Semisoft Generalized Total Variation Minimization for Image Reconstruction in Computed Tomography

Semisoft Generalized Total Variation Minimization for Image Reconstruction in Computed Tomography

The generalized l<sub>1</sub> greedy algorithm was recently proposed and shown to outperform the standard reweighted l<sub>1</sub>-minimization and l<sub>1</sub>-greedy algorithms for image reconstruction in computed tomography (CT). Herein, this algorithm is exte...

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Main Authors: Xiezhang Li, Fangjun Arroyo, Jiehua Zhu, Jianing Sun
Format: Article
Language:English
Published: IEEE 2017-01-01
Series:IEEE Access
Subjects:
Generalized <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">l</italic>₁ greedy algorithm
reweighted <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">l</italic>₁-minimization
semisoft thresholding
total variation
Online Access:https://ieeexplore.ieee.org/document/7909042/
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spelling doaj-f00c66befd704018a3488f86b8a645a62021-03-29T20:04:28ZengIEEEIEEE Access2169-35362017-01-0158475848110.1109/ACCESS.2017.26922457909042Semisoft Generalized Total Variation Minimization for Image Reconstruction in Computed TomographyXiezhang Li0Fangjun Arroyo1Jiehua Zhu2https://orcid.org/0000-0002-8623-9447Jianing Sun3Department of Mathematical Sciences, Georgia Southern University, Statesboro, GA, USADepartment of Mathematics, Francis Marion University, Florence, SC, USADepartment of Mathematical Sciences, Georgia Southern University, Statesboro, GA, USASchool of mathematics, Northeast Normal University, Changchun, ChinaThe generalized l<sub>1</sub> greedy algorithm was recently proposed and shown to outperform the standard reweighted l<sub>1</sub>-minimization and l<sub>1</sub>-greedy algorithms for image reconstruction in computed tomography (CT). Herein, this algorithm is extended as a semisoft generalized l<sub>1</sub> greedy algorithm by adapting the wavelet technique of semisoft thresholding. The extended algorithm can also be applied to image reconstruction by incorporating it into the BCPCS framework, resulting in a semisoft generalized total variation minimization (SSGTV) algorithm for CT. Numerical tests indicate that the proposed SSGTV algorithm improves the image reconstruction for CT.https://ieeexplore.ieee.org/document/7909042/Generalized <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">l</italic>₁ greedy algorithmreweighted <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">l</italic>₁-minimizationsemisoft thresholdingtotal variation
collection DOAJ
language English
format Article
sources DOAJ
author Xiezhang Li
Fangjun Arroyo
Jiehua Zhu
Jianing Sun
spellingShingle Xiezhang Li
Fangjun Arroyo
Jiehua Zhu
Jianing Sun
Semisoft Generalized Total Variation Minimization for Image Reconstruction in Computed Tomography
IEEE Access
Generalized <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">l</italic>₁ greedy algorithm
reweighted <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">l</italic>₁-minimization
semisoft thresholding
total variation
author_facet Xiezhang Li
Fangjun Arroyo
Jiehua Zhu
Jianing Sun
author_sort Xiezhang Li
title Semisoft Generalized Total Variation Minimization for Image Reconstruction in Computed Tomography
title_short Semisoft Generalized Total Variation Minimization for Image Reconstruction in Computed Tomography
title_full Semisoft Generalized Total Variation Minimization for Image Reconstruction in Computed Tomography
title_fullStr Semisoft Generalized Total Variation Minimization for Image Reconstruction in Computed Tomography
title_full_unstemmed Semisoft Generalized Total Variation Minimization for Image Reconstruction in Computed Tomography
title_sort semisoft generalized total variation minimization for image reconstruction in computed tomography
publisher IEEE
series IEEE Access
issn 2169-3536
publishDate 2017-01-01
description The generalized l<sub>1</sub> greedy algorithm was recently proposed and shown to outperform the standard reweighted l<sub>1</sub>-minimization and l<sub>1</sub>-greedy algorithms for image reconstruction in computed tomography (CT). Herein, this algorithm is extended as a semisoft generalized l<sub>1</sub> greedy algorithm by adapting the wavelet technique of semisoft thresholding. The extended algorithm can also be applied to image reconstruction by incorporating it into the BCPCS framework, resulting in a semisoft generalized total variation minimization (SSGTV) algorithm for CT. Numerical tests indicate that the proposed SSGTV algorithm improves the image reconstruction for CT.
topic Generalized <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">l</italic>₁ greedy algorithm
reweighted <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">l</italic>₁-minimization
semisoft thresholding
total variation
url https://ieeexplore.ieee.org/document/7909042/
work_keys_str_mv AT xiezhangli semisoftgeneralizedtotalvariationminimizationforimagereconstructionincomputedtomography
AT fangjunarroyo semisoftgeneralizedtotalvariationminimizationforimagereconstructionincomputedtomography
AT jiehuazhu semisoftgeneralizedtotalvariationminimizationforimagereconstructionincomputedtomography
AT jianingsun semisoftgeneralizedtotalvariationminimizationforimagereconstructionincomputedtomography
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