@inproceedings{db3bc4edfd8d475eb438e2e9163e97d1,

title = "Rate-distortion bounds for sparse approximation",

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.",

keywords = "Basis pursuit, Compressed sensing, Estimation, Matching pursuit, Maximum likelihood, Unions of subspaces",

author = "Fletcher, {Alyson K.} and Sundeep Rangan and Goyal, {Vivek K.}",

year = "2007",

doi = "10.1109/SSP.2007.4301258",

language = "English (US)",

isbn = "142441198X",

series = "IEEE Workshop on Statistical Signal Processing Proceedings",

pages = "254--258",

booktitle = "2007 IEEE/SP 14th Workshop on Statistical Signal Processing, SSP 2007, Proceedings",

note = "2007 IEEE/SP 14th WorkShoP on Statistical Signal Processing, SSP 2007 ; Conference date: 26-08-2007 Through 29-08-2007",

}