Research On Extended Models And Algorithms For Blind Source Separation

Finding a suitable representation of multivariate data is an important problem instatistics signal processing and related areas. Optimal representation means that the datais proper transformed so that its essential structure is made more visible or more easilyaccessible, blind source separation (BSS) is a feasible efficient method to treat aboveproblem. BSS consists of recovering mutually independent/uncorrelated but otherwiseunobserved source signals from their mixtures without any prior knowledge of thechannel. In the past three decades, BSS has attracted growing attention in biomedicalsignal processing, audio and acoustics signal processing, multi-user communications,geosciences data analysis and data mining, and so on. In this dissertation, we focus onhow to build the generalized BSS model for different applications, and based on thebuilt models, the corresponding BSS/BSE algorithms are derived in detail. Accordingly,the main contributions of this dissertation are summarized as follows:1. The model inherent connections between underdetermined BSS and compressedsensing (CS) were analyzed firstly, and then the underdetermined blind signalreconstruction mathematical model using compressed sensing is built. Then, there arefour questions remain to be solved: estimating the measurement matrix; establishing thecompressed reconstruction model; realizing the sparse signal reconstruction andestimating the source signals. The mixing matrix is estimated using two methods:1)thestructure of the time domain or transform domain of the source signals;2) the waveletpacket transform and k-means clustering method up to permutation and scaling. Basedon the estimated mixing matrix, the measurement matrix and the measurement equationare obtained. As a consequence, we get the compressed reconstruction model. Based onthe measurement matrix and measurement signal, two proposed compressedreconstruction algorithm are derived based on the greedy orthogonal matching pursuitmethod and compressive sampling matching pursuit (CoSaMP) method to realize thereconstruction of the under-determined sparse source signals. Simulations are providedto show the effectiveness of the proposed two methods.2. Model and algorithms analysis of multiple measurement vectors for compressedsensing is proposed. In the basic CS, the unknown sparse signal is recovered from asingle measurement vector, this is referred to as a single measurement vector (SMV)model. But in many applications, we should recover the joint sparse source signals froma set of measurement vectors. This is called the multiple measurement vectors (MMV)problem of CS, which addresses the recovery of a set of sparse signal vectors that share common non-zero support. This paper begins with the basic mathematic model of SMVand MMV in detail, followed by the existences and uniqueness conditions of thesolution to the SMV and MMV. Then, the algorithms treating MMV model areoverviewed and analyzed in detail, which are divided into three classes: convex method,greedy method and Bayesian method. These algorithms mathematics frameworks andperformances are especially analyzed. At last, the existing problems that need furtherresearch are pointed out and some current challenges and future trends are summed upand predicted.3. A series novel methods for one dimensional harmonic retrieval in additivecolored Gaussian or non-Gaussian noise when the frequencies of the harmonic signalsare closely spaced in frequency domain are proposed. Firstly, we establish the BSSbased harmonic retrieval model in additive noise using only one mixed channel signal,at the same time, the fundamental principles of different BSS based harmonics retrievalalgorithms are analyzed in detail. Then, we established a series harmonic retrievalalgorithms including: higher order statistics based method;2-D weighted histogram andW-disjoint orthogonality based method; period blind source extraction based methodand wavelet packet decomposition based method. Simulation results show that theproposed algorithms are able to retrieve the harmonic source signals and yield idealperformance.4. Dependent Component Analysis (DCA) as an extension of IndependentComponent Analysis (ICA) for BSS has more applications than ICA and received moreand more attentions during the last several years in the study of signal processing andneural networks. After a general and detailed definition of the DCA model is given, theseparateness and uniqueness of the DCA model have been discussed in theory. Then, thestate-of-art DCA algorithms are overviewed, some DCA algorithms, such asmultidimensional ICA, variance dependent BSS, subband decomposition ICA,maximum non-Gaussianity method, Wold decomposition method and time-frequencymethod are constructed in theories and some simulations of these algorithms are alsoexhibited for different applications. In addition, the general and detailed definition ofindependent subspace analysis (ISA) model is given and the relationship between ICAand ISA is also discussed. Moreover, the separateness and uniqueness of the ISA modelis discussed. Based on the maximum likelihood theory and natural gradient method, thenatural gradient separation algorithm for ISA model is constructed. Simulation resultshows that the proposed algorithm is able to separate the ISA mixed source signals.