Adaptive signal processing algorithms for noncircular complex data

The complex domain provides a natural processing framework for a large class of signals encountered in communications, radar, biomedical engineering and renewable energy. Statistical signal processing in C has traditionally been viewed as a straightforward extension of the corresponding algorithms in the real domain R, however, recent developments in augmented complex statistics show that, in general, this leads to under-modelling. This direct treatment of complex-valued signals has led to advances in so called widely linear modelling and the introduction of a generalised framework for the differentiability of both analytic and non-analytic complex and quaternion functions. In this thesis, supervised and blind complex adaptive algorithms capable of processing the generality of complex and quaternion signals (both circular and noncircular) in both noise-free and noisy environments are developed; their usefulness in real-world applications is demonstrated through case studies. The focus of this thesis is on the use of augmented statistics and widely linear modelling. The standard complex least mean square (CLMS) algorithm is extended to perform optimally for the generality of complex-valued signals, and is shown to outperform the CLMS algorithm. Next, extraction of latent complex-valued signals from large mixtures is addressed. This is achieved by developing several classes of complex blind source extraction algorithms based on fundamental signal properties such as smoothness, predictability and degree of Gaussianity, with the analysis of the existence and uniqueness of the solutions also provided. These algorithms are shown to facilitate real-time applications, such as those in brain computer interfacing (BCI). Due to their modified cost functions and the widely linear mixing model, this class of algorithms perform well in both noise-free and noisy environments. Next, based on a widely linear quaternion model, the FastICA algorithm is extended to the quaternion domain to provide separation of the generality of quaternion signals. The enhanced performances of the widely linear algorithms are illustrated in renewable energy and biomedical applications, in particular, for the prediction of wind profiles and extraction of artifacts from EEG recordings

Overlearning in marginal distribution-based ICA: analysis and solutions

The present paper is written as a word of caution, with users of independent component analysis (ICA) in mind, to overlearning phenomena that are often observed.\\ We consider two types of overlearning, typical to high-order statistics based ICA. These algorithms can be seen to maximise the negentropy of the source estimates. The first kind of overlearning results in the generation of spike-like signals, if there are not enough samples in the data or there is a considerable amount of noise present. It is argued that, if the data has power spectrum characterised by $1/f$ curve, we face a more severe problem, which cannot be solved inside the strict ICA model. This overlearning is better characterised by bumps instead of spikes. Both overlearning types are demonstrated in the case of artificial signals as well as magnetoencephalograms (MEG). Several methods are suggested to circumvent both types, either by making the estimation of the ICA model more robust or by including further modelling of the data

The LOST Algorithm: finding lines and separating speech mixtures

Robust clustering of data into linear subspaces is a frequently encountered problem. Here, we treat clustering of one-dimensional subspaces that cross the origin. This problem arises in blind source separation, where the subspaces correspond directly to columns of a mixing matrix. We propose the LOST algorithm, which identifies such subspaces using a procedure similar in spirit to EM. This line finding procedure combined with a transformation into a sparse domain and an L1-norm minimisation constitutes a blind source separation algorithm for the separation of instantaneous mixtures with an arbitrary number of mixtures and sources. We perform an extensive investigation on the general separation performance of the LOST algorithm using randomly generated mixtures, and empirically estimate the performance of the algorithm in the presence of noise. Furthermore, we implement a simple scheme whereby the number of sources present in the mixtures can be detected automaticall

Independent component analysis of magnetoencephalographic signals

EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Generalized Canonical Correlation Analysis and Its Application to Blind Source Separation Based on a Dual-Linear Predictor Structure

Blind source separation (BSS) is one of the most important and established research topics in signal processing and many algorithms have been proposed based on different statistical properties of the source signals. For second-order statistics (SOS) based methods, canonical correlation analysis (CCA) has been proved to be an effective solution to the problem. In this work, the CCA approach is generalized to accommodate the case with added white noise and it is then applied to the BSS problem for noisy mixtures. In this approach, the noise component is assumed to be spatially and temporally white, but the variance information of noise is not required. An adaptive blind source extraction algorithm is derived based on this idea and a further extension is proposed by employing a dual-linear predictor structure for blind source extraction (BSE).Comment: 7 pages and 5 figures. The main aim is to show the inherent relationship between generalised canonical correlation analysis and the dual-linear predictor approach presented in two separate conference papers (references [15] and [16]

Fast and accurate methods of independent component analysis: A survey

summary:This paper presents a survey of recent successful algorithms for blind separation of determined instantaneous linear mixtures of independent sources such as natural speech or biomedical signals. These algorithms rely either on non-Gaussianity, nonstationarity, spectral diversity, or on a combination of them. Performance of the algorithms will be demonstrated on separation of a linear instantaneous mixture of audio signals (music, speech) and on artifact removal in electroencephalogram (EEG)

