Well-posedness of the permutation problem in sparse filter estimation with lp minimization

TL;DR

This paper investigates the use of temporal sparsity of filters to resolve permutation ambiguities in convolutive source separation, providing theoretical insights and experimental validation of its potential and limitations.

Contribution

It introduces a novel approach to address the filter permutation problem using sparsity, analyzing its theoretical foundations and practical effectiveness.

Findings

Sparsity can help resolve permutation ambiguities under certain conditions

Theoretical analysis clarifies when sparsity-based permutation correction is feasible

Experimental results demonstrate the approach's potential and limitations

Abstract

Convolutive source separation is often done in two stages: 1) estimation of the mixing filters and 2) estimation of the sources. Traditional approaches suffer from the ambiguities of arbitrary permutations and scaling in each frequency bin of the estimated filters and/or the sources, and they are usually corrected by taking into account some special properties of the filters/sources. This paper focusses on the filter permutation problem in the absence of scaling, investigating the possible use of the temporal sparsity of the filters as a property enabling permutation correction. Theoretical and experimental results highlight the potential as well as the limits of sparsity as an hypothesis to obtain a well-posed permutation problem.