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Bibliographic Details
Main Authors: Beinert, Robert, Bresch, Jonas
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2410.16149
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Table of Contents:
  • 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 ansätze 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.