# Modular proximal optimization for multidimensional total-variation regularization

Source: [Modular proximal optimization for multidimensional total-variation regularization](<https://www.sota2.com/research/paper/68fa54751e209131ce98bc03>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-12-02T10:17:54.788Z

Authors: \\'Alvaro Barbero, Suvrit Sra

Published: 2014-11-03T18:08:44.000Z

## Abstract

We study \\emph{TV regularization}, a widely used technique for eliciting structured sparsity. In particular, we propose efficient algorithms for computing prox-operators for $\\ell\_p$-norm TV. The most important among these is $\\ell\_1$-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.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

- [3D CT Reconstruction on Synthetic CT datasets (engine, foot, jaw, pepper, teapot) P50 noise level](<https://www.sota2.com/research/sota/3d-ct-reconstruction-on-synthetic-ct-datasets-engine-foot-jaw-pepper-teapot-p50-noise-level.md>): 3D CT Reconstruction; Synthetic CT datasets (engine, foot, jaw, pepper, teapot) P50 noise level; MS-SSIM (2D): 0.703.

- [3D CT Reconstruction on CT datasets engine, foot, jaw, pepper, teapot synthetic (P100)](<https://www.sota2.com/research/sota/3d-ct-reconstruction-on-ct-datasets-engine-foot-jaw-pepper-teapot-synthetic-p100.md>): 3D CT Reconstruction; CT datasets engine, foot, jaw, pepper, teapot synthetic (P100); 2D MS-SSIM: 0.739.

- [3D CT Reconstruction on CT datasets engine, foot, jaw, pepper, teapot noise level synthetic (P1000)](<https://www.sota2.com/research/sota/3d-ct-reconstruction-on-ct-datasets-engine-foot-jaw-pepper-teapot-noise-level-synthetic-p1000.md>): 3D CT Reconstruction; CT datasets engine, foot, jaw, pepper, teapot noise level synthetic (P1000); 2D MS-SSIM: 82.9.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1411.0589>)

[PDF](<https://arxiv.org/pdf/1411.0589.pdf>)