1 research outputs found
Approximate Message Passing under Finite Alphabet Constraints
In this paper we consider Basis Pursuit De-Noising (BPDN) problems in which
the sparse original signal is drawn from a finite alphabet. To solve this
problem we propose an iterative message passing algorithm, which capitalises
not only on the sparsity but by means of a prior distribution also on the
discrete nature of the original signal. In our numerical experiments we test
this algorithm in combination with a Rademacher measurement matrix and a
measurement matrix derived from the random demodulator, which enables
compressive sampling of analogue signals. Our results show in both cases
significant performance gains over a linear programming based approach to the
considered BPDN problem. We also compare the proposed algorithm to a similar
message passing based algorithm without prior knowledge and observe an even
larger performance improvement.Comment: 4 pages, 2 figures, to appear in IEEE International Conference on
Acoustics, Speech, and Signal Processing ICASSP 201