Study Of The Algorithms And Applications Of Blind Source Separation

Blind source separation (BSS) is a hot topic in signal processing. It attracts more and more attentions because of its widely applications in wireless communication, speech identification, signal encryption, feature extraction, signal anti-interference, remote sensing image interpretation, and biomedical signal processing. The study about BSS develops very fast, but there still exist some problems, such as how to separate the dependent sources? How to solve large-scale or real time dataset? How to solve the underdetermined mixed model, especially when the source number is unknown? How to use BSS technology practically? This thesis exploits BSS problems from the following facts:First, study the BSS method based on nonnegative matrix factorization (NMF) systematically. According to the geometrical feature of the observations, a volume constraint is added to the traditional NMF model. The separability conditions are proposed. And the relation between these conditions and the sparseness features are discussed. Also, a natural gradient based algorithm is utilized, such that the traditional alternative least square multiplication updating rule can solve the constrained NMF model. The proposed constrained NMF method is particularly suitable for the separation of dependent sources. Also, due to the volume constraint, the identifiability of NMF based method is enhanced and the requirement of sparseness to sources is reduced.Second, online or incremental BSS algorithms are introduced for real-time or large-scale dataset, where the incremental NMF algorithm is mainly derived. Using an amnesic average method which allows full use of every sample, it realizes the statistical efficiency for learning and reduces the computational cost. As the cost is low at each iteration, the proposed method is particularly suitable for solving online BSS problem.Then, the underdetermined BSS problem for sparse sources is analyzed. Two kinds of separation methods are introduced: 1) two-stage-method, i.e., estimating the mixing matrix using support vector machine (SVM) which has powerful performance for classification firstly, then recovering the sources by solving the linear program problems. For the estimation of the mixing matrix, the traditional two-classifying SVM is extended to multi-classifying by directed acyclic graph method. 2) one-stage-method, i.e., estimating the mixing matrix and the sources simultaneously using constrained natural gradient based alternative updating method. In stead of traditional method for learning the mixing matrix using approximate gradient, a strict natural gradient is derived in the proposed method. As a result, it has a much better performance. Furthermore, the BSS scheme is used for speech and image encryption, and a new type cryptosystem is proposed. The structure is analyzed in detail, including preprocessing, encryption, decryption, reconstruction. The corresponding security under normal attacks is also analyzed. Compared with the state-of-the-art, the proposed cryptosystems have the following advantages: the structure is simpler, the usage of the cipher is more convenient, and the security is higher.At last, the BSS scheme is used for remote sensing image interpretation or spectral unmixing. A novel measure of sparseness using higher order statistics of signals is proposed. It features the physical significance and is convenient to be optimized. Based on this measure, a sparse NMF/BSS algorithm is proposed for solving SU, where the endmembers and abundances are simultaneously estimated. Simulations based on synthetic mixtures and real images show that the proposed method outperforms the state-of-the-art methods, including the convergence, sensitivities to the noise, etc. It is particularly suitable for processing sparse endmembers, but also robust to process the endmembers which are not sparse enough.