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

Statistical single channel source separation

PhD ThesisSingle channel source separation (SCSS) principally is one of the challenging fields in signal processing and has various significant applications. Unlike conventional SCSS methods which were based on linear instantaneous model, this research sets out to investigate the separation of single channel in two types of mixture which is nonlinear instantaneous mixture and linear convolutive mixture. For the nonlinear SCSS in instantaneous mixture, this research proposes a novel solution based on a two-stage process that consists of a Gaussianization transform which efficiently compensates for the nonlinear distortion follow by a maximum likelihood estimator to perform source separation. For linear SCSS in convolutive mixture, this research proposes new methods based on nonnegative matrix factorization which decomposes a mixture into two-dimensional convolution factor matrices that represent the spectral basis and temporal code. The proposed factorization considers the convolutive mixing in the decomposition by introducing frequency constrained parameters in the model. The method aims to separate the mixture into its constituent spectral-temporal source components while alleviating the effect of convolutive mixing. In addition, family of Itakura-Saito divergence has been developed as a cost function which brings the beneficial property of scale-invariant. Two new statistical techniques are proposed, namely, Expectation-Maximisation (EM) based algorithm framework which maximizes the log-likelihood of a mixed signals, and the maximum a posteriori approach which maximises the joint probability of a mixed signal using multiplicative update rules. To further improve this research work, a novel method that incorporates adaptive sparseness into the solution has been proposed to resolve the ambiguity and hence, improve the algorithm performance. The theoretical foundation of the proposed solutions has been rigorously developed and discussed in details. Results have concretely shown the effectiveness of all the proposed algorithms presented in this thesis in separating the mixed signals in single channel and have outperformed others available methods.Universiti Teknikal Malaysia Melaka(UTeM), Ministry of Higher Education of Malaysi

Enhanced IVA for audio separation in highly reverberant environments

Blind Audio Source Separation (BASS), inspired by the "cocktail-party problem", has been a leading research application for blind source separation (BSS). This thesis concerns the enhancement of frequency domain convolutive blind source separation (FDCBSS) techniques for audio separation in highly reverberant room environments. Independent component analysis (ICA) is a higher order statistics (HOS) approach commonly used in the BSS framework. When applied to audio FDCBSS, ICA based methods suffer from the permutation problem across the frequency bins of each source. Independent vector analysis (IVA) is an FD-BSS algorithm that theoretically solves the permutation problem by using a multivariate source prior, where the sources are considered to be random vectors. The algorithm allows independence between multivariate source signals, and retains dependency between the source signals within each source vector. The source prior adopted to model the nonlinear dependency structure within the source vectors is crucial to the separation performance of the IVA algorithm. The focus of this thesis is on improving the separation performance of the IVA algorithm in the application of BASS. An alternative multivariate Student's t distribution is proposed as the source prior for the batch IVA algorithm. A Student's t probability density function can better model certain frequency domain speech signals due to its tail dependency property. Then, the nonlinear score function, for the IVA, is derived from the proposed source prior. A novel energy driven mixed super Gaussian and Student's t source prior is proposed for the IVA and FastIVA algorithms. The Student's t distribution, in the mixed source prior, can model the high amplitude data points whereas the super Gaussian distribution can model the lower amplitude information in the speech signals. The ratio of both distributions can be adjusted according to the energy of the observed mixtures to adapt for different types of speech signals. A particular multivariate generalized Gaussian distribution is adopted as the source prior for the online IVA algorithm. The nonlinear score function derived from this proposed source prior contains fourth order relationships between different frequency bins, which provides a more informative and stronger dependency structure and thereby improves the separation performance. An adaptive learning scheme is developed to improve the performance of the online IVA algorithm. The scheme adjusts the learning rate as a function of proximity to the target solutions. The scheme is also accompanied with a novel switched source prior technique taking the best performance properties of the super Gaussian source prior and the generalized Gaussian source prior as the algorithm converges. The methods and techniques, proposed in this thesis, are evaluated with real speech source signals in different simulated and real reverberant acoustic environments. A variety of measures are used within the evaluation criteria of the various algorithms. The experimental results demonstrate improved performance of the proposed methods and their robustness in a wide range of situations

Enhanced independent vector analysis for audio separation in a room environment

Independent vector analysis (IVA) is studied as a frequency domain blind source separation method, which can theoretically avoid the permutation problem by retaining the dependency between different frequency bins of the same source vector while removing the dependency between different source vectors. This thesis focuses upon improving the performance of independent vector analysis when it is used to solve the audio separation problem in a room environment. A specific stability problem of IVA, i.e. the block permutation problem, is identified and analyzed. Then a robust IVA method is proposed to solve this problem by exploiting the phase continuity of the unmixing matrix. Moreover, an auxiliary function based IVA algorithm with an overlapped chain type source prior is proposed as well to mitigate this problem. Then an informed IVA scheme is proposed which combines the geometric information of the sources from video to solve the problem by providing an intelligent initialization for optimal convergence. The proposed informed IVA algorithm can also achieve a faster convergence in terms of iteration numbers and better separation performance. A pitch based evaluation method is defined to judge the separation performance objectively when the information describing the mixing matrix and sources is missing. In order to improve the separation performance of IVA, an appropriate multivariate source prior is needed to better preserve the dependency structure within the source vectors. A particular multivariate generalized Gaussian distribution is adopted as the source prior. The nonlinear score function derived from this proposed source prior contains the fourth order relationships between different frequency bins, which provides a more informative and stronger dependency structure compared with the original IVA algorithm and thereby improves the separation performance. Copula theory is a central tool to model the nonlinear dependency structure. The t copula is proposed to describe the dependency structure within the frequency domain speech signals due to its tail dependency property, which means if one variable has an extreme value, other variables are expected to have extreme values. A multivariate student's t distribution constructed by using a t copula with the univariate student's t marginal distribution is proposed as the source prior. Then the IVA algorithm with the proposed source prior is derived. The proposed algorithms are tested with real speech signals in different reverberant room environments both using modelled room impulse response and real room recordings. State-of-the-art criteria are used to evaluate the separation performance, and the experimental results confirm the advantage of the proposed algorithms

