# Modular proximal optimization for multidimensional total-variation regularization

arXiv: https://arxiv.org/abs/1411.0589 · HTML: https://mlsanity.com/paper/1411.0589/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Nov 2014.

## Built on by (most cited first, 10 of 10)

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- [Measuring Uncertainty Calibration](https://mlsanity.com/paper/2512.13872/) (2025)
- [Untangling Lariats: Subgradient Following of Variationally Penalized Objectives](https://mlsanity.com/paper/2405.04710/) (2024)
- [cryoSENSE: Compressive Sensing Enables High-throughput Microscopy with Sparse and Generative Priors on the Protein Cryo-EM Image Manifold](https://mlsanity.com/paper/2511.12931/) (2025)
- [3D Field of Junctions: A Noise-Robust, Training-Free Structural Prior for Volumetric Inverse Problems](https://mlsanity.com/paper/2603.02149/) (2026)

## Abstract (arXiv)

We study TV regularization, a widely used technique for eliciting structured sparsity. In particular, we propose efficient algorithms for computing prox-operators for ℓp-norm TV. The most important among these is ℓ1-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.