Noise-Robust Image Reconstruction Based on Minimizing Extended Class of Power-Divergence Measures
The problem of tomographic image reconstruction can be reduced to an optimization problem of finding unknown pixel values subject to minimizing the difference between the measured and forward projections. Iterative image reconstruction algorithms provide significant improvements over transform metho...
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MDPI AG
2021-07-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/23/8/1005 |
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| author | Ryosuke Kasai Yusaku Yamaguchi Takeshi Kojima Omar M. Abou Al-Ola Tetsuya Yoshinaga |
| author_facet | Ryosuke Kasai Yusaku Yamaguchi Takeshi Kojima Omar M. Abou Al-Ola Tetsuya Yoshinaga |
| author_sort | Ryosuke Kasai |
| collection | DOAJ |
| description | The problem of tomographic image reconstruction can be reduced to an optimization problem of finding unknown pixel values subject to minimizing the difference between the measured and forward projections. Iterative image reconstruction algorithms provide significant improvements over transform methods in computed tomography. In this paper, we present an extended class of power-divergence measures (PDMs), which includes a large set of distance and relative entropy measures, and propose an iterative reconstruction algorithm based on the extended PDM (EPDM) as an objective function for the optimization strategy. For this purpose, we introduce a system of nonlinear differential equations whose Lyapunov function is equivalent to the EPDM. Then, we derive an iterative formula by multiplicative discretization of the continuous-time system. Since the parameterized EPDM family includes the Kullback–Leibler divergence, the resulting iterative algorithm is a natural extension of the maximum-likelihood expectation-maximization (MLEM) method. We conducted image reconstruction experiments using noisy projection data and found that the proposed algorithm outperformed MLEM and could reconstruct high-quality images that were robust to measured noise by properly selecting parameters. |
| first_indexed | 2024-03-10T08:49:40Z |
| format | Article |
| id | doaj.art-5941a80eec7d41a19d25549b5ea0395b |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T08:49:40Z |
| publishDate | 2021-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-5941a80eec7d41a19d25549b5ea0395b2023-11-22T07:34:54ZengMDPI AGEntropy1099-43002021-07-01238100510.3390/e23081005Noise-Robust Image Reconstruction Based on Minimizing Extended Class of Power-Divergence MeasuresRyosuke Kasai0Yusaku Yamaguchi1Takeshi Kojima2Omar M. Abou Al-Ola3Tetsuya Yoshinaga4Graduate School of Health Sciences, Tokushima University, 3-18-15 Kuramoto, Tokushima 770-8509, JapanShikoku Medical Center for Children and Adults, National Hospital Organization, 2-1-1 Senyu, Zentsuji 765-8507, JapanInstitute of Biomedical Sciences, Tokushima University, 3-18-15 Kuramoto, Tokushima 770-8509, JapanFaculty of Science, Tanta University, El-Giesh Street, Tanta 31527, EgyptInstitute of Biomedical Sciences, Tokushima University, 3-18-15 Kuramoto, Tokushima 770-8509, JapanThe problem of tomographic image reconstruction can be reduced to an optimization problem of finding unknown pixel values subject to minimizing the difference between the measured and forward projections. Iterative image reconstruction algorithms provide significant improvements over transform methods in computed tomography. In this paper, we present an extended class of power-divergence measures (PDMs), which includes a large set of distance and relative entropy measures, and propose an iterative reconstruction algorithm based on the extended PDM (EPDM) as an objective function for the optimization strategy. For this purpose, we introduce a system of nonlinear differential equations whose Lyapunov function is equivalent to the EPDM. Then, we derive an iterative formula by multiplicative discretization of the continuous-time system. Since the parameterized EPDM family includes the Kullback–Leibler divergence, the resulting iterative algorithm is a natural extension of the maximum-likelihood expectation-maximization (MLEM) method. We conducted image reconstruction experiments using noisy projection data and found that the proposed algorithm outperformed MLEM and could reconstruct high-quality images that were robust to measured noise by properly selecting parameters.https://www.mdpi.com/1099-4300/23/8/1005power-divergence measurecomputed tomographyiterative reconstructionmaximum-likelihood expectation-maximization methodcontinuous-time image reconstruction |
| spellingShingle | Ryosuke Kasai Yusaku Yamaguchi Takeshi Kojima Omar M. Abou Al-Ola Tetsuya Yoshinaga Noise-Robust Image Reconstruction Based on Minimizing Extended Class of Power-Divergence Measures Entropy power-divergence measure computed tomography iterative reconstruction maximum-likelihood expectation-maximization method continuous-time image reconstruction |
| title | Noise-Robust Image Reconstruction Based on Minimizing Extended Class of Power-Divergence Measures |
| title_full | Noise-Robust Image Reconstruction Based on Minimizing Extended Class of Power-Divergence Measures |
| title_fullStr | Noise-Robust Image Reconstruction Based on Minimizing Extended Class of Power-Divergence Measures |
| title_full_unstemmed | Noise-Robust Image Reconstruction Based on Minimizing Extended Class of Power-Divergence Measures |
| title_short | Noise-Robust Image Reconstruction Based on Minimizing Extended Class of Power-Divergence Measures |
| title_sort | noise robust image reconstruction based on minimizing extended class of power divergence measures |
| topic | power-divergence measure computed tomography iterative reconstruction maximum-likelihood expectation-maximization method continuous-time image reconstruction |
| url | https://www.mdpi.com/1099-4300/23/8/1005 |
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