# Tikhonov Regularization of Circle-Valued Signals

arXiv: https://arxiv.org/abs/2108.02602 · HTML: https://mlsanity.com/paper/2108.02602/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 41 references that are in the map.
- First posted on arXiv 5 Aug 2021.

## Builds on (most cited first, 7 of 7)

- [A Comparative Study of Modern Inference Techniques for Structured Discrete Energy Minimization Problems](https://mlsanity.com/paper/1404.0533/) (2014)
- [Proximal Splitting Algorithms for Convex Optimization: A Tour of Recent Advances, with New Twists](https://mlsanity.com/paper/1912.00137/) (2019)
- [Good Colour Maps: How to Design Them](https://mlsanity.com/paper/1509.03700/) (2015)
- [Total variation regularization for manifold-valued data](https://mlsanity.com/paper/1312.7710/) (2013)
- [Mumford-Shah and Potts Regularization for Manifold-Valued Data with Applications to DTI and Q-Ball Imaging](https://mlsanity.com/paper/1410.1699/) (2014)
- [Variational Regularization of Inverse Problems for Manifold-Valued Data](https://mlsanity.com/paper/1804.10432/) (2018)
- [Exact algorithms for L1-TV regularization of real-valued or circle-valued signals](https://mlsanity.com/paper/1504.00499/) (2015)

## Abstract (arXiv)

It is common to have to process signals or images whose values are cyclic and can be represented as points on the complex circle, like wrapped phases, angles, orientations, or color hues. We consider a Tikhonov-type regularization model to smoothen or interpolate circle-valued signals defined on arbitrary graphs. We propose a convex relaxation of this nonconvex problem as a semidefinite program, and an efficient algorithm to solve it.