{"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/deep-convolutional-framelets-a-general-deep","title":"Deep Convolutional Framelets: A General Deep Learning Framework for Inverse Problems","arxiv_id":"1707.00372","date":"2017-07-03","proceeding":null,"authors":["Jong Chul Ye","Yoseob Han","Eunju Cha"],"abstract":"Recently, deep learning approaches with various network architectures have\nachieved significant performance improvement over existing iterative\nreconstruction methods in various imaging problems. However, it is still\nunclear why these deep learning architectures work for specific inverse\nproblems. To address these issues, here we show that the long-searched-for\nmissing link is the convolution framelets for representing a signal by\nconvolving local and non-local bases. The convolution framelets was originally\ndeveloped to generalize the theory of low-rank Hankel matrix approaches for\ninverse problems, and this paper further extends the idea so that we can obtain\na deep neural network using multilayer convolution framelets with perfect\nreconstruction (PR) under rectilinear linear unit nonlinearity (ReLU). Our\nanalysis also shows that the popular deep network components such as residual\nblock, redundant filter channels, and concatenated ReLU (CReLU) do indeed help\nto achieve the PR, while the pooling and unpooling layers should be augmented\nwith high-pass branches to meet the PR condition. Moreover, by changing the\nnumber of filter channels and bias, we can control the shrinkage behaviors of\nthe neural network. This discovery leads us to propose a novel theory for deep\nconvolutional framelets neural network. Using numerical experiments with\nvarious inverse problems, we demonstrated that our deep convolution framelets\nnetwork shows consistent improvement over existing deep architectures.This\ndiscovery suggests that the success of deep learning is not from a magical\npower of a black-box, but rather comes from the power of a novel signal\nrepresentation using non-local basis combined with data-driven local basis,\nwhich is indeed a natural extension of classical signal processing theory.","url_abs":"http://arxiv.org/abs/1707.00372v5","url_pdf":"http://arxiv.org/pdf/1707.00372v5.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":"deep-convolutional-framelets-a-general-deep","repo_url":"https://github.com/anzhao0503/deep-convolutional-framelets.pytorch","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null},{"paper_slug":"deep-convolutional-framelets-a-general-deep","repo_url":"https://github.com/hanyoseob/framing-u-net","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"unanswered"}},{"paper_slug":"deep-convolutional-framelets-a-general-deep","repo_url":"https://github.com/hjahan58/framing-u-net","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"unanswered"}},{"paper_slug":"deep-convolutional-framelets-a-general-deep","repo_url":"https://github.com/jongcye/FramingUNet","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"unanswered"}}],"tasks":[],"methods":[{"method_slug":"convolution","method_name":"Convolution"},{"method_slug":"relu","method_name":"ReLU"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}