The convergence of the block cyclic projection with an overrelaxation parameter for compressed sensing based tomography

The convergence of the block cyclic projection for compressed sensing based tomography (BCPCS) algorithm had been proven recently in the case of underrelaxation parameter λ∈(0,1]. In this paper, we prove its convergence with overrelaxation parameter λ∈(1,2). As a result, the convergence of the other...

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Vydáno v:	Journal of computational and applied mathematics Ročník 280; s. 59 - 67
Hlavní autoři:	Arroyo, Fangjun, Arroyo, Edward, Li, Xiezhang, Zhu, Jiehua
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Elsevier B.V 15.05.2015
Témata:	Algorithms Amalgamated projection method Block iterative algorithm Blocking Compressed Compressed sensing Convergence Detection Image reconstruction Mathematical analysis Projection Tomography Total variation minimization Amalgamated projection method Total variation minimization Block iterative algorithm Compressed sensing Image reconstruction
ISSN:	0377-0427, 1879-1778
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Abstract	The convergence of the block cyclic projection for compressed sensing based tomography (BCPCS) algorithm had been proven recently in the case of underrelaxation parameter λ∈(0,1]. In this paper, we prove its convergence with overrelaxation parameter λ∈(1,2). As a result, the convergence of the other two algorithms (BCAVCS and BDROPCS) with overrelaxation parameter λ∈(1,2) in a special case is derived. Experiments are given to demonstrate the convergence behavior of the BCPCS algorithm with different values of λ.
AbstractList	The convergence of the block cyclic projection for compressed sensing based tomography (BCPCS) algorithm had been proven recently in the case of underrelaxation parameter λ∈(0,1]. In this paper, we prove its convergence with overrelaxation parameter λ∈(1,2). As a result, the convergence of the other two algorithms (BCAVCS and BDROPCS) with overrelaxation parameter λ∈(1,2) in a special case is derived. Experiments are given to demonstrate the convergence behavior of the BCPCS algorithm with different values of λ. The convergence of the block cyclic projection for compressed sensing based tomography (BCPCS) algorithm had been proven recently in the case of underrelaxation parameter . In this paper, we prove its convergence with overrelaxation parameter . As a result, the convergence of the other two algorithms (BCAVCS and BDROPCS) with overrelaxation parameter in a special case is derived. Experiments are given to demonstrate the convergence behavior of the BCPCS algorithm with different values of .
Author	Arroyo, Edward Arroyo, Fangjun Zhu, Jiehua Li, Xiezhang
Author_xml	– sequence: 1 givenname: Fangjun surname: Arroyo fullname: Arroyo, Fangjun email: farroyo@fmarion.edu organization: Department of Mathematics, Francis Marion University, Florence, SC 29501, USA – sequence: 2 givenname: Edward surname: Arroyo fullname: Arroyo, Edward organization: School of Science, Technology, Engineering and Mathematics, American Public University System, Manassas, VA 20109, USA – sequence: 3 givenname: Xiezhang surname: Li fullname: Li, Xiezhang organization: Department of Mathematical Sciences, Georgia Southern University, Statesboro, GA 30460, USA – sequence: 4 givenname: Jiehua surname: Zhu fullname: Zhu, Jiehua organization: Department of Mathematical Sciences, Georgia Southern University, Statesboro, GA 30460, USA
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Keywords	Amalgamated projection method Total variation minimization Block iterative algorithm Compressed sensing Image reconstruction
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SubjectTerms	Algorithms Amalgamated projection method Block iterative algorithm Blocking Compressed Compressed sensing Convergence Detection Image reconstruction Mathematical analysis Projection Tomography Total variation minimization
Title	The convergence of the block cyclic projection with an overrelaxation parameter for compressed sensing based tomography
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