{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/bayesian-image-restoration-for-poisson","title":"Bayesian Image Restoration for Poisson Corrupted Image using a Latent Variational Method with Gaussian MRF","arxiv_id":"1412.2342","date":"2014-12-07","proceeding":null,"authors":["Hayaru Shouno"],"abstract":"We treat an image restoration problem with a Poisson noise chan- nel using a\nBayesian framework. The Poisson randomness might be appeared in observation of\nlow contrast object in the field of imaging. The noise observation is often\nhard to treat in a theo- retical analysis. In our formulation, we interpret the\nobservation through the Poisson noise channel as a likelihood, and evaluate the\nbound of it with a Gaussian function using a latent variable method. We then\nintroduce a Gaussian Markov random field (GMRF) as the prior for the Bayesian\napproach, and derive the posterior as a Gaussian distribution. The latent\nparameters in the likelihood and the hyperparameter in the GMRF prior could be\ntreated as hid- den parameters, so that, we propose an algorithm to infer them\nin the expectation maximization (EM) framework using loopy belief\npropagation(LBP). We confirm the ability of our algorithm in the computer\nsimulation, and compare it with the results of other im- age restoration\nframeworks.","url_abs":"http://arxiv.org/abs/1412.2342v1","url_pdf":"http://arxiv.org/pdf/1412.2342v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"bayesian-image-restoration-for-poisson","repo_url":"https://github.com/shouno/PoissonNoiseReduction","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"image-restoration","task_name":"Image Restoration"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}