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Proceedings Paper

Sparse approximation, denoising, and large random frames
Author(s): Alyson K. Fletcher; Sundeep Rangan; Vivek K. Goyal
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Paper Abstract

If a signal x is known to have a sparse representation with respect to a frame, the signal can be estimated from a noise-corrupted observation y by finding the best sparse approximation to y. The ability to remove noise in this manner depends on the frame being designed to efficiently represent the signal while it inefficiently represents the noise. This paper analyzes the mean squared error (MSE) of this denoising scheme and the probability that the estimate has the same sparsity pattern as the original signal. Analyses are for dictionaries generated randomly according to a spherically-symmetric distribution. Easily-computed approximations for the probability of selecting the correct dictionary element and the MSE are given. In the limit of large dimension, these approximations have simple forms. The asymptotic expressions reveal a critical input signal-to-noise ratio (SNR) for signal recovery.

Paper Details

Date Published: 17 September 2005
PDF: 10 pages
Proc. SPIE 5914, Wavelets XI, 59140M (17 September 2005); doi: 10.1117/12.615772
Show Author Affiliations
Alyson K. Fletcher, Univ. of California, Berkeley (United States)
Sundeep Rangan, Flarion Technologies (United States)
Vivek K. Goyal, Massachusetts Institute of Technology (United States)

Published in SPIE Proceedings Vol. 5914:
Wavelets XI
Manos Papadakis; Andrew F. Laine; Michael A. Unser, Editor(s)

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