{"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/learning-the-invisible-a-hybrid-deep-learning","title":"Learning The Invisible: A Hybrid Deep Learning-Shearlet Framework for Limited Angle Computed Tomography","arxiv_id":"1811.04602","date":"2018-11-12","proceeding":null,"authors":["T. A. Bubba","G. Kutyniok","M. Lassas","M. März","W. Samek","S. Siltanen","V. Srinivasan"],"abstract":"The high complexity of various inverse problems poses a significant challenge\nto model-based reconstruction schemes, which in such situations often reach\ntheir limits. At the same time, we witness an exceptional success of data-based\nmethodologies such as deep learning. However, in the context of inverse\nproblems, deep neural networks mostly act as black box routines, used for\ninstance for a somewhat unspecified removal of artifacts in classical image\nreconstructions. In this paper, we will focus on the severely ill-posed inverse\nproblem of limited angle computed tomography, in which entire boundary sections\nare not captured in the measurements. We will develop a hybrid reconstruction\nframework that fuses model-based sparse regularization with data-driven deep\nlearning. Our method is reliable in the sense that we only learn the part that\ncan provably not be handled by model-based methods, while applying the\ntheoretically controllable sparse regularization technique to the remaining\nparts. Such a decomposition into visible and invisible segments is achieved by\nmeans of the shearlet transform that allows to resolve wavefront sets in the\nphase space. Furthermore, this split enables us to assign the clear task of\ninferring unknown shearlet coefficients to the neural network and thereby\noffering an interpretation of its performance in the context of limited angle\ncomputed tomography. Our numerical experiments show that our algorithm\nsignificantly surpasses both pure model- and more data-based reconstruction\nmethods.","url_abs":"http://arxiv.org/abs/1811.04602v1","url_pdf":"http://arxiv.org/pdf/1811.04602v1.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":"learning-the-invisible-a-hybrid-deep-learning","repo_url":"https://github.com/alexdenker/htc2022_lpd","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1811.04602","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}