Testing blind separability of complex Gaussian mixtures

The separation of a complex mixture based solely on second-order statistics can be achieved using the Strong Uncorrelating Transform (SUT) if and only if all sources have distinct circularity coefficients. However, in most problems we do not know the circularity coefficients, and they must be estimated from observed data. In this work, we propose a detector, based on the generalized likelihood ratio test (GLRT), to test the separability of a complex Gaussian mixture using the SUT. For the separable case (distinct circularity coefficients), the maximum likelihood (ML) estimates are straightforward. On the other hand, for the non-separable case (at least one circularity coefficient has multiplicity greater than one), the ML estimates are much more difficult to obtain. To set the threshold, we exploit Wilks' theorem, which gives the asymptotic distribution of the GLRT under the null hypothesis. Finally, numerical simulations show the good performance of the proposed detector and the accuracy of Wilks' approximation

Single-Channel Signal Separation Using Spectral Basis Correlation with Sparse Nonnegative Tensor Factorization

A novel approach for solving the single-channel signal separation is presented the proposed sparse nonnegative tensor factorization under the framework of maximum a posteriori probability and adaptively fine-tuned using the hierarchical Bayesian approach with a new mixing mixture model. The mixing mixture is an analogy of a stereo signal concept given by one real and the other virtual microphones. An “imitated-stereo” mixture model is thus developed by weighting and time-shifting the original single-channel mixture. This leads to an artificial mixing system of dual channels which gives rise to a new form of spectral basis correlation diversity of the sources. Underlying all factorization algorithms is the principal difficulty in estimating the adequate number of latent components for each signal. This paper addresses these issues by developing a framework for pruning unnecessary components and incorporating a modified multivariate rectified Gaussian prior information into the spectral basis features. The parameters of the imitated-stereo model are estimated via the proposed sparse nonnegative tensor factorization with Itakura–Saito divergence. In addition, the separability conditions of the proposed mixture model are derived and demonstrated that the proposed method can separate real-time captured mixtures. Experimental testing on real audio sources has been conducted to verify the capability of the proposed method

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

Nonlinear unmixing of hyperspectral images: Models and algorithms

When considering the problem of unmixing hyperspectral images, most of the literature in the geoscience and image processing areas relies on the widely used linear mixing model (LMM). However, the LMM may be not valid, and other nonlinear models need to be considered, for instance, when there are multiscattering effects or intimate interactions. Consequently, over the last few years, several significant contributions have been proposed to overcome the limitations inherent in the LMM. In this article, we present an overview of recent advances in nonlinear unmixing modeling

Contributions to theory and algorithms of independent component analysis and signal separation

This thesis addresses the problem of blind signal separation (BSS) using independent component analysis (ICA). In blind signal separation, signals from multiple sources arrive simultaneously at a sensor array, so that each sensor array output contains a mixture of source signals. Sets of sensor outputs are processed to recover the source signals or to identify the mixing system. The term blind refers to the fact that no explicit knowledge of source signals or mixing system is available. Independent component analysis approach uses statistical independence of the source signals to solve the blind signal separation problems. Application domains for the material presented in this thesis include communications, biomedical, audio, image, and sensor array signal processing. In this thesis reliable algorithms for ICA-based blind source separation are developed. In blind source separation problem the goal is to recover all original source signals using the observed mixtures only. The objective is to develop algorithms that are either adaptive to unknown source distributions or do not need to utilize the source distribution information at all. Two parametric methods that can adapt to a wide class of source distributions including skewed distributions are proposed. Another nonparametric technique with desirable large sample properties is also proposed. It is based on characteristic functions and thereby avoids the need to model the source distributions. Experimental results showing reliable performance are given on all of the presented methods. In this thesis theoretical conditions under which instantaneous ICA-based blind signal processing problems can be solved are established. These results extend the celebrated results by Comon of the traditional linear real-valued model. The results are further extended to complex-valued signals and to nonlinear mixing systems. Conditions for identification, uniqueness, and separation are established both for real and complex-valued linear models, and for a proposed class of non-linear mixing systems.reviewe

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

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