{"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/alternating-minimization-algorithm-with","title":"Alternating Minimization Algorithm with Automatic Relevance Determination for Transmission Tomography under Poisson Noise","arxiv_id":"1412.8464","date":"2014-12-29","proceeding":null,"authors":["Yan Kaganovsky","Shaobo Han","Soysal Degirmenci","David G. Politte","David J. Brady","Joseph A. O'Sullivan","Lawrence Carin"],"abstract":"We propose a globally convergent alternating minimization (AM) algorithm for\nimage reconstruction in transmission tomography, which extends automatic\nrelevance determination (ARD) to Poisson noise models with Beer's law. The\nalgorithm promotes solutions that are sparse in the pixel/voxel-differences\ndomain by introducing additional latent variables, one for each pixel/voxel,\nand then learning these variables from the data using a hierarchical Bayesian\nmodel. Importantly, the proposed AM algorithm is free of any tuning parameters\nwith image quality comparable to standard penalized likelihood methods. Our\nalgorithm exploits optimization transfer principles which reduce the problem\ninto parallel 1D optimization tasks (one for each pixel/voxel), making the\nalgorithm feasible for large-scale problems. This approach considerably reduces\nthe computational bottleneck of ARD associated with the posterior variances.\nPositivity constraints inherent in transmission tomography problems are also\nenforced. We demonstrate the performance of the proposed algorithm for x-ray\ncomputed tomography using synthetic and real-world datasets. The algorithm is\nshown to have much better performance than prior ARD algorithms based on\napproximate Gaussian noise models, even for high photon flux.","url_abs":"http://arxiv.org/abs/1412.8464v2","url_pdf":"http://arxiv.org/pdf/1412.8464v2.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":"alternating-minimization-algorithm-with","repo_url":"https://github.com/yankagan/VARD-for-CT","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"image-reconstruction","task_name":"Image Reconstruction"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}