{"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/modular-proximal-optimization-for","title":"Modular proximal optimization for multidimensional total-variation regularization","arxiv_id":"1411.0589","date":"2014-11-03","proceeding":null,"authors":["Álvaro Barbero","Suvrit Sra"],"abstract":"We study \\emph{TV regularization}, a widely used technique for eliciting\nstructured sparsity. In particular, we propose efficient algorithms for\ncomputing prox-operators for $\\ell_p$-norm TV. The most important among these\nis $\\ell_1$-norm TV, for whose prox-operator we present a new geometric\nanalysis which unveils a hitherto unknown connection to taut-string methods.\nThis connection turns out to be remarkably useful as it shows how our geometry\nguided implementation results in efficient weighted and unweighted 1D-TV\nsolvers, surpassing state-of-the-art methods. Our 1D-TV solvers provide the\nbackbone for building more complex (two or higher-dimensional) TV solvers\nwithin a modular proximal optimization approach. We review the literature for\nan array of methods exploiting this strategy, and illustrate the benefits of\nour modular design through extensive suite of experiments on (i) image\ndenoising, (ii) image deconvolution, (iii) four variants of fused-lasso, and\n(iv) video denoising. To underscore our claims and permit easy reproducibility,\nwe provide all the reviewed and our new TV solvers in an easy to use\nmulti-threaded C++, Matlab and Python library.","url_abs":"http://arxiv.org/abs/1411.0589v3","url_pdf":"http://arxiv.org/pdf/1411.0589v3.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":"modular-proximal-optimization-for","repo_url":"https://github.com/albarji/proxTV","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"NOASSERTION"}},{"paper_slug":"modular-proximal-optimization-for","repo_url":"https://github.com/elras/SoftsegmentNeurons","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"modular-proximal-optimization-for","repo_url":"https://github.com/farrowlab/Neuron-Softsegmentation","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[{"task_slug":"denoising","task_name":"Denoising"},{"task_slug":"image-deconvolution","task_name":"Image Deconvolution"},{"task_slug":"image-denoising","task_name":"Image Denoising"},{"task_slug":"video-denoising","task_name":"Video Denoising"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1411.0589","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1411.0589"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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