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A Fast and Accurate Reconstruction Algorithm for Compressed Sensing of Complex Sinusoids | IEEE Journals & Magazine | IEEE Xplore

A Fast and Accurate Reconstruction Algorithm for Compressed Sensing of Complex Sinusoids


Abstract:

The standard compressed sensing (CS) theory reconstructs a signal by recovering a sparse representation of the signal over a pre-specified dictionary. For CS of complex s...Show More

Abstract:

The standard compressed sensing (CS) theory reconstructs a signal by recovering a sparse representation of the signal over a pre-specified dictionary. For CS of complex sinusoids, this dictionary is usually set to be a DFT matrix corresponding to a uniform frequency grid. However, such a setting can make conventional CS reconstruction methods degrade considerably, since component frequencies of practical signals do not necessarily align with the specified grid. To deal with this problem, we apply a linear approximation to the true unknown dictionary and establish a more accurate model for sparse approximation of practical complex sinusoids. Based on this model, signal reconstruction is reformulated as a problem that recovers two sparse coefficient vectors over two known dictionaries under the constraint that the vectors share the same support. To solve such a problem, we develop a fast iterative algorithm under a variational Bayesian inference framework. Results of extensive numerical experiments demonstrate that the algorithm can achieve CS of complex sinusoids with low computational cost as well as high reconstruction accuracy.
Published in: IEEE Transactions on Signal Processing ( Volume: 61, Issue: 22, November 2013)
Page(s): 5744 - 5754
Date of Publication: 29 August 2013

ISSN Information:


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