Study On Underdetermined Blind Source Separation Based On Matrix Diagonal Ratio

As a branch of enhancement technology, blind source separation has been achieved extensive attention. It becomes a hot topic, because of its wide applications, such as image processing, speech processing, medicine signal processing, radar signal processing. If the number of observations is less than that of sources, blind source separation is named as underdetermined blind source separation. And the "two-stage" strategy is an effective way: first get the estimated mixing matrix, then separate the sources by using the estimated mixing matrix. The estimated mixing matrix influence the source separation directly whether it is estimated accurately or not, so it plays important role for underdetermined blind source separation. Meanwhile, source separation algorithm is also important.This paper mainly research the underdetermined blind source separation under the linear instantaneous mixed model, involving mixing matrix estimation and source separation. The content is detailed on the following three topics:(1) Focusing on mixing matrix estimation, this paper proposes an method, whose objective function has better attenuation characteristic. In addition, this objective function overcomes the problem that it is inappropriate to local its maximums using gradient based methods, which is present in NPCM algorithm. The experimental result demonstrates that the proposed method estimates mixing matrix more accurately than NPCM algorithm.(2) This paper proposes a matrix diagonal ratio based source separation method under the analysis of all time-frequency points’diagonal ratios. Firstly, the method constructs all the submatrices of the mixing matrix and multiplies the mixture vector from the left-hand side by the inversion of every submatrix to get the whole pre-extracted source signal vector as well as their covariance matrices simultaneously. Secondly, computing all the diagonal ratios of the covariance matrices and searching the identical vectors (one or more) contained in all the submatrices correspond to the equal ratios. The column labels of the identical vectors in mixing matrix are the indexes of the sources overlapped at this TF point. Finally, the separation stage is performed to obtain the extracted sources in time-frequency domain and then transform them into the time domain to obtain the separation sources. Numerical experiments demonstrate this method can precisely classify all the time-frequency points, and then accomplish the source separation with precision. (3) Under the further analysis on the time-frequency points, this paper improves the above-mentioned source separation method, and provides a method with more precision. This method first searches the optimal submatrix corresponding to the maximal diagonal ratio. Then use the optimal sunmatrix to separate the sources. A number of experiments demonstrate this method can more accurately separate sources.