Study On Sparse Underdetermined Blind Signal Separation Problem With A Two-Stage Approach

The main parts of this paper study on the underdetermined BSS theory and modified sparse component analysis (SCA) algorithm in different practical field based on instantaneous and linear underdetermined mixing model. The main contributions of this paper are as follows: First, we focus on solving the problem of mixing matrix estimation under the multiple components dominant sparse circumstance. Different to traditional K-subspace clustering method, we propose a weighted K-means clustering-weighted hyperline clustering (K-WHLC) approach to solve this challenging problem. The main advantages of this improvement include two aspects:1) It can strengthen the robustness of algorithm through mining the samples'sparseness as much as possible by introducing Gaussian membership function as weighted factor.2) To the medium and large-scale problem, it successfully avoids sinking into the dilemma of enormous time consumption like as the performance of K-subspace clustering algorithm. Furthermore, we also propose a valid probabilistic criterion for sources number detection in the case of unknown sources number in advance. A series of simulation comparisons prove its high performance on mixing matrix estimation and sources number determination. Secondly, to solve the problem of finding sparse solutions from lp optimization model (0