The Research Of Blind Separation Of Overcomplete Mixtures Of Sparse Sources

Blind sources separation (BSS) is process of estimating unknown source signals from observed signals which are mixtures of unknown source signals. Recently, the problem of blind source separation has received considerable attention, because of its wide application in various fields such as biomedical signal analysis, speech enhancement, image recognition, wireless communications, etc. In practical, the BSS with the number of observed signals is less than the number of sources because of the restriction on the number of sensors, referred to as overcomplete BSS. Recently, most of overcomplete BSS algorithms assume that the source number is known; the source signals are sufficiently sparse and observed signals are not contaminated by additive noise and including singular values. However, these conditions are usually absent. In this dissertation, we focus on investigating the problem of the overcomplete BSS with an unknown number of sources, the source signals are insufficiently sparse and observed signals are contaminated by additive noise. The main contributions of this dissertation are summarized blow:1. With unknown number of source signals, a robust algorithm for the overcomplete BSS is proposed when the source signals are insufficiently sparse and the observed signals are contaminated by additive noises. First, by introducing the robust competitive agglomeration algorithm into the K-plane clustering algorithm, a robust K-plane clustering algorithm is proposed to estimate the K-dimensional concentration hyperplanes, and then to estimate the mixing vectors using them. The robust K-plane clustering algorithm can reduce the sensitivity of the traditional K-plane clustering algorithm to noises and the predefined number of clustering is not necessary. Second, the source signals can be recovered by using the sparsity of source signals.2. Based on a novel Cauchy Potential Function, a new algorithm is proposed for estimating the mixing matrix in the overcomplete BSS when the number of sources is unknown; the source signals are insufficiently sparse (a small number of the source samples satisfy sufficiently sparse) and the mixture signals are contaminated by additive noise and outliers. By estimating the local maxim of a global Cauchy Potential Function instead of directly estimating the local maxim of the Cauchy Potential Function, the robustness of the proposed algorithm to the noise and sparsity of the sources can be increased. Meanwhile, the robustness of the algorithm is measured in the dissertation.