Wavelet Sparse Regularization for Manifold-Valued Data
This work addresses sparse regularization for manifold-valued data, which is incremental as it extends existing wavelet methods to the manifold setting.
The authors tackled the problem of sparse regularization for manifold-valued data using an interpolatory wavelet transform, proposing variational models and algorithms for numerical realization, and demonstrated the potential of their schemes through experimental results.
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.