Block Coordinate Descent for Sparse NMF

Nonnegative matrix factorization (NMF) has become a ubiquitous tool for data analysis. An important variant is the sparse NMF problem which arises when we explicitly require the learnt features to be sparse. A natural measure of sparsity is the L$_0$ norm, however its optimization is NP-hard. Mixed norms, such as L$_1$/L$_2$ measure, have been shown to model sparsity robustly, based on intuitive attributes that such measures need to satisfy. This is in contrast to computationally cheaper alternatives such as the plain L$_1$ norm. However, present algorithms designed for optimizing the mixed norm L$_1$/L$_2$ are slow and other formulations for sparse NMF have been proposed such as those based on L$_1$ and L$_0$ norms. Our proposed algorithm allows us to solve the mixed norm sparsity constraints while not sacrificing computation time. We present experimental evidence on real-world datasets that shows our new algorithm performs an order of magnitude faster compared to the current state-of-the-art solvers optimizing the mixed norm and is suitable for large-scale datasets

Single channel blind source separation

Single channel blind source separation (SCBSS) is an intensively researched field with numerous important applications. This research sets out to investigate the separation of monaural mixed audio recordings without relying on training knowledge. This research proposes a novel method based on variable regularised sparse nonnegative matrix factorization which decomposes an information-bearing matrix into two-dimensional convolution of factor matrices that represent the spectral basis and temporal code of the sources. In this work, a variational Bayesian approach has been developed for computing the sparsity parameters of the matrix factorization. To further improve the previous work, this research proposes a new method based on decomposing the mixture into a series of oscillatory components termed as the intrinsic mode functions (IMF). It is shown that IMFs have several desirable properties unique to SCBSS problem and how these properties can be advantaged to relax the constraints posed by the problem. In addition, this research develops a novel method for feature extraction using psycho-acoustic model. The monaural mixed signal is transformed to a cochleagram using the gammatone filterbank, whose bandwidths increase incrementally as the center frequency increases; thus resulting to non-uniform time-frequency (TF) resolution in the analysis of audio signal. Within this domain, a family of Itakura-Saito (IS) divergence based novel two-dimensional matrix factorization has been developed. The proposed matrix factorizations have the property of scale invariant which enables lower energy components in the cochleagram to be treated with equal importance as the high energy ones. Results show that all the developed algorithms presented in this thesis have outperformed conventional methods.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

A combined statistical and machine learning approach for single channel speech enhancement

University of Minnesota Ph.D. dissertation. May 2015. Major: Electrical Engineering. Advisor: Zhi-Quan Luo. 1 computer file (PDF); ix, 116 pages.In this thesis, we study the single-channel speech enhancement problem, the goal of which is to recover a desired speech from a monaural noisy recording. Speech enhancement is a focal issue to study due to is widespread usage in speech-related applications, such as hearing aids, mobile communications, and speech recognition systems. Three speech enhancement algorithms are proposed. In the rst algorithm, the Wiener Non-negative Matrix Factorization (WNMF), we combine the traditional Wiener ltering and the NMF into a single optimization problem. The objective is to minimize the mean square error, similar to Wiener ltering, and the constraints ensure the enhanced speeches are sparsely representable by the speech model learned by NMF. WNMF is novel because it utilizes NMF to capture the speech-specific structure while simultaneously leveraging it, thus improving the Wiener filtering. For the second algorithm, we propose a Sparse Gaussian Mixture Model (SGMM) that extends the traditional NMF and the Gaussian model. SGMM better captures the complex structure of speech than the traditional NMF. To control for overrepresentation of SGMM, we impose sparsity in order to ensure that only a few Gaussian models are simultaneously active. Computationally, it is achieved by using a l0-norm in the constraint of the maximum-likelihood (ML) estimation. The contribution of SGMM is in solving the constrained ML estimation, which has a closed form update even with the non-convex and non-smooth l0-norm constraint. The final algorithm proposed is the Sparse NMF + Deep Neural Network (SNMF-DNN), in which we treat speech enhancement as a supervised regression problem - the goal being to estimate the optimal enhancement gain. SNMF, originally designed for source separation, is used to extract features from the noisy recording. DNN is subsequently trained to estimate the optimal enhancement gain. Although our system is simple and does not require any sophisticated handcrafted features, we are able to demonstrate a substantial improvement in both intelligibility and enhanced speech quality

