Research On Underdetermined Mixture Blind Signal Separation Problem

Blind Source Separation (BSS) is to recover original signal from the available observations without knowledge of source and the mixing channels. Because of extensive application in the domains of speech recognition, image processing、medical signal analysis and processing (EEG、MEG、ECG)、data mining、signal processing、wireless communication and optical communications, BSS becomes one of the hottest spots in signal processing field and neural network field.After more than twenty years, the theory and applications of BSS have got rapid development, and many effective algorithms have been presented. Under the condition that the number of observed signals is not less than the number of source signals (that ism≥n), by using the classic Independent Component Analysis method, we get that the restore of BSS is effective. With the development of BSS, Underdetermined Blind Source Separation (that ism<n) becomes one of the focus problems. At present, we solve the UBSS by applying the sparse property of signal, which is called as Sparse Component Analysis (SCA). However, these algorithms are not perfect, many problems are still being studied. Hence, I am engaged in research on UBSS.The main work of this thesis that studied on instantaneous and linear UBSS is as follows:It presents a new algorithm to estimate the mixing matrix under the source signal not strictly sparse. Based on Bernoulli-Gaussian Model, it estimates the mixing matrix by searching the cluster points which are found through evaluating the density of points in the region. Adopting the optimize method to improve the estimate accuracy, the simulations show the good performance of the proposed algorithm.In the case of knowing the mixing matrix, approximate equivalent of l0norm is taken as the objective function in the paper, and the function of block matrix is used to reduce the dimensions of variables. By applying the advantages of global searching of genetic algorithm to restore source signals, it overcomes the defects of traditional algorithm, which extremely falls into local optimal solution. This thesis introduces a new kind of signal sampling theory (Compressed Sensing). It reduces the strict request of traditional Nyquist signal sampling theory:only when the sampling rate is more than twice as much as the signal bandwidth, can it accurate reconstruction of the original signal. Compressed Sensing reduces the signal processing time、calculating cost and storage cost. By analyzing the relationship between Compressed Sensing and UBSS, it provides another research direction for UBSS.