Mixing Matrix Estimation based on Directional Density Detection and Hough Transform

Abstract

Mixing matrix estimation (MME) algorithm was proposed for the mixing matrix estimation problem of underdetermined blind source separation. The algorithm is based on a combination of processing of isolated time–frequency points from local directional density detection and Hough transform (HT). Firstly, signal sparsity was strengthened through the processing of single-source time–frequency points in the transform domain. Next, HT was applied to the directional straight lines in the scatter plot and realized the spatial transformation. The number of source signals and mixing matrix were estimated by determining the local maxima of cumulative array. To deal with the peak values clustering issue that commonly arises with HT, the local directional density detection method was used to identify and eliminate isolated time–frequency points. HT was then used to improve the accuracy of MME. The experimental results indicate that the proposed method is able to achieve MME under the condition when the number of source signals is unknown. Further, the accuracy of estimation is better than other commonlyused methods such as K-means.