Multiresolution Adaptive Block-Coordinate Forward-Backward for Image Reconstruction
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917305948045312 |
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| author | Desainte-Maréville, Edgar Foare, Marion Gonçalves, Paulo Pustelnik, Nelly Riccietti, Elisa |
| author_facet | Desainte-Maréville, Edgar Foare, Marion Gonçalves, Paulo Pustelnik, Nelly Riccietti, Elisa |
| contents | Classical first-order optimization methods for imaging inverse problems scale poorly with image resolution. Wavelet based multilevel strategies can accelerate convergence under strong blur, but their fixed coarse-to-fine schedules lose effectiveness in moderate-blur or noise-dominated regimes. In this work, we propose an adaptive multiresolution block coordinate Forward-Backward algorithm for image restoration. Multiresolution block selection is driven by the local magnitude of the proximal update via a stochastic non-smooth Gauss-Southwell rule applied to the wavelet decomposition of the image. This adaptive selection strategy dynamically balances updates across scales, emphasizing coarse or fine blocks according to the degradation regime. As a result, the proposed method automatically adapts to varying blur and noise levels without relying on a predefined hierarchical update scheme. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_01860 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Multiresolution Adaptive Block-Coordinate Forward-Backward for Image Reconstruction Desainte-Maréville, Edgar Foare, Marion Gonçalves, Paulo Pustelnik, Nelly Riccietti, Elisa Signal Processing Optimization and Control Classical first-order optimization methods for imaging inverse problems scale poorly with image resolution. Wavelet based multilevel strategies can accelerate convergence under strong blur, but their fixed coarse-to-fine schedules lose effectiveness in moderate-blur or noise-dominated regimes. In this work, we propose an adaptive multiresolution block coordinate Forward-Backward algorithm for image restoration. Multiresolution block selection is driven by the local magnitude of the proximal update via a stochastic non-smooth Gauss-Southwell rule applied to the wavelet decomposition of the image. This adaptive selection strategy dynamically balances updates across scales, emphasizing coarse or fine blocks according to the degradation regime. As a result, the proposed method automatically adapts to varying blur and noise levels without relying on a predefined hierarchical update scheme. |
| title | Multiresolution Adaptive Block-Coordinate Forward-Backward for Image Reconstruction |
| topic | Signal Processing Optimization and Control |
| url | https://arxiv.org/abs/2603.01860 |