  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.
