Papers › Denoising of Sphere- and SO(3)-Valued Data by Relaxed Tikhonov Regularization
Denoising of Sphere- and SO(3)-Valued Data by Relaxed Tikhonov Regularization
Robert Beinert, Jonas Bresch, Gabriele Steidl
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
Manifold-valued signal- and image processing has received attention due to modern image acquisition techniques. Recently, a convex relaxation of the otherwise nonconvex Tikhonov-regularization for denoising circle-valued data has been proposed by Condat (2022). The circle constraints are here encoded in a series of low-dimensional, positive semi-definite matrices. Using Schur complement arguments, we show that the resulting variational model can be simplified while leading to the same solution. The simplified model can be generalized to higher dimensional spheres and to SO(3)-valued data, where we rely on the quaternion representation of the latter. Standard algorithms from convex analysis can be applied to solve the resulting convex minimization problem. As proof-of-the-concept, we use the alternating direction method of multipliers to demonstrate the denoising behavior of the proposed method. In a series of experiments, we demonstrate the numerical convergence of the signal- or image values to the underlying manifold.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections