3 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
Structure-Based Bayesian Sparse Reconstruction
Sparse signal reconstruction algorithms have attracted research attention due
to their wide applications in various fields. In this paper, we present a
simple Bayesian approach that utilizes the sparsity constraint and a priori
statistical information (Gaussian or otherwise) to obtain near optimal
estimates. In addition, we make use of the rich structure of the sensing matrix
encountered in many signal processing applications to develop a fast sparse
recovery algorithm. The computational complexity of the proposed algorithm is
relatively low compared with the widely used convex relaxation methods as well
as greedy matching pursuit techniques, especially at a low sparsity rate.Comment: 29 pages, 15 figures, accepted in IEEE Transactions on Signal
Processing (July 2012