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arXiv · 1201.4949

Approximate Message Passing under Finite Alphabet Constraints

Andreas Muller·Dino Sejdinovic·Robert Piechocki
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Abstract

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.

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Andreas Muller, Dino Sejdinovic, Robert Piechocki. 2012-01-24. Approximate Message Passing under Finite Alphabet Constraints. https://doi.org/10.1109/icassp.2012.6288590

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