Efficient Constrained Signal Reconstruction by Randomized Epigraphical Projection
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arXiv
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| Format: | Preprint |
| Published: |
2018
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| _version_ | 1866914849408155648 |
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| author | Ono, Shunsuke |
| author_facet | Ono, Shunsuke |
| contents | This paper proposes a randomized optimization framework for constrained signal reconstruction, where the word "constrained" implies that data-fidelity is imposed as a hard constraint instead of adding a data-fidelity term to an objective function to be minimized. Such formulation facilitates the selection of regularization terms and hyperparameters, but due to the non-separability of the data-fidelity constraint, it does not suit block-coordinate-wise randomization as is. To resolve this, we give another expression of the data-fidelity constraint via epigraphs, which enables to design a randomized solver based on a stochastic proximal algorithm with randomized epigraphical projection. Our method is very efficient especially when the problem involves non-structured large matrices. We apply our method to CT image reconstruction, where the advantage of our method over the deterministic counterpart is demonstrated. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1810_12249 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Efficient Constrained Signal Reconstruction by Randomized Epigraphical Projection Ono, Shunsuke Optimization and Control Signal Processing This paper proposes a randomized optimization framework for constrained signal reconstruction, where the word "constrained" implies that data-fidelity is imposed as a hard constraint instead of adding a data-fidelity term to an objective function to be minimized. Such formulation facilitates the selection of regularization terms and hyperparameters, but due to the non-separability of the data-fidelity constraint, it does not suit block-coordinate-wise randomization as is. To resolve this, we give another expression of the data-fidelity constraint via epigraphs, which enables to design a randomized solver based on a stochastic proximal algorithm with randomized epigraphical projection. Our method is very efficient especially when the problem involves non-structured large matrices. We apply our method to CT image reconstruction, where the advantage of our method over the deterministic counterpart is demonstrated. |
| title | Efficient Constrained Signal Reconstruction by Randomized Epigraphical Projection |
| topic | Optimization and Control Signal Processing |
| url | https://arxiv.org/abs/1810.12249 |