Sparse Power Factorization: Balancing peakiness and sample complexity

TL;DR

This paper extends the theoretical guarantees of Sparse Power Factorization (SPF) for recovering bilinear signals with sparse components, broadening its applicability while maintaining manageable measurement requirements.

Contribution

The authors generalize SPF recovery guarantees to a larger, more realistic class of signals, relaxing previous restrictions and slightly increasing measurement complexity.

Findings

Recovery guarantees hold for a broader class of signals.

Measurement complexity increases moderately with the generalization.

Theoretical analysis supports practical applicability of SPF.

Abstract

In many applications, one is faced with an inverse problem, where the known signal depends in a bilinear way on two unknown input vectors. Often at least one of the input vectors is assumed to be sparse, i.e., to have only few non-zero entries. Sparse Power Factorization (SPF), proposed by Lee, Wu, and Bresler, aims to tackle this problem. They have established recovery guarantees for a somewhat restrictive class of signals under the assumption that the measurements are random. We generalize these recovery guarantees to a significantly enlarged and more realistic signal class at the expense of a moderately increased number of measurements.