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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.17506 |
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| _version_ | 1866910384061939712 |
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| author | Bonettini, Silvia Calatroni, Luca Pezzi, Danilo Prato, Marco |
| author_facet | Bonettini, Silvia Calatroni, Luca Pezzi, Danilo Prato, Marco |
| contents | We propose an unfolded accelerated projected-gradient descent procedure to estimate model and algorithmic parameters for image super-resolution and molecule localization problems in image microscopy. The variational lower-level constraint enforces sparsity of the solution and encodes different noise statistics (Gaussian, Poisson), while the upper-level cost assesses optimality w.r.t.~the task considered. In more detail, a standard $\ell_2$ cost is considered for image reconstruction (e.g., deconvolution/super-resolution, semi-blind deconvolution) problems, while a smoothed $\ell_1$ is employed to assess localization precision in some exemplary fluorescence microscopy problems exploiting single-molecule activation. Several numerical experiments are reported to validate the proposed approach on synthetic and realistic ISBI data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_17506 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Algorithmic unfolding for image reconstruction and localization problems in fluorescence microscopy Bonettini, Silvia Calatroni, Luca Pezzi, Danilo Prato, Marco Numerical Analysis We propose an unfolded accelerated projected-gradient descent procedure to estimate model and algorithmic parameters for image super-resolution and molecule localization problems in image microscopy. The variational lower-level constraint enforces sparsity of the solution and encodes different noise statistics (Gaussian, Poisson), while the upper-level cost assesses optimality w.r.t.~the task considered. In more detail, a standard $\ell_2$ cost is considered for image reconstruction (e.g., deconvolution/super-resolution, semi-blind deconvolution) problems, while a smoothed $\ell_1$ is employed to assess localization precision in some exemplary fluorescence microscopy problems exploiting single-molecule activation. Several numerical experiments are reported to validate the proposed approach on synthetic and realistic ISBI data. |
| title | Algorithmic unfolding for image reconstruction and localization problems in fluorescence microscopy |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2403.17506 |