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Entropy 2016, 18(6), 207; doi:10.3390/e18060207

Sparse Estimation Based on a New Random Regularized Matching Pursuit Generalized Approximate Message Passing Algorithm

1
Department of Electronic Engineering, University of Electronic Science and Technology of China, No. 2006, Xiyuan Ave., West Hi-Tech Zone, Chengdu 611731, China
2
College of Telecommunication and Information Engineering, Nanjing University of Posts and Telecommunications, 66 Xinmofan Road, Nanjing 210003, China
*
Author to whom correspondence should be addressed.
Academic Editors: Badong Chen and Jose C. Principe
Received: 14 February 2016 / Revised: 13 May 2016 / Accepted: 19 May 2016 / Published: 28 May 2016
(This article belongs to the Special Issue Information Theoretic Learning)
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Abstract

Approximate Message Passing (AMP) and Generalized AMP (GAMP) algorithms usually suffer from serious convergence issues when the elements of the sensing matrix do not exactly match the zero-mean Gaussian assumption. To stabilize AMP/GAMP in these contexts, we have proposed a new sparse reconstruction algorithm, termed the Random regularized Matching pursuit GAMP (RrMpGAMP). It utilizes a random splitting support operation and some dropout/replacement support operations to make the matching pursuit steps regularized and uses a new GAMP-like algorithm to estimate the non-zero elements in a sparse vector. Moreover, our proposed algorithm can save much memory, be equipped with a comparable computational complexity as GAMP and support parallel computing in some steps. We have analyzed the convergence of this GAMP-like algorithm by the replica method and provided the convergence conditions of it. The analysis also gives an explanation about the broader variance range of the elements of the sensing matrix for this GAMP-like algorithm. Experiments using simulation data and real-world synthetic aperture radar tomography (TomoSAR) data show that our method provides the expected performance for scenarios where AMP/GAMP diverges. View Full-Text
Keywords: compressed sensing; random regularization; matching pursuit; generalized approximate message passing; replica method compressed sensing; random regularization; matching pursuit; generalized approximate message passing; replica method
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Luo, Y.; Gui, G.; Cong, X.; Wan, Q. Sparse Estimation Based on a New Random Regularized Matching Pursuit Generalized Approximate Message Passing Algorithm. Entropy 2016, 18, 207.

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