HPPP: Halpern-type Preconditioned Proximal Point Algorithms and Applications to Image Restoration
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| Format: | Preprint |
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2024
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| _version_ | 1866915630177845248 |
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| author | Zhang, Shuchang Zhang, Hui Wang, Hongxia |
| author_facet | Zhang, Shuchang Zhang, Hui Wang, Hongxia |
| contents | Recently, the degenerate preconditioned proximal point (PPP) method provides a unified and flexible framework for designing and analyzing operator-splitting algorithms such as Douglas-Rachford (DR). However, the degenerate PPP method exhibits weak convergence in the infinite-dimensional Hilbert space and lacks accelerated variants. To address these issues, we propose a Halpern-type PPP (HPPP) algorithm, which leverages the strong convergence and acceleration properties of Halpern's iteration method. Moreover, we propose a novel algorithm for image restoration by combining HPPP with denoiser priors such as Plug-and-Play (PnP) prior, which can be viewed as an accelerated PnP method. Finally, numerical experiments including several toy examples and image restoration validate the effectiveness of our proposed algorithms. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_13120 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | HPPP: Halpern-type Preconditioned Proximal Point Algorithms and Applications to Image Restoration Zhang, Shuchang Zhang, Hui Wang, Hongxia Computer Vision and Pattern Recognition Optimization and Control Recently, the degenerate preconditioned proximal point (PPP) method provides a unified and flexible framework for designing and analyzing operator-splitting algorithms such as Douglas-Rachford (DR). However, the degenerate PPP method exhibits weak convergence in the infinite-dimensional Hilbert space and lacks accelerated variants. To address these issues, we propose a Halpern-type PPP (HPPP) algorithm, which leverages the strong convergence and acceleration properties of Halpern's iteration method. Moreover, we propose a novel algorithm for image restoration by combining HPPP with denoiser priors such as Plug-and-Play (PnP) prior, which can be viewed as an accelerated PnP method. Finally, numerical experiments including several toy examples and image restoration validate the effectiveness of our proposed algorithms. |
| title | HPPP: Halpern-type Preconditioned Proximal Point Algorithms and Applications to Image Restoration |
| topic | Computer Vision and Pattern Recognition Optimization and Control |
| url | https://arxiv.org/abs/2407.13120 |