Wavelet Sparse Regularization for Manifold-Valued Data

TL;DR

This paper introduces wavelet-based sparse regularization techniques for manifold-valued data, establishing their theoretical foundations, algorithms, and demonstrating their effectiveness through experiments.

Contribution

It proposes variational models for wavelet sparse regularization on manifolds, along with algorithms and analysis of their well-posedness.

Findings

Successful implementation of algorithms for manifold data

Experimental results demonstrate potential applications

Theoretical analysis confirms model well-posedness

Abstract

In this paper, we consider the sparse regularization of manifold-valued data with respect to an interpolatory wavelet/multiscale transform. We propose and study variational models for this task and provide results on their well-posedness. We present algorithms for a numerical realization of these models in the manifold setup. Further, we provide experimental results to show the potential of the proposed schemes for applications.