Study On The Mixing Matrix Estimation In Underdetermined Blind Separation

Underdetermined blind source separation technology has been widely used into areas such as audio signal processing, image processing, biology medicine signal processing, and digital communication. Two-stage algorithm is a simple and efficient method to solve the underdetermined blind source separation problem, which firstly estimates the mixing matrix and recovers the source signals by the corresponding separation algorithm on the basis of the known mixing matrix. As the accuracy of the mixing matrix directly affects the quality of the final separation signals, the mixing matrix estimation plays a key role in underdetermined blind source separation algorithm.Based on previous researchers'efforts and achievements, this thesis is mainly studying three algorithms for solving the mixing matrix estimation problem. Specifically includes:(1) Since hard line orientation separation technique estimates the mixing matrix non-exact and time consuming by modified K-means clustering, this paper presents an improved algorithm. The improved algorithm firstly removes the low-energy points, which can obtain better clustering features and reduce the computation cost, then initializes the line vector by Euclidian distance rule, making it closer to the target line vector. Experimental results show that the proposed algorithm have less running time and can estimate the mixing matrix with higher accuracy, compared with the original algorithm.(2) A mixing matrix estimation algorithm based on Hough transform is studied. As for the estimated mixing matrix is non-exact by K-means algorithm and there exists the peak clustering problem in Hough transform, this paper introduces a K-Hough algorithm combining K-means algorithm and Hough transform. K-means algorithm intensively depends on the selection of initial clustering centers, and the original K-means algorithm randomly chooses initial clustering centers, local minimum problem appears easily in the iteration process which results in the non-exact clustering. To solve this problem, this paper gives a modified K-means algorithm based on selection of initial clustering centers, and combines it with Hough transform to estimate the mixing matrix, and better results have been achieved.(3) A mixing matrix estimation algorithm by modified time and frequency ratio of mixtures algorithm is studied and a post-processing method is proposed. Compared with degenerate un-mixing estimation technique algorithm and original time and frequency ratio of mixtures algorithm, modified time and frequency ratio of mixtures algorithm reduces the requirements of signal sparsity. But due to the own reasons of modified time and frequency ratio of mixtures algorithm, there are many identical columns in the estimated mixing matrix, it has to be handled manually, which is a trouble. This paper proposes a post-processing method for the estimated mixing matrix which can get the final estimated mixing matrix self-adaptively. Experimental results show that the estimated mixing matrix has high accuracy obtained by modified time and frequency ratio of mixtures algorithm and the post-processing method achieves ideal effects.