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

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...

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Vydáno v:Entropy (Basel, Switzerland) Ročník 18; číslo 6; s. 207
Hlavní autoři: Luo, Yongjie, Gui, Guan, Cong, Xunchao, Wan, Qun
Médium: Journal Article
Jazyk:angličtina
Vydáno: Basel MDPI AG 01.06.2016
Témata:
Algorithms
Approximation
compressed sensing
Computation
Convergence
Detection
Entropy
generalized approximate message passing
Matching
matching pursuit
Message passing
random regularization
replica method
ISSN:1099-4300, 1099-4300
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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.
AbstractList 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.
Author Cong, Xunchao
Wan, Qun
Luo, Yongjie
Gui, Guan
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CitedBy_id crossref_primary_10_1016_j_sigpro_2018_05_007
crossref_primary_10_1109_TVT_2018_2883669
crossref_primary_10_3390_s17051120
crossref_primary_10_3390_a9040079
crossref_primary_10_1016_j_jfranklin_2018_12_013
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SubjectTerms Algorithms
Approximation
compressed sensing
Computation
Convergence
Detection
Entropy
generalized approximate message passing
Matching
matching pursuit
Message passing
random regularization
replica method
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