Extension of replica analysis to MAP estimation with applications to compressed sensing
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Goyal_Extension of replica.pdf
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Author(s)
Rangan, Sundeep
Fletcher, Alyson K.
Goyal, Vivek K.
Date Issued
July 2010
Journal
2010 IEEE International Symposium on Information Theory Proceedings (ISIT)
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
Rangan, Sundeep, Alyson K. Fletcher, and Vivek K Goyal. “Extension of Replica Analysis to MAP Estimation with Applications to Compressed Sensing.” IEEE, 2010. 1543–1547. © Copyright 2010 IEEE
Version
Final published version
Abstract
The replica method is a non-rigorous but widely-accepted technique from statistical physics used in the asymptotic analysis of large, random, nonlinear problems. This paper applies the replica method to analyze non-Gaussian maximum a posteriori (MAP) estimation. The main result is a counterpart to Guo and Verdú's replica analysis of minimum mean-squared error estimation. The replica MAP analysis can be readily applied to many estimators used in compressed sensing, including basis pursuit, lasso, linear estimation with thresholding, and zero norm-regularized estimation. Among other benefits, the replica method provides a computationally-tractable method for exactly computing various performance metrics including mean-squared error and sparsity pattern recovery probability.
MIT Department
Massachusetts Institute of Technology. Research Laboratory of Electronics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1109/ISIT.2010.5513520
