Underdetermined blind separation of weak sparse sources via matrix transform layer by layer in the Time-Frequency domain

This paper presents a novel two-step approach for underdetermined blind source separation in the time-frequency domain. First, the single-source-points (SSPs), each of that is occupied by a single source, are detected through identifying the Time-Frequency (TF) points of observations using the complex value phase; the mixing matrix is then estimated accurately by employing K-means method among those SSPs with high energies. In the separation procedure, we find the time-frequency points that incorporate one source, two sources, and so on, through matrix transforms. Then, these sources at the points can be solved out explicitly under a weak sparse condition. Remarkably, the method holds some advantages, such as simplicity, parallelism, and possibility that can be extended to one source extraction. Detailed experimental results also show the validity of the method.