Research on Mixed Matrix Estimation Algorithm Based on Improved Sparse Representation Model in Underdetermined Blind Source Separation System

Abstract

The estimation accuracy of the mixed matrix is very important to the performance of the underdetermined blind source separation (UBSS) system. To improve the estimation accuracy of the mixed matrix, the sparsity of the mixed signal is required. The novel fractional domain time–frequency plane is obtained by rotating the time–frequency plane after the short-time Fourier transform. This plane represents the fine characteristics of the mixed signal in the time domain and the frequency domain. The rotation angle is determined by global searching for the minimum L1 norm to make the mixed signal sufficiently sparse. The obtained time–frequency points do not need single source point detection, reducing the calculation amount of the original algorithm, and the insensitivity to noise in the fractional domain improves the robustness of the algorithm in the noise environment. The simulation results show that the sparsity of the mixed signal and the estimation accuracy of the mixed matrix are improved. Compared with the existing mixed matrix estimation algorithms, the proposed method is effective.

Advances in Time-Frequency Analysis for Blind Source Separation: Challenges, Contributions, and Emerging Trends

“…The algorithm first estimates the mixing matrix by clustering algorithm, and then restores the source signal by shortest path method. Since then, there have been many UBSS two-step methods for sparse source signals [44], called Sparse Component Analysis (SCA).…”

“…For the first step, the mixed matrix estimation method: Bofill proposed the potential function method to find the straight-line trend in the signal scatter diagram and determine the mixed matrix, which belongs to the estimation method of statistical clustering [44]. Y, Li uses the K-means [45] statistical clustering method to estimate the mixed matrix.…”

Exploiting Time–Frequency Sparsity for Dual-Sensor Blind Source Separation

“…For the first issue, various MME methods [18,21,27,[31][32][33][34][35][36][37][38] consider the TF points where only single source occurs or possesses dominant energy. These single-source TF points (SSPs) provide a directional clustering property, which can be associated with each column of the mixing matrix.…”