Compressive sampling-based informed source separation
The paradigm of using a very simple encoder and a sophisticated decoder for compression of signals became popular with the theory of distributed coding and it has been exercised for the compression of various types of signals such as images and video. The theory of compressive sampling later introduced a similar concept but with the focus on guarantees of signal recovery using sparse and low rank priors lying in an incoherent domain to the domain of sampling. In this paper, we bring together the concepts introduced in distributed coding and compressive sampling with the informed source separation, in which the goal is to efficiently compress the audio sources so that they can be decoded with the knowledge of the mixture of the sources. The proposed framework uses a very simple time domain sampling scheme to encode the sources, and a sophisticated decoding algorithm that makes use of the low rank non-negative tensor factorization model of the distribution of short-time Fourier transform coefficients to recover the sources, which is a direct application of the principles of both compressive sampling and distributed coding.