Modular proximal optimization for multidimensional total-variation regularization
Name
13-538.pdf
Description
Published version
Size
7.73 MB
Format
Adobe PDF
Checksum (MD5)
c27ca039246164b7a53d0a2876a3425b
Author(s)
Sra, Suvrit
Date Issued
November 2018
Journal
Journal of Machine Learning Research
Citation
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)
Version
Final published version
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
Creative Commons Attribution 4.0 International license
Persistent DSpace Link
DOI of Published Version
https://www.jmlr.org/papers/volume19/13-538/13-538.pdf
