Average error in recovery of sparse signals and discrete fourier transform

Date
2012-04
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Source Title
20th Signal Processing and Communications Applications Conference (SIU), IEEE 2012
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Publisher
IEEE
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Language
Turkish
Type
Conference Paper
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Abstract

In compressive sensing framework it has been shown that a sparse signal can be successfully recovered from a few random measurements. The Discrete Fourier Transform (DFT) is one of the transforms that provide the best performance guarantees regardless of which components of the signal are nonzero. This result is based on the performance criterion of signal recovery with high probability. Whether the DFT is the optimum transform under average error criterion, instead of high probability criterion, has not been investigated. Here we consider this optimization problem. For this purpose, we model the signal as a random process, and propose a model where the covariance matrix of the signal is used as a measure of sparsity. We show that the DFT is, in general, not optimal despite numerous results that suggest otherwise. © 2012 IEEE.

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Keywords
Average errors, Compressive sensing, High probability, Optimization problems, Performance criterion, Performance guarantees, Random measurement, Signal recovery, Sparse signals, Covariance matrix, Optimization, Random processes, Signal reconstruction, Discrete Fourier transforms
Citation
Published Version (Please cite this version)