Under-Determined Convolutive Blind Source Separation Combining Density-Based Clustering and Sparse Reconstruction in Time-Frequency Domain

Blind source separation (BSS) in time-frequency (TF) domain is a versatile framework to recover sources from the recorded mixture signals in a reverberant environment. In general, a two-stage strategy is one of the popular BSS frameworks for the underdetermined BSS case (the number of mixtures is less than the number of sources), which is a tough problem due to the mixing matrix is not invertible. In this paper, we propose a new two-stage scheme combining density-based clustering and sparse reconstruction to estimate mixing matrix and sources, respectively. At the first stage, we transform the mixing matrix estimation as an eigenvector clustering problem based on a particular local dominant assumption. The eigenvectors are first exploited from the rank-one structure of local covariance matrices of mixture TF vectors. These eigenvectors are then clustered and adjusted to give estimated mixing matrix by cooperating density-based clustering and weight clustering. At the second stage, we transform the source reconstruction as a
$\ell _{p}$
norm
$(0 < p \leq 1)$
minimization by an iterative Lagrange multiplier method. With a proper initialization, the obtained solution is a global minimum for any
$p$
in (0, 1] with convergence guarantee. The proposed approach is demonstrated to be superior to the state-of-the-art baseline methods in various underdetermined experiments.