applied to acoustic echo and reverberation mitigation for hands-free telephony

In this thesis we investigate the applicability and utility of Monaural Sound Source Separation (MSSS) via Nonnegative Matrix Factorization (NMF) for various problems related to audio for hands-free telephony. We first investigate MSSS via NMF as an alternative acoustic echo reduction approach to existing approaches such as Acoustic Echo Cancellation (AEC). To this end, we present the single-channel acoustic echo problem as an MSSS problem, in which the objective is to extract the users signal from a mixture also containing acoustic echo and noise. To perform separation, NMF is used to decompose the near-end microphone signal onto the union of two nonnegative bases in the magnitude Short Time Fourier Transform domain. One of these bases is for the spectral energy of the acoustic echo signal, and is formed from the in- coming far-end user’s speech, while the other basis is for the spectral energy of the near-end speaker, and is trained with speech data a priori. In comparison to AEC, the speaker extraction approach obviates Double-Talk Detection (DTD), and is demonstrated to attain its maximal echo mitigation performance immediately upon initiation and to maintain that performance during and after room changes for similar computational requirements. Speaker extraction is also shown to introduce distortion of the near-end speech signal during double-talk, which is quantified by means of a speech distortion measure and compared to that of AEC. Subsequently, we address Double-Talk Detection (DTD) for block-based AEC algorithms. We propose a novel block-based DTD algorithm that uses the available signals and the estimate of the echo signal that is produced by NMF-based speaker extraction to compute a suitably normalized correlation-based decision variable, which is compared to a fixed threshold to decide on doubletalk. Using a standard evaluation technique, the proposed algorithm is shown to have comparable detection performance to an existing conventional block-based DTD algorithm. It is also demonstrated to inherit the room change insensitivity of speaker extraction, with the proposed DTD algorithm generating minimal false doubletalk indications upon initiation and in response to room changes in comparison to the existing conventional DTD. We also show that this property allows its paired AEC to converge at a rate close to the optimum. Another focus of this thesis is the problem of inverting a single measurement of a non- minimum phase Room Impulse Response (RIR). We describe the process by which percep- tually detrimental all-pass phase distortion arises in reverberant speech filtered by the inverse of the minimum phase component of the RIR; in short, such distortion arises from inverting the magnitude response of the high-Q maximum phase zeros of the RIR. We then propose two novel partial inversion schemes that precisely mitigate this distortion. One of these schemes employs NMF-based MSSS to separate the all-pass phase distortion from the target speech in the magnitude STFT domain, while the other approach modifies the inverse minimum phase filter such that the magnitude response of the maximum phase zeros of the RIR is not fully compensated. Subjective listening tests reveal that the proposed schemes generally produce better quality output speech than a comparable inversion technique

An investigation of the utility of monaural sound source separation via nonnegative matrix factorization applied to acoustic echo and reverberation mitigation for hands-free telephony

In this thesis we investigate the applicability and utility of Monaural Sound Source Separation (MSSS) via Nonnegative Matrix Factorization (NMF) for various problems related to audio for hands-free telephony. We first investigate MSSS via NMF as an alternative acoustic echo reduction approach to existing approaches such as Acoustic Echo Cancellation (AEC). To this end, we present the single-channel acoustic echo problem as an MSSS problem, in which the objective is to extract the users signal from a mixture also containing acoustic echo and noise. To perform separation, NMF is used to decompose the near-end microphone signal onto the union of two nonnegative bases in the magnitude Short Time Fourier Transform domain. One of these bases is for the spectral energy of the acoustic echo signal, and is formed from the in- coming far-end user’s speech, while the other basis is for the spectral energy of the near-end speaker, and is trained with speech data a priori. In comparison to AEC, the speaker extraction approach obviates Double-Talk Detection (DTD), and is demonstrated to attain its maximal echo mitigation performance immediately upon initiation and to maintain that performance during and after room changes for similar computational requirements. Speaker extraction is also shown to introduce distortion of the near-end speech signal during double-talk, which is quantified by means of a speech distortion measure and compared to that of AEC. Subsequently, we address Double-Talk Detection (DTD) for block-based AEC algorithms. We propose a novel block-based DTD algorithm that uses the available signals and the estimate of the echo signal that is produced by NMF-based speaker extraction to compute a suitably normalized correlation-based decision variable, which is compared to a fixed threshold to decide on doubletalk. Using a standard evaluation technique, the proposed algorithm is shown to have comparable detection performance to an existing conventional block-based DTD algorithm. It is also demonstrated to inherit the room change insensitivity of speaker extraction, with the proposed DTD algorithm generating minimal false doubletalk indications upon initiation and in response to room changes in comparison to the existing conventional DTD. We also show that this property allows its paired AEC to converge at a rate close to the optimum. Another focus of this thesis is the problem of inverting a single measurement of a non- minimum phase Room Impulse Response (RIR). We describe the process by which percep- tually detrimental all-pass phase distortion arises in reverberant speech filtered by the inverse of the minimum phase component of the RIR; in short, such distortion arises from inverting the magnitude response of the high-Q maximum phase zeros of the RIR. We then propose two novel partial inversion schemes that precisely mitigate this distortion. One of these schemes employs NMF-based MSSS to separate the all-pass phase distortion from the target speech in the magnitude STFT domain, while the other approach modifies the inverse minimum phase filter such that the magnitude response of the maximum phase zeros of the RIR is not fully compensated. Subjective listening tests reveal that the proposed schemes generally produce better quality output speech than a comparable inversion technique