{"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/cosharp-a-convex-program-for-single-shot","title":"CoShaRP: A Convex Program for Single-shot Tomographic Shape Sensing","arxiv_id":"2012.04551","date":"2020-12-08","proceeding":null,"authors":["Ajinkya Kadu","Tristan van Leeuwen","K. Joost Batenburg"],"abstract":"We introduce single-shot X-ray tomography that aims to estimate the target image from a single cone-beam projection measurement. This linear inverse problem is extremely under-determined since the measurements are far fewer than the number of unknowns. Moreover, it is more challenging than conventional tomography where a sufficiently large number of projection angles forms the measurements, allowing for a simple inversion process. However, single-shot tomography becomes less severe if the target image is only composed of known shapes. Hence, the shape prior transforms a linear ill-posed image estimation problem to a non-linear problem of estimating the roto-translations of the shapes. In this paper, we circumvent the non-linearity by using a dictionary of possible roto-translations of the shapes. We propose a convex program CoShaRP to recover the dictionary-coefficients successfully. CoShaRP relies on simplex-type constraint and can be solved quickly using a primal-dual algorithm. The numerical experiments show that CoShaRP recovers shapes stably from moderately noisy measurements.","url_abs":"https://arxiv.org/abs/2012.04551v2","url_pdf":"https://arxiv.org/pdf/2012.04551v2.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":"cosharp-a-convex-program-for-single-shot","repo_url":"https://github.com/ajinkyakadu125/CoShaRP","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"cosharp-a-convex-program-for-single-shot","repo_url":"https://github.com/ajinkyakadu/CoShaRP","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"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}