Optimal quantization for compressive sensing under message passing reconstruction
Files
Accepted manuscript
Date
2011-07
Authors
Kamilov, Ulugbek
Goyal, Vivek K.
Rangan, Sundeep
Version
Accepted manuscript
OA Version
Citation
Ulugbek Kamilov, Vivek K Goyal, Sundeep Rangan. 2011. "Optimal quantization for compressive sensing under message passing reconstruction." 2011 IEEE International Symposium on Information Theory Proceedings. 2011 IEEE International Symposium on Information Theory - ISIT. 2011-07-31 - 2011-08-05. https://doi.org/10.1109/isit.2011.6034168
Abstract
We consider the optimal quantization of compressive sensing measurements along with estimation from quantized samples using generalized approximate message passing (GAMP). GAMP is an iterative reconstruction scheme inspired by the belief propagation algorithm on bipartite graphs which generalizes approximate message passing (AMP) for arbitrary measurement channels. 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 GAMP signal reconstruction and empirically demonstrate the superior error performance of the resulting quantizers.