Study On Blind Signal Separation Algorithm Based On Sparse Representation

Blind Signal Separation is a challenging and very practical significance of research topic in signal processing field. After many years of exploration research, Blind Signal Separation theory has been got faster and larger development put forward many efficient algorithms. Blind Signal Separation actually means in the case of unknown a priori knowledge of the source signal and transmission channel, based on various statistical properties of the input source signal, only to separate the observed mixture signal or restore the source signal. With the continued development of the blind signal separation, its applications are more widely, mainly used in biomedical analysis (EEG、MEG、ECG)、speech signal recognition and enhancement、image processing、sonar detection problem、wireless communication、data mining、geophysical et al. Early blind signal separation research focuses on independent component analysis (ICA)(the number of sensors is not less than the number of source signals, i.e. m≥n),this is a very efficient blind signal separation technique, however, as this theory gradually mature, the researchers have known many of the limitations and deficiencies of the blind source separation algorithm.As a result, many scholars gradually begin to turn their interest to research the underdetermined (the number of sensors is less than the number of source signals, i.e. m<n) or ill-posed BSS, and have put forward some efficient algorithm, further broaden the research and application range of BSS. To this day, the research on BSS of underdetermined mixtures is far from mature, many BSS algorithms and theory problems are expected to continue to be discussed. This is why I am engaged in study on underdetermined BSS algorithm.For instantaneous linear underdetermined blind separation problem, the main parts of this paper are studied on underdetermined blind separation theory and made better sparse component analysis (SCA) algorithm based on a number of shortcoming and problem in sparse component analysis algorithm. The main content of this thesis is summarized as the following two aspects: (1) A new two-step algorithm for underdetermined source separation is proposed. Mixing matrix is estimated using clustering methods based on potential function. Sources are estimated using a fast sparse reconstructed algorithm。 every solution of system equation As(t)=x(t),which express as the sum of one of its special solution and a group of linear combination of basic solution of the corresponding homogeneous linear equation。The number of independent variable s(t) which is needed to estimate is reduced from n to n-m.we realize blind source separation of signal by means of sparse representation finally. The new algorithm is easily implemented and runs fast, which can well meet the requirements of the blind separation on speed. Simulation experiments show that the proposed algorithm is very good separation efficiency and precision.(2) Compressed sensing(CS)theory is a novel data collection and coding theory under the condition that signal is sparse or compressible. The reconstruction for noisy signal is the key technique in compressed sensing. Technique which is commonly used in this setting is the basis pursuit(BP). Under the condition that the noise distribution is known, the BP method is used to suppress noise, namely CSDN method. CSDN was improved, l1norm was transformed to lp norm in expressing signal sparse solution, which enhanced the effect of signal reconstruction. Simulation experiments show that the new algorithm not only reduces the computational complexity than CSDN method, but also the effect of reconstructed signal is better.