2024/04/19 by Robert Beinert, Beinert, Robert, Jonas Bresch +1 · 1 citation
Computer Science · Earth and Planetary Sciences · #65J22 #90C22 #90C25 #94A08 #94A12 #FOS: Mathematics #Image and Signal Denoising Methods #Medical Image Segmentation Techniques #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #Seismic Imaging and Inversion Techniques
paper · pdf · doi:10.48550/arxiv.2404.13181
openalex publication_date 2024/04/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Circle- and sphere-valued data play a significant role in inverse problems like magnetic resonance phase imaging and radar interferometry, in the analysis of directional information, and in color restoration tasks. In this paper, we aim to restore (d-1)-sphere-valued signals exploiting the classical anisotropic total variation on the surrounding d-dimensional Euclidean space. For this, we propose a novel variational formulation, whose data fidelity is based on inner products instead of the usually employed squared norms. Convexifying the resulting non-convex problem and using ADMM, we derive an efficient and fast numerical denoiser. In the special case of binary (0-sphere-valued) signals, the relaxation is provable tight, i.e. the relaxed solution can be used to construct a solution of the original non-convex problem. Moreover, the tightness can be numerically observed for barcode and QR code denoising as well as in higher dimensional experiments like the color restoration using hue and chromaticity and the recovery of SO(3)-valued signals.