Wavelet sparse regularization for manifold-valued data. (English) Zbl 1457.94026
Summary: 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.
MSC:
| 94A08 | Image processing (compression, reconstruction, etc.) in information and communication theory |
| 42C40 | Nontrigonometric harmonic analysis involving wavelets and other special systems |
| 90C90 | Applications of mathematical programming |
| 65T60 | Numerical methods for wavelets |
| 53B99 | Local differential geometry |
| 53C35 | Differential geometry of symmetric spaces |
| 65K10 | Numerical optimization and variational techniques |
Keywords:
manifold-valued data; sparse regularization; interpolatory wavelets; interpolatory multiscale transforms; denoising; symmetric spacesReferences:
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