Characterization and processing of atrial fibrillation episodes by convolutive blind source separation algorithms and nonlinear analysis of spectral features

Las arritmias supraventriculares, en particular la fibrilación auricular (FA), son las enfermedades cardíacas más comúnmente encontradas en la práctica clínica rutinaria. La prevalencia de la FA es inferior al 1\% en la población menor de 60 años, pero aumenta de manera significativa a partir de los 70 años, acercándose al 10\% en los mayores de 80. El padecimiento de un episodio de FA sostenida, además de estar ligado a una mayor tasa de mortalidad, aumenta la probabilidad de sufrir tromboembolismo, infarto de miocardio y accidentes cerebrovasculares. Por otro lado, los episodios de FA paroxística, aquella que termina de manera espontánea, son los precursores de la FA sostenida, lo que suscita un alto interés entre la comunidad científica por conocer los mecanismos responsables de perpetuar o conducir a la terminación espontánea de los episodios de FA. El análisis del ECG de superficie es la técnica no invasiva más extendida en la diagnosis médica de las patologías cardíacas. Para utilizar el ECG como herramienta de estudio de la FA, se necesita separar la actividad auricular (AA) de las demás señales cardioeléctricas. En este sentido, las técnicas de Separación Ciega de Fuentes (BSS) son capaces de realizar un análisis estadístico multiderivación con el objetivo de recuperar un conjunto de fuentes cardioeléctricas independientes, entre las cuales se encuentra la AA. A la hora de abordar un problema de BSS, se hace necesario considerar un modelo de mezcla de las fuentes lo más ajustado posible a la realidad para poder desarrollar algoritmos matemáticos que lo resuelvan. Un modelo viable es aquel que supone mezclas lineales. Dentro del modelo de mezclas lineales se puede además hacer la restricción de que estas sean instantáneas. Este modelo de mezcla lineal instantánea es el utilizado en el Análisis de Componentes Independientes (ICA).Vayá Salort, C. (2010). Characterization and processing of atrial fibrillation episodes by convolutive blind source separation algorithms and nonlinear analysis of spectral features [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/8416Palanci

Enhanced independent vector analysis for speech separation in room environments

PhD ThesisThe human brain has the ability to focus on a desired sound source in the presence of several active sound sources. The machine based method lags behind in mimicking this particular skill of human beings. In the domain of digital signal processing this problem is termed as the cocktail party problem. This thesis thus aims to further the eld of acoustic source separation in the frequency domain based on exploiting source independence. The main challenge in such frequency domain algorithms is the permutation problem. Independent vector analysis (IVA) is a frequency domain blind source separation algorithm which can theoretically obviate the permutation problem by preserving the dependency structure within each source vector whilst eliminating the dependency between the frequency bins of di erent source vectors. This thesis in particular focuses on improving the separation performance of IVA algorithms which are used for frequency domain acoustic source separation in real room environments. The source prior is crucial to the separation performance of the IVA algorithm as it is used to model the nonlinear dependency structure within the source vectors. An alternative multivariate Student's t distribution source prior is proposed for the IVA algorithm as it is known to be well suited for modelling certain speech signals due to its heavy tail nature. Therefore the nonlinear score function that is derived from the proposed Student's t source prior can better model the dependency structure within the frequency bins and thereby enhance the separation performance and the convergence speed of the IVA and the Fast version of the IVA (FastIVA) algorithms. 4 5 A novel energy driven mixed Student's t and the original super Gaussian source prior is also proposed for the IVA algorithms. As speech signals can be composed of many high and low amplitude data points, therefore the Student's t distribution in the mixed source prior can account for the high amplitude data points whereas the original su- per Gaussian distribution can cater for the other information in the speech signals. Furthermore, the weight of both distributions in the mixed source prior can be ad- justed according to the energy of the observed mixtures. Therefore the mixed source prior adapts the measured signals and further enhances the performance of the IVA algorithm. A common approach within the IVA algorithm is to model di erent speech sources with an identical source prior, however this does not account for the unique characteristics of each speech signal. Therefore dependency modelling for di erent speech sources can be improved by modelling di erent speech sources with di erent source priors. Hence, the Student's t mixture model (SMM) is introduced as a source prior for the IVA algorithm. This new source prior can adapt according to the nature of di erent speech signals and the parameters for the proposed SMM source prior are estimated by deriving an e cient expectation maximization (EM) algorithm. As a result of this study, a novel EM framework for the IVA algorithm with the SMM as a source prior is proposed which is capable of separating the sources in an e cient manner. The proposed algorithms are tested in various realistic reverberant room environments with real speech signals. All the experiments and evaluation demonstrate the robustness and enhanced separation performance of the proposed algorithms