# Total variation regularization for manifold-valued data

arXiv: https://arxiv.org/abs/1312.7710 · HTML: https://mlsanity.com/paper/1312.7710/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Dec 2013.

## Built on by (most cited first, 4 of 4)

- [Image Denoising: The Deep Learning Revolution and Beyond -- A Survey Paper --](https://mlsanity.com/paper/2301.03362/) (2023)
- [Lifting the Convex Conjugate in Lagrangian Relaxations: A Tractable Approach for Continuous Markov Random Fields](https://mlsanity.com/paper/2107.06028/) (2021)
- [Tikhonov Regularization of Circle-Valued Signals](https://mlsanity.com/paper/2108.02602/) (2021)
- [1-Lipschitz Neural Networks on Hadamard Manifolds](https://mlsanity.com/paper/2607.19335/) (2026)

## Abstract (arXiv)

We consider total variation minimization for manifold valued data. We propose a cyclic proximal point algorithm and a parallel proximal point algorithm to minimize TV functionals with ℓp-type data terms in the manifold case. These algorithms are based on iterative geodesic averaging which makes them easily applicable to a large class of data manifolds. As an application, we consider denoising images which take their values in a manifold. We apply our algorithms to diffusion tensor images, interferometric SAR images as well as sphere and cylinder valued images. For the class of Cartan-Hadamard manifolds (which includes the data space in diffusion tensor imaging) we show the convergence of the proposed TV minimizing algorithms to a global minimizer.