# Denoising Hyperbolic-Valued Data by Relaxed Regularizations

arXiv: https://arxiv.org/abs/2410.16149 · HTML: https://mlsanity.com/paper/2410.16149/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Oct 2024.

## Built on by (most cited first, 1 of 1)

- [Denoising Multi-Color QR Codes and Stiefel-Valued Data by Relaxed Regularizations](https://mlsanity.com/paper/2506.22826/) (2025)

## Abstract (arXiv)

We introduce a novel relaxation strategy for denoising hyperbolic-valued data. The main challenge is here the non-convexity of the hyperbolic sheet. Instead of considering the denoising problem directly on the hyperbolic space, we exploit the Euclidean embedding and encode the hyperbolic sheet using a novel matrix representation. For denoising, we employ the Euclidean Tikhonov and total variation (TV) model, where we incorporate our matrix representation. The major contribution is then a convex relaxation of the variational ans"atze allowing the utilization of well-established convex optimization procedures like the alternating directions method of multipliers (ADMM). The resulting denoisers are applied to a real-world Gaussian image processing task, where we simultaneously restore the pixelwise mean and standard deviation of a retina scan series.