Title :
Average error in recovery of sparse signals and discrete fourier transform
Author :
Özçelikkale, Ayça ; Yüksel, Serdar ; Özaktas, Haldun M.
Author_Institution :
Elektr. Elektron. Muhendisligi Bolumu, Bilkent Univ., Ankara, Turkey
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.
Keywords :
compressed sensing; covariance matrices; discrete Fourier transforms; optimisation; average error criterion; compressive sensing framework; covariance matrix; discrete Fourier transform; high probability criterion; optimization problem; performance criterion; random process; signal recovery; sparse signals; Abstracts; Compressed sensing; Discrete Fourier transforms; Information theory; Random access memory; Sparse matrices;
Conference_Titel :
Signal Processing and Communications Applications Conference (SIU), 2012 20th
Conference_Location :
Mugla
Print_ISBN :
978-1-4673-0055-1
Electronic_ISBN :
978-1-4673-0054-4
DOI :
10.1109/SIU.2012.6204499