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

Audio source separation for music in low-latency and high-latency scenarios

Aquesta tesi proposa mètodes per tractar les limitacions de les tècniques existents de separació de fonts musicals en condicions de baixa i alta latència. En primer lloc, ens centrem en els mètodes amb un baix cost computacional i baixa latència. Proposem l'ús de la regularització de Tikhonov com a mètode de descomposició de l'espectre en el context de baixa latència. El comparem amb les tècniques existents en tasques d'estimació i seguiment dels tons, que són passos crucials en molts mètodes de separació. A continuació utilitzem i avaluem el mètode de descomposició de l'espectre en tasques de separació de veu cantada, baix i percussió. En segon lloc, proposem diversos mètodes d'alta latència que milloren la separació de la veu cantada, gràcies al modelatge de components específics, com la respiració i les consonants. Finalment, explorem l'ús de correlacions temporals i anotacions manuals per millorar la separació dels instruments de percussió i dels senyals musicals polifònics complexes.Esta tesis propone métodos para tratar las limitaciones de las técnicas existentes de separación de fuentes musicales en condiciones de baja y alta latencia. En primer lugar, nos centramos en los métodos con un bajo coste computacional y baja latencia. Proponemos el uso de la regularización de Tikhonov como método de descomposición del espectro en el contexto de baja latencia. Lo comparamos con las técnicas existentes en tareas de estimación y seguimiento de los tonos, que son pasos cruciales en muchos métodos de separación. A continuación utilizamos y evaluamos el método de descomposición del espectro en tareas de separación de voz cantada, bajo y percusión. En segundo lugar, proponemos varios métodos de alta latencia que mejoran la separación de la voz cantada, gracias al modelado de componentes que a menudo no se toman en cuenta, como la respiración y las consonantes. Finalmente, exploramos el uso de correlaciones temporales y anotaciones manuales para mejorar la separación de los instrumentos de percusión y señales musicales polifónicas complejas.This thesis proposes specific methods to address the limitations of current music source separation methods in low-latency and high-latency scenarios. First, we focus on methods with low computational cost and low latency. We propose the use of Tikhonov regularization as a method for spectrum decomposition in the low-latency context. We compare it to existing techniques in pitch estimation and tracking tasks, crucial steps in many separation methods. We then use the proposed spectrum decomposition method in low-latency separation tasks targeting singing voice, bass and drums. Second, we propose several high-latency methods that improve the separation of singing voice by modeling components that are often not accounted for, such as breathiness and consonants. Finally, we explore using temporal correlations and human annotations to enhance the separation of drums and complex polyphonic music signals

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

Single channel signal separation using pseudo-stereo model and time-freqency masking

PhD ThesisIn many practical applications, one sensor is only available to record a mixture of a number of signals. Single-channel blind signal separation (SCBSS) is the research topic that addresses the problem of recovering the original signals from the observed mixture without (or as little as possible) any prior knowledge of the signals. Given a single mixture, a new pseudo-stereo mixing model is developed. A “pseudo-stereo” mixture is formulated by weighting and time-shifting the original single-channel mixture. This creates an artificial resemblance of a stereo signal given by one location which results in the same time-delay but different attenuation of the source signals. The pseudo-stereo mixing model relaxes the underdetermined ill-conditions associated with monaural source separation and begets the advantage of the relationship of the signals between the readily observed mixture and the pseudo-stereo mixture. This research proposes three novel algorithms based on the pseudo-stereo mixing model and the binary time-frequency (TF) mask. Firstly, the proposed SCBSS algorithm estimates signals’ weighted coefficients from a ratio of the pseudo-stereo mixing model and then constructs a binary maximum likelihood TF masking for separating the observed mixture. Secondly, a mixture in noisy background environment is considered. Thus, a mixture enhancement algorithm has been developed and the proposed SCBSS algorithm is reformulated using an adaptive coefficients estimator. The adaptive coefficients estimator computes the signal characteristics for each time frame. This property is desirable for both speech and audio signals as they are aptly characterized as non-stationary AR processes. Finally, a multiple-time delay (MTD) pseudo-stereo SINGLE CHANNEL SIGNAL SEPARATION ii mixture is developed. The MTD mixture enhances the flexibility as well as the separability over the originally proposed pseudo-stereo mixing model. The separation algorithm of the MTD mixture has also been derived. Additionally, comparison analysis between the MTD mixture and the pseudo-stereo mixture has also been identified. All algorithms have been demonstrated by synthesized and real-audio signals. The performance of source separation has been assessed by measuring the distortion between original source and the estimated one according to the signal-to-distortion (SDR) ratio. Results show that all proposed SCBSS algorithms yield a significantly better separation performance with an average SDR improvement that ranges from 2.4dB to 5dB per source and they are computationally faster over the benchmarked algorithms.Payap University