Abstract:
Tensor decompositions such as the canonical polyadic decomposition (CPD) or the block term decomposition (BTD) are basic tools for blind signal separation. Most of the li...Show MoreMetadata
Abstract:
Tensor decompositions such as the canonical polyadic decomposition (CPD) or the block term decomposition (BTD) are basic tools for blind signal separation. Most of the literature concerns instantaneous mixtures/memoryless channels. In this paper, we focus on convolutive extensions. More precisely, we present a connection between convolutive CPD/BTD models and coupled but instantaneous CPD/BTD. We derive a new identifiability condition dedicated to convolutive low-rank factorization problems. We explain that under this condition, the convolutive extension of CPD/BTD can be computed by means of an algebraic method, guaranteeing perfect source separation in the noiseless case. In the inexact case, the algorithm can be used as a cheap initialization for an optimization-based method. We explain that, in contrast to the memoryless case, convolutive signal separation is in certain cases possible despite only two-way diversities (e.g., space × time).
Published in: IEEE Transactions on Signal Processing ( Volume: 65, Issue: 15, 01 August 2017)