The Convergence of Block Cyclic Projection with Underrelaxation Parameters for Compressed Sensing Based Tomography

Fangjun Arroyo; Edward Arroyo; Xiezhang Li; Jiehua Zhu

doi:10.3233/XST-140419

The Convergence of Block Cyclic Projection with Underrelaxation Parameters for Compressed Sensing Based Tomography

Fangjun Arroyo, Edward Arroyo, Xiezhang Li, Jiehua Zhu

Mathematical Sciences

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2 Scopus citations

Abstract

The block cyclic projection method in the compressed sensing framework (BCPCS) was introduced for image reconstruction in computed tomography and its convergence had been proven in the case of unity relaxation (λ=1). In this paper, we prove its convergence with underrelaxation parameters λ∈(0,1). As a result, the convergence of compressed sensing based block component averaging algorithm (BCAVCS) and block diagonally-relaxed orthogonal projection algorithm (BDROPCS) with underrelaxation parameters under a certain condition are derived. Experiments are given to illustrate the convergence behavior of these algorithms with selected parameters.

Original language	American English
Journal	Journal of X-Ray Science and Technology
Volume	22
DOIs	https://doi.org/10.3233/XST-140419
State	Published - Jan 1 2014

Keywords

Compressed sensing
amalgamated projection method
block iterative algorithm
image reconstruction
total variation minimization

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title = "The Convergence of Block Cyclic Projection with Underrelaxation Parameters for Compressed Sensing Based Tomography",

abstract = "The block cyclic projection method in the compressed sensing framework (BCPCS) was introduced for image reconstruction in computed tomography and its convergence had been proven in the case of unity relaxation (λ=1). In this paper, we prove its convergence with underrelaxation parameters λ∈(0,1). As a result, the convergence of compressed sensing based block component averaging algorithm (BCAVCS) and block diagonally-relaxed orthogonal projection algorithm (BDROPCS) with underrelaxation parameters under a certain condition are derived. Experiments are given to illustrate the convergence behavior of these algorithms with selected parameters.",

keywords = "Compressed sensing, amalgamated projection method, block iterative algorithm, image reconstruction, total variation minimization",

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

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doi = "10.3233/XST-140419",

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T1 - The Convergence of Block Cyclic Projection with Underrelaxation Parameters for Compressed Sensing Based Tomography

AU - Arroyo, Fangjun

AU - Arroyo, Edward

AU - Li, Xiezhang

AU - Zhu, Jiehua

PY - 2014/1/1

Y1 - 2014/1/1

N2 - The block cyclic projection method in the compressed sensing framework (BCPCS) was introduced for image reconstruction in computed tomography and its convergence had been proven in the case of unity relaxation (λ=1). In this paper, we prove its convergence with underrelaxation parameters λ∈(0,1). As a result, the convergence of compressed sensing based block component averaging algorithm (BCAVCS) and block diagonally-relaxed orthogonal projection algorithm (BDROPCS) with underrelaxation parameters under a certain condition are derived. Experiments are given to illustrate the convergence behavior of these algorithms with selected parameters.

AB - The block cyclic projection method in the compressed sensing framework (BCPCS) was introduced for image reconstruction in computed tomography and its convergence had been proven in the case of unity relaxation (λ=1). In this paper, we prove its convergence with underrelaxation parameters λ∈(0,1). As a result, the convergence of compressed sensing based block component averaging algorithm (BCAVCS) and block diagonally-relaxed orthogonal projection algorithm (BDROPCS) with underrelaxation parameters under a certain condition are derived. Experiments are given to illustrate the convergence behavior of these algorithms with selected parameters.

KW - Compressed sensing

KW - amalgamated projection method

KW - block iterative algorithm

KW - image reconstruction

KW - total variation minimization

UR - https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/85

UR - https://doi.org/10.3233/XST-140419

U2 - 10.3233/XST-140419

DO - 10.3233/XST-140419

M3 - Article

SN - 0895-3996

VL - 22

JO - Journal of X-Ray Science and Technology

JF - Journal of X-Ray Science and Technology

ER -

The Convergence of Block Cyclic Projection with Underrelaxation Parameters for Compressed Sensing Based Tomography

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