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.

1. Introduction

Audio source separation is a challenging task in audio signal processing [1], in which the quality of the reconstructed sources depends strongly on the particular task and the amount of prior information that can be exploited. Informed source separation (ISS) [2]–[5], which is also strongly related to spatial audio object coding (SAOC) [6], is a new trend in source separation, where some side-information about the sources and/or the mixing system is extracted at a stage where the clean sources are still available, e.g., during the mixing of a music recording by a sound engineer. A natural constraint is that this side-information should be small enough as compared to encoding the sources independently. More precisely, an ISS method is based on a so-called encoding stage, where the side-information is extracted, given both the sources and their mixture, and a so-called decoding stage, where the sources are not available any more and estimated from the mixture, given the side-information. As such, the ISS being at the crossroads of source separation and compression [7], it usually leads to much better quality of reconstructed sources than the conventional audio source separation at the expense of some bitrate required for side-information transmission. Indeed, the quality of reconstructed sources can be fully controlled during the encoding stage [5], [7], and perceptual psycho-acoustic aspects can be taken into account [6], [8].