NDLI: Rate-Distortion Bounds for Sparse Approximation

Content Provider	IEEE Xplore Digital Library
Author	Fletcher, Alyson K. Rangan, Sundeep Goyal, Vivek K.
Copyright Year	2007
Description	Author affiliation: University of California, Berkeley (Fletcher, Alyson K.) \|\| Massachusetts Institute of Technology (Goyal, Vivek K) \|\| QUALCOMM Flarion Technologies (Rangan, Sundeep)
Abstract	Sparse signal models arise commonly in audio and image processing. Recent work in the area of compressed sensing has provided estimates of the performance of certain widely-used sparse signal processing techniques such as basis pursuit and matching pursuit. However, the optimal achievable performance with sparse signal approximation remains unknown. This paper provides bounds on the ability to estimate a sparse signal in noise. Specifically, we show that there is a critical minimum signal-to-noise ratio (SNR) that is required for reliable detection of the sparsity pattern of the signal. We furthermore relate this critical SNR to the asymptotic mean squared error of the maximum likelihood estimate of a sparse signal in additive Gaussian noise. The critical SNR is a simple function of the problem dimensions.
Starting Page	254
Ending Page	258
File Size	420735
Page Count	5
File Format	PDF
ISBN	9781424411979
DOI	10.1109/SSP.2007.4301258
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2007-08-26
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Rate-distortion Signal to noise ratio Signal processing Image processing Compressed sensing Matching pursuit algorithms Maximum likelihood detection Maximum likelihood estimation Additive noise Gaussian noise unions of subspaces basis pursuit compressed sensing estimation matching pursuit maximum likelihood
Content Type	Text
Resource Type	Article

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