Study On Underdetermined Blind Source Separation Of Less Sparse Signal

In practical applications, the observed signal received by the sensor is often a mixture of many signals generated by different sources. The technique of Blind Source Separation (BSS) is to recover the underlying original signals completely or partially from the observations without any knowledge of the sources and channels. It has received considerable attention for its potential applications in speech processing, radar system, biomedical engineering, image processing, and digital communication and so on. When the number of sources is more than the number of observations, we call it Underdetermined Blind Source Separation (UBSS), which is more close to real situation and a more challenging problem in linear instantaneous mixed BSS.This paper focuses on the basic theory and main algorithm of linear instantaneous mixed problem in UBSS. The researches concentrate on the following topics:(1) Mixing matrix is the key issue in the UBSS with sparse representation. The performance of traditional clustering method degrades when the sources do not satisfy completely sparse condition. This paper gives an effective method to detect the points in the time-frequency domain that only single source contributes. Samples at these points are more reliable for the mixing matrix estimation. The given method, which sets less condition on the sparseness of the sources, has improved the estimation of the mixing matrix.(2) For the traditional K-means algorithm, the number of the clusters needs to be specified in advance and it is sensitive to the initial clustering centers. This paper gives a method that accurately estimates the number of sources based on histogram of the angle between observation vector and the reference vector. For the cluster center selection, this paper constructs Differences Matrix and finds N most apart vectors which are selected as cluster centers. This method obtains robust result.(3) When the sources are non-disjoint in the TF domain, there are several sources active at a TF point simultaneously. This paper gives a method based on the Orthogonal Projection 'Matrix on each TF plane to classify the TF points. After identifying the sources present at each TF point, this paper executes the separation of the sources. This approach sets less condition on the characteristic of the sources. It can still process dependent sources and non-disjoint sources.Experimental results reveal the efficiency of the methods given in this paper.