Exploratory source separation in biomedical systems

Contemporary science produces vast amounts of data. The analysis of this data is in a central role for all empirical sciences as well as humanities and arts using quantitative methods. One central role of an information scientist is to provide this research with sophisticated, computationally tractable data analysis tools. When the information scientist confronts a new target field of research producing data for her to analyse, she has two options: She may make some specific hypotheses, or guesses, on the contents of the data, and test these using statistical analysis. On the other hand, she may use general purpose statistical models to get a better insight into the data before making detailed hypotheses. Latent variable models present a case of such general models. In particular, such latent variable models are discussed where the measured data is generated by some hidden sources through some mapping. The task of source separation is to recover the sources. Additionally, one may be interested in the details of the generation process itself. We argue that when little is known of the target field, independent component analysis (ICA) serves as a valuable tool to solve a problem called blind source separation (BSS). BSS means solving a source separation problem with no, or at least very little, prior information. In case more is known of the target field, it is natural to incorporate the knowledge in the separation process. Hence, we also introduce methods for this incorporation. Finally, we suggest a general framework of denoising source separation (DSS) that can serve as a basis for algorithms ranging from almost blind approach to highly specialised and problem-tuned source separation algoritms. We show that certain ICA methods can be constructed in the DSS framework. This leads to new, more robust algorithms. It is natural to use the accumulated knowledge from applying BSS in a target field to devise more detailed source separation algorithms. We call this process exploratory source separation (ESS). We show that DSS serves as a practical and flexible framework to perform ESS, too. Biomedical systems, the nervous system, heart, etc., constitute arguably the most complex systems that human beings have ever studied. Furthermore, the contemporary physics and technology have made it possible to study these systems while they operate in near-natural conditions. The usage of these sophisticated instruments has resulted in a massive explosion of available data. In this thesis, we apply the developed source separation algorithms in the analysis of the human brain, using mainly magnetoencephalograms (MEG). The methods are directly usable for electroencephalograms (EEG) and with small adjustments for other imaging modalities, such as (functional) magnetic resonance imaging (fMRI), too.reviewe

Applications of Blind Source Separation to the Magnetoencephalogram Background Activity in Alzheimer’s Disease

En esta Tesis Doctoral se ha analizado actividad basal de magnetoencefalograma (MEG) de 36 pacientes con la Enfermedad de Alzheimer (Alzheimer’s Disease, AD) y 26 sujetos de control de edad avanzada con técnicas de separación ciega de fuentes (Blind Source Separation, BSS). El objetivo era aplicar los métodos de BSS para ayudar en el análisis e interpretación de este tipo de actividad cerebral, prestando especial atención a la AD. El término BSS denota un conjunto de técnicas útiles para descomponer registros multicanal en las componentes que los dieron lugar. Cuatro diferentes aplicaciones han sido desarrolladas. Los resultados de esta Tesis Doctoral sugieren la utilidad de la BSS para ayudar en el procesado de la actividad basal de MEG y para identificar y caracterizar la AD.Departamento de Teoría de la Señal y Comunicaciones e Ingeniería Telemátic

Efficient Multiband Algorithms for Blind Source Separation

The problem of blind separation refers to recovering original signals, called source signals, from the mixed signals, called observation signals, in a reverberant environment. The mixture is a function of a sequence of original speech signals mixed in a reverberant room. The objective is to separate mixed signals to obtain the original signals without degradation and without prior information of the features of the sources. The strategy used to achieve this objective is to use multiple bands that work at a lower rate, have less computational cost and a quicker convergence than the conventional scheme. Our motivation is the competitive results of unequal-passbands scheme applications, in terms of the convergence speed. The objective of this research is to improve unequal-passbands schemes by improving the speed of convergence and reducing the computational cost. The first proposed work is a novel maximally decimated unequal-passbands scheme.This scheme uses multiple bands that make it work at a reduced sampling rate, and low computational cost. An adaptation approach is derived with an adaptation step that improved the convergence speed. The performance of the proposed scheme was measured in different ways. First, the mean square errors of various bands are measured and the results are compared to a maximally decimated equal-passbands scheme, which is currently the best performing method. The results show that the proposed scheme has a faster convergence rate than the maximally decimated equal-passbands scheme. Second, when the scheme is tested for white and coloured inputs using a low number of bands, it does not yield good results; but when the number of bands is increased, the speed of convergence is enhanced. Third, the scheme is tested for quick changes. It is shown that the performance of the proposed scheme is similar to that of the equal-passbands scheme. Fourth, the scheme is also tested in a stationary state. The experimental results confirm the theoretical work. For more challenging scenarios, an unequal-passbands scheme with over-sampled decimation is proposed; the greater number of bands, the more efficient the separation. The results are compared to the currently best performing method. Second, an experimental comparison is made between the proposed multiband scheme and the conventional scheme. The results show that the convergence speed and the signal-to-interference ratio of the proposed scheme are higher than that of the conventional scheme, and the computation cost is lower than that of the conventional scheme