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

Fangjun Arroyo; Edward Arroyo; Xiezhang Li; Jiehua Zhu

doi:10.1016/j.cam.2014.11.036

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

Fangjun Arroyo, Edward Arroyo, Xiezhang Li, Jiehua Zhu

Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

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 λε(0,1]. In this paper, we prove its convergence with overrelaxation parameter λε(1,2). As a result, the convergence of the other two algorithms (BCAVCS and BDROPCS) with overrelaxation parameter λε(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.

Original language	English
Pages (from-to)	59-67
Number of pages	9
Journal	Journal of Computational and Applied Mathematics
Volume	280
DOIs	https://doi.org/10.1016/j.cam.2014.11.036
State	Published - Aug 1 2015

Scopus Subject Areas

Computational Mathematics
Applied Mathematics

Keywords

Amalgamated projection method
Block iterative algorithm
Compressed sensing
Image reconstruction
Total variation minimization

Access to Document

10.1016/j.cam.2014.11.036

Cite this

@article{1e57582deabf4e6fae306f1654d9a2a6,

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

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 λε(0,1]. In this paper, we prove its convergence with overrelaxation parameter λε(1,2). As a result, the convergence of the other two algorithms (BCAVCS and BDROPCS) with overrelaxation parameter λε(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.",

keywords = "Amalgamated projection method, Block iterative algorithm, Compressed sensing, Image reconstruction, Total variation minimization",

author = "Fangjun Arroyo and Edward Arroyo and Xiezhang Li and Jiehua Zhu",

year = "2015",

month = aug,

day = "1",

doi = "10.1016/j.cam.2014.11.036",

language = "English",

volume = "280",

pages = "59--67",

journal = "Journal of Computational and Applied Mathematics",

issn = "0377-0427",

publisher = "Elsevier B.V.",

}

TY - JOUR

T1 - The convergence of the block cyclic projection with an overrelaxation parameter for compressed sensing based tomography

AU - Arroyo, Fangjun

AU - Arroyo, Edward

AU - Li, Xiezhang

AU - Zhu, Jiehua

PY - 2015/8/1

Y1 - 2015/8/1

N2 - The convergence of the block cyclic projection for compressed sensing based tomography (BCPCS) algorithm had been proven recently in the case of underrelaxation parameter λε(0,1]. In this paper, we prove its convergence with overrelaxation parameter λε(1,2). As a result, the convergence of the other two algorithms (BCAVCS and BDROPCS) with overrelaxation parameter λε(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.

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

KW - Amalgamated projection method

KW - Block iterative algorithm

KW - Compressed sensing

KW - Image reconstruction

KW - Total variation minimization

UR - http://www.scopus.com/inward/record.url?scp=84922374812&partnerID=8YFLogxK

U2 - 10.1016/j.cam.2014.11.036

DO - 10.1016/j.cam.2014.11.036

M3 - Article

SN - 0377-0427

VL - 280

SP - 59

EP - 67

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

ER -

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

Abstract

Scopus Subject Areas

Keywords

Access to Document

Other files and links

Fingerprint

Cite this