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

A machine learning approach to nonlinear modal analysis

Although linear modal analysis has proved itself to be the method of choice for the analysis of linear dynamic structures, its extension to nonlinear structures has proved to be a problem. A number of competing viewpoints on nonlinear modal analysis have emerged, each of which preserves a subset of the properties of the original linear theory. From the geometrical point of view, one can argue that the invariant manifold approach of Shaw and Pierre is the most natural generalisation. However, the Shaw–Pierre approach is rather demanding technically, depending as it does on the analytical construction of a mapping between spaces, which maps physical coordinates into invariant manifolds spanned by independent subsets of variables. The objective of the current paper is to demonstrate a data-based approach motivated by Shaw–Pierre method which exploits the idea of statistical independence to optimise a parametric form of the mapping. The approach can also be regarded as a generalisation of the Principal Orthogonal Decomposition (POD). A machine learning approach to inversion of the modal transformation is presented, based on the use of Gaussian processes, and this is equivalent to a nonlinear form of modal superposition. However, it is shown that issues can arise if the forward transformation is a polynomial and can thus have a multi-valued inverse. The overall approach is demonstrated using a number of case studies based on both simulated and experimental data

Flexible methods for blind separation of complex signals

One of the main matter in Blind Source Separation (BSS) performed with a neural network approach is the choice of the nonlinear activation function (AF). In fact if the shape of the activation function is chosen as the cumulative density function (c.d.f.) of the original source the problem is solved. For this scope in this thesis a flexible approach is introduced and the shape of the activation functions is changed during the learning process using the so-called “spline functions”. The problem is complicated in the case of separation of complex sources where there is the problem of the dichotomy between analyticity and boundedness of the complex activation functions. The problem is solved introducing the “splitting function” model as activation function. The “splitting function” is a couple of “spline function” which wind off the real and the imaginary part of the complex activation function, each of one depending from the real and imaginary variable. A more realistic model is the “generalized splitting function”, which is formed by a couple of two bi-dimensional functions (surfaces), one for the real and one for the imaginary part of the complex function, each depending by both the real and imaginary part of the complex variable. Unfortunately the linear environment is unrealistic in many practical applications. In this way there is the need of extending BSS problem in the nonlinear environment: in this case both the activation function than the nonlinear distorting function are realized by the “splitting function” made of “spline function”. The complex and instantaneous separation in linear and nonlinear environment allow us to perform a complex-valued extension of the well-known INFOMAX algorithm in several practical situations, such as convolutive mixtures, fMRI signal analysis and bandpass signal transmission. In addition advanced characteristics on the proposed approach are introduced and deeply described. First of all it is shows as splines are universal nonlinear functions for BSS problem: they are able to perform separation in anyway. Then it is analyzed as the “splitting solution” allows the algorithm to obtain a phase recovery: usually there is a phase ambiguity. Finally a Cramér-Rao lower bound for ICA is discussed. Several experimental results, tested by different objective indexes, show the effectiveness of the proposed approaches

Flexible methods for blind separation of complex signals

One of the main matter in Blind Source Separation (BSS) performed with a neural network approach is the choice of the nonlinear activation function (AF). In fact if the shape of the activation function is chosen as the cumulative density function (c.d.f.) of the original source the problem is solved. For this scope in this thesis a flexible approach is introduced and the shape of the activation functions is changed during the learning process using the so-called “spline functions”. The problem is complicated in the case of separation of complex sources where there is the problem of the dichotomy between analyticity and boundedness of the complex activation functions. The problem is solved introducing the “splitting function” model as activation function. The “splitting function” is a couple of “spline function” which wind off the real and the imaginary part of the complex activation function, each of one depending from the real and imaginary variable. A more realistic model is the “generalized splitting function”, which is formed by a couple of two bi-dimensional functions (surfaces), one for the real and one for the imaginary part of the complex function, each depending by both the real and imaginary part of the complex variable. Unfortunately the linear environment is unrealistic in many practical applications. In this way there is the need of extending BSS problem in the nonlinear environment: in this case both the activation function than the nonlinear distorting function are realized by the “splitting function” made of “spline function”. The complex and instantaneous separation in linear and nonlinear environment allow us to perform a complex-valued extension of the well-known INFOMAX algorithm in several practical situations, such as convolutive mixtures, fMRI signal analysis and bandpass signal transmission. In addition advanced characteristics on the proposed approach are introduced and deeply described. First of all it is shows as splines are universal nonlinear functions for BSS problem: they are able to perform separation in anyway. Then it is analyzed as the “splitting solution” allows the algorithm to obtain a phase recovery: usually there is a phase ambiguity. Finally a Cramér-Rao lower bound for ICA is discussed. Several experimental results, tested by different objective indexes, show the effectiveness of the proposed approaches

Noiseless Independent Factor Analysis with mixing constraints in a semi-supervised framework. Application to railway device fault diagnosis.

International audienceIn Independent Factor Analysis (IFA), latent components (or sources) are recovered from only their linear observed mixtures. Both the mixing process and the source densities (that are assumed to be gener- ated according to mixtures of Gaussians) are learned from observed data. This paper investigates the possibility of estimating the IFA model in its noiseless setting when two kinds of prior information are incorporated: constraints on the mixing process and partial knowledge on the cluster membership of some examples. Semi-supervised or partially supervised learning frameworks can thus be handled. These two proposals have been initially motivated by a real-world application that concerns fault diag- nosis of a railway device. Results from this application are provided to demonstrate the ability of our approach to enhance estimation accuracy and remove indeterminacy commonly encountered in unsupervised IFA such as source permutations

A cascade form blind source separation connecting source separation and linearization for nonlinear mixtures

A network structure and its learning algorithm have been proposed for blind source separation applied to nonlinear mixtures. The network has a cascade form consists of a source separation block and a linearization block in this order. The conventional learning algorithm is employed for the separation block. A new learning algorithm is proposed for the linearization block assuming 2nd-order nonlinearity. After, source separation, the outputs include the nonlinear components for the same signal source. This nonlinearity is suppressed through the linearization block. Parameters in this block are iteratively adjusted based on a process of solving a 2nd-order equation of a single variable. Simulation results, using 2-channel speech signals and an instantaneous nonlinear mixing process, show good separation performance