Optimal Quantization for Compressive Sensing under Message Passing Reconstruction

Details Optimal Quantization for Compressive Sensing under Message Passing Reconstruction Optimal Quantization for Compressive Sensing under Message Passing Reconstruction

2011-02-23

arxiv.org/abs/1102.4652v2

Computer Science

Information Theory

5 pages, 3 figures, submitted to IEEE International Symposium on Information Theory (ISIT) 2011; minor corrections in v2

Scientific paper

We consider the optimal quantization of compressive sensing measurements following the work on generalization of relaxed belief propagation (BP) for arbitrary measurement channels. Relaxed BP is an iterative reconstruction scheme inspired by message passing algorithms on bipartite graphs. Its asymptotic error performance can be accurately predicted and tracked through the state evolution formalism. We utilize these results to design mean-square optimal scalar quantizers for relaxed BP signal reconstruction and empirically demonstrate the superior error performance of the resulting quantizers.

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