Modular proximal optimization for multidimensional total-variation regularization
We study TV regularization, a widely used technique for eliciting structured sparsity. In particular, we propose efficient algorithms for computing prox-operators for `p-norm TV. The most important among these is `1-norm TV, for whose prox-operator we present a new geometric analysis which unveils a...
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
2021
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| Online Access: | https://hdl.handle.net/1721.1/130520 |
| _version_ | 1811073062092668928 |
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| author | Sra, Suvrit |
| author2 | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science |
| author_facet | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Sra, Suvrit |
| author_sort | Sra, Suvrit |
| collection | MIT |
| description | We study TV regularization, a widely used technique for eliciting structured sparsity. In particular, we propose efficient algorithms for computing prox-operators for `p-norm TV. The most important among these is `1-norm TV, for whose prox-operator we present a new geometric analysis which unveils a hitherto unknown connection to taut-string methods. This connection turns out to be remarkably useful as it shows how our geometry guided implementation results in efficient weighted and unweighted 1D-TV solvers, surpassing state-of-the-art methods. Our 1D-TV solvers provide the backbone for building more complex (two or higher-dimensional) TV solvers within a modular proximal optimization approach. We review the literature for an array of methods exploiting this strategy, and illustrate the benefits of our modular design through extensive suite of experiments on (i) image denoising, (ii) image deconvolution, (iii) four variants of fused-lasso, and (iv) video denoising. To underscore our claims and permit easy reproducibility, we provide all the reviewed and our new TV solvers in an easy to use multi-threaded C++, Matlab and Python library. |
| first_indexed | 2024-09-23T09:28:00Z |
| format | Article |
| id | mit-1721.1/130520 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T09:28:00Z |
| publishDate | 2021 |
| record_format | dspace |
| spelling | mit-1721.1/1305202022-09-26T11:35:01Z Modular proximal optimization for multidimensional total-variation regularization Sra, Suvrit Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science We study TV regularization, a widely used technique for eliciting structured sparsity. In particular, we propose efficient algorithms for computing prox-operators for `p-norm TV. The most important among these is `1-norm TV, for whose prox-operator we present a new geometric analysis which unveils a hitherto unknown connection to taut-string methods. This connection turns out to be remarkably useful as it shows how our geometry guided implementation results in efficient weighted and unweighted 1D-TV solvers, surpassing state-of-the-art methods. Our 1D-TV solvers provide the backbone for building more complex (two or higher-dimensional) TV solvers within a modular proximal optimization approach. We review the literature for an array of methods exploiting this strategy, and illustrate the benefits of our modular design through extensive suite of experiments on (i) image denoising, (ii) image deconvolution, (iii) four variants of fused-lasso, and (iv) video denoising. To underscore our claims and permit easy reproducibility, we provide all the reviewed and our new TV solvers in an easy to use multi-threaded C++, Matlab and Python library. 2021-04-26T11:59:20Z 2021-04-26T11:59:20Z 2018-11 2018-10 2021-04-06T18:21:59Z Article http://purl.org/eprint/type/JournalArticle 1533-7928 1532-4435 https://hdl.handle.net/1721.1/130520 Barbero, Alvaro and Suvrit Sra. “Modular proximal optimization for multidimensional total-variation regularization.” Journal of Machine Learning Research, 19 (November 2018): 1-82 © 2018 The Author(s) en https://www.jmlr.org/papers/volume19/13-538/13-538.pdf Journal of Machine Learning Research Creative Commons Attribution 4.0 International license https://creativecommons.org/licenses/by/4.0/ application/pdf Journal of Machine Learning Research |
| spellingShingle | Sra, Suvrit Modular proximal optimization for multidimensional total-variation regularization |
| title | Modular proximal optimization for multidimensional total-variation regularization |
| title_full | Modular proximal optimization for multidimensional total-variation regularization |
| title_fullStr | Modular proximal optimization for multidimensional total-variation regularization |
| title_full_unstemmed | Modular proximal optimization for multidimensional total-variation regularization |
| title_short | Modular proximal optimization for multidimensional total-variation regularization |
| title_sort | modular proximal optimization for multidimensional total variation regularization |
| url | https://hdl.handle.net/1721.1/130520 |
| work_keys_str_mv | AT srasuvrit modularproximaloptimizationformultidimensionaltotalvariationregularization |