Sparse Power Factorization: Balancing peakiness and sample complexity
For researchers working on bilinear inverse problems with sparsity, this work extends theoretical guarantees to broader signal classes, though it is an incremental improvement over existing results.
The paper generalizes recovery guarantees for Sparse Power Factorization to a larger and more realistic signal class, requiring only a moderately increased number of measurements.
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.