Study On Some Algorithms For Blind Source Separation And Their Applications

Blind source separation (BSS) has found many applications in digital image processing, speech signal processing, medical signal processing, geophysical signal processing, communication signal processing, remote sensing image processing, etc. When the mixing process and the original signals are unknown, BSS tries decomposing the observed sensor signals in order to obtain the unmixed source signals, as seems mysterious. However, given some assumptions, BSS has had great success and many novel and effective methods have been emerging. The thesis concerning this hot research area does some research work as follows:(1) The blind source extraction (BSE) methods are analyzed in the third chapter. BSE for signal with temporal structure is focused on. After analysis in depth of two representative algorithms in the literature, two conclusions are reached:firstly, one of them claims that its method is more robust to the additive Gaussian white noise, as is incorrect. Our theoretical analysis shows that anti-noise performance of these two method are the same. Secondly, these two algorithms reach the same goal by different routes, and their cost functions can both be transformed to the autocorrelation function of the observed signals. Based on these points, a few more robust algorithms are obtained, which are more robust to the estimation of the temporal structure information and have better extraction results.(2) Independent component analysis with reference (ICA-R) is an important method for BSE. However, our analysis indicates that it has two deficiencies. Firstly, it is time-consuming; secondly, its threshold parameter has an important effect on its performance, once its value is improperly set, it will fail. Many improved versions of ICA-R still have these drawbacks. Three improved algorithms for ICA-R are proposed in the fourth chapter, which completely avoid inherent drawbacks on ICA-R. Simulation experiments demonstrate their better performance.(3) The fifth chapter is about BSS methods based on generalized eigen-value decomposition (GED). Three algorithms, which is based on linear prediction, temporal predictability, and is proposed in " On blind source separation using generalized eigenvalues with a new metric", respectively, are investigated. They all acquire the demixing matrix through optimizing some cost function with the form of generalized Rayleigh quotient (GRQ). The optimization is transformed to the corresponding GED, whose eigen-vectors constitutes the demixing matrix. The original article of the third algorithm proved that one source signal can be obtained by maximizing of the cost function with the form of GRQ. But the problem is: whether any other extreme point of GEQ corresponds to its critical point, respectively. It is the fundamental premise for the transformation from the optimization of GRQ for BSS to GED. Our analysis shows that the proof in the original article of the third algorithm is not rigorous. We give three cost functions based on linear prediction, whose meanings are much more clear. We also give an algorithm based on the third method above, then we give a unifying framework and prove it. The framework covers all BSS methods based on the optimization of some cost function with the form of GRQ, which provides a solid theoretical basis for methods with the help of GED, also an sample for building a cost function with the form of GRQ.(4) Methods for BSS based on joint diagonalization (JD) of matrices are studied in the sixth chapter. Early algorithms are all based on orthogonal JD, but the constraint of orthogonality influences separation result, so in recent years all research is on the methods based on non-orthogonal JD. Denoting the diagonlized matrix as Bi whose its kl-th element is bkl, a very natural criterion for measurement of diagonalization extent is J(W)=∑off(Bi), where off(B)=∑k≠l(bkl)2 In order to avoid singular or degenerate solution, some constrained term is added to the aforementioned simple criterion. By this means, two simple non-orthogonal JD algorithms are proposed. Moreover, we give a novel JD criterion as follows:J(W)=∑off(Bi)/‖B‖, where‖.‖denote Euclidean norm. It simultaneously considers the diagonal elements and off- diagonal elements and its better diagonalization and BSS performance is validated by simulation experiments.