The Convergence of Two Algorithms for Compressed Sensing Based Tomography

Xiezhang Li; Jiehua Zhu

doi:10.4236/act.2012.13007

The Convergence of Two Algorithms for Compressed Sensing Based Tomography

Xiezhang Li, Jiehua Zhu

Mathematical Sciences

Georgia Southern University

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

Abstract

The constrained total variation minimization has been developed successfully for image reconstruction in computed tomography. In this paper, the block component averaging and diagonally-relaxed orthogonal projection methods are proposed to incorporate with the total variation minimization in the compressed sensing framework. The convergence of the algorithms under a certain condition is derived. Examples are given to illustrate their convergence behavior and noise performance.

Original language	American English
Journal	Advanced in Computed Tomography
Volume	1
DOIs	https://doi.org/10.4236/act.2012.13007
State	Published - Dec 20 2012

Keywords

Block iterative methods
Compressed sensing
Image reconstruction
Total variation minimization

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http://dx.doi.org/10.4236/act.2012.13007

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abstract = " The constrained total variation minimization has been developed successfully for image reconstruction in computed tomography. In this paper, the block component averaging and diagonally-relaxed orthogonal projection methods are proposed to incorporate with the total variation minimization in the compressed sensing framework. The convergence of the algorithms under a certain condition is derived. Examples are given to illustrate their convergence behavior and noise performance.",

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N2 - The constrained total variation minimization has been developed successfully for image reconstruction in computed tomography. In this paper, the block component averaging and diagonally-relaxed orthogonal projection methods are proposed to incorporate with the total variation minimization in the compressed sensing framework. The convergence of the algorithms under a certain condition is derived. Examples are given to illustrate their convergence behavior and noise performance.

AB - The constrained total variation minimization has been developed successfully for image reconstruction in computed tomography. In this paper, the block component averaging and diagonally-relaxed orthogonal projection methods are proposed to incorporate with the total variation minimization in the compressed sensing framework. The convergence of the algorithms under a certain condition is derived. Examples are given to illustrate their convergence behavior and noise performance.

KW - Block iterative methods

KW - Compressed sensing

KW - Image reconstruction

KW - Total variation minimization

UR - https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/87

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DO - 10.4236/act.2012.13007

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VL - 1

JO - Advanced in Computed Tomography

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ER -

The Convergence of Two Algorithms for Compressed Sensing Based Tomography

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