Volume 34, Issue 6
Reducing Staircasing Artifacts in SPECT Reconstruction by an Infimal Convolution Regularization

Zhifeng Wu, Si Li, Xueying Zeng, Yuesheng Xu & A. Krol

J. Comp. Math., 34 (2016), pp. 626-647.

Published online: 2016-12

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  • Abstract

The purpose of this paper is to investigate the ability of the infimal convolution regularization in curing the staircasing artifacts of the TV model in the SPECT reconstruction. We formulate the problem of SPECT reconstruction with the infimal convolution regularization as a convex three-block optimization problem and characterize its solution by a system of fixed-point equations in terms of the proximity operator of the functions involved in its objective function. We then develop a novel fixed-point proximity algorithm based on the fixed-point equations. Moreover, we introduce a preconditioning matrix motivated by the classical MLEM (maximum-likelihood expectation maximization) algorithm. We prove convergence of the proposed algorithm. The numerical results are included to show that the infimal convolution regularization is capable of effectively reducing the staircasing artifacts, while maintaining comparable image quality in terms of the signal-to-noise ratio and coefficient recovery contrast.

  • Keywords

SPECT Infimal Convolution Regularization Staircasing Artifacts Fixed-point Proximity Algorithm

  • AMS Subject Headings

68U10 49Q20.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

whutxxz@163.com (Zhifeng Wu)

reesiloveu@163.com (Si Li)

zxying@ouc.edu.cn (Xueying Zeng)

yxu06@syr.edu (Yuesheng Xu)

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@Article{JCM-34-626, author = {Wu , Zhifeng and Li , Si and Zeng , Xueying and Xu , Yuesheng and Krol , A. }, title = {Reducing Staircasing Artifacts in SPECT Reconstruction by an Infimal Convolution Regularization}, journal = {Journal of Computational Mathematics}, year = {2016}, volume = {34}, number = {6}, pages = {626--647}, abstract = { The purpose of this paper is to investigate the ability of the infimal convolution regularization in curing the staircasing artifacts of the TV model in the SPECT reconstruction. We formulate the problem of SPECT reconstruction with the infimal convolution regularization as a convex three-block optimization problem and characterize its solution by a system of fixed-point equations in terms of the proximity operator of the functions involved in its objective function. We then develop a novel fixed-point proximity algorithm based on the fixed-point equations. Moreover, we introduce a preconditioning matrix motivated by the classical MLEM (maximum-likelihood expectation maximization) algorithm. We prove convergence of the proposed algorithm. The numerical results are included to show that the infimal convolution regularization is capable of effectively reducing the staircasing artifacts, while maintaining comparable image quality in terms of the signal-to-noise ratio and coefficient recovery contrast.}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1607-m2016-0537}, url = {http://global-sci.org/intro/article_detail/jcm/9817.html} }
TY - JOUR T1 - Reducing Staircasing Artifacts in SPECT Reconstruction by an Infimal Convolution Regularization AU - Wu , Zhifeng AU - Li , Si AU - Zeng , Xueying AU - Xu , Yuesheng AU - Krol , A. JO - Journal of Computational Mathematics VL - 6 SP - 626 EP - 647 PY - 2016 DA - 2016/12 SN - 34 DO - http://doi.org/10.4208/jcm.1607-m2016-0537 UR - https://global-sci.org/intro/article_detail/jcm/9817.html KW - SPECT KW - Infimal Convolution Regularization KW - Staircasing Artifacts KW - Fixed-point Proximity Algorithm AB - The purpose of this paper is to investigate the ability of the infimal convolution regularization in curing the staircasing artifacts of the TV model in the SPECT reconstruction. We formulate the problem of SPECT reconstruction with the infimal convolution regularization as a convex three-block optimization problem and characterize its solution by a system of fixed-point equations in terms of the proximity operator of the functions involved in its objective function. We then develop a novel fixed-point proximity algorithm based on the fixed-point equations. Moreover, we introduce a preconditioning matrix motivated by the classical MLEM (maximum-likelihood expectation maximization) algorithm. We prove convergence of the proposed algorithm. The numerical results are included to show that the infimal convolution regularization is capable of effectively reducing the staircasing artifacts, while maintaining comparable image quality in terms of the signal-to-noise ratio and coefficient recovery contrast.
Zhifeng Wu , Si Li , Xueying Zeng , Yuesheng Xu & A. Krol . (2020). Reducing Staircasing Artifacts in SPECT Reconstruction by an Infimal Convolution Regularization. Journal of Computational Mathematics. 34 (6). 626-647. doi:10.4208/jcm.1607-m2016-0537
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