Name
Abstract | ||
|---|---|---|
We analyze a new notion of total anisotropic higher-order variation which, differently from total generalized variation in [K. Bredies, K. Kunisch, and T. Pock, SIAM J. Imaging Sci., 3 (2010), pp. 492-526], quantifies for possibly nonsymmetric tensor fields their variations at arbitrary order weighted by possibly inhomogeneous, smooth elliptic anisotropies. We prove some properties of this total variation and of the associated spaces of tensors with finite variations. We show the existence of solutions to a related regularity-fidelity optimization problem. We also prove a decomposition formula which appears to be helpful for the design of numerical schemes, as shown in a companion paper, where several applications to image processing are studied. |
Year | DOI | Venue |
|---|---|---|
2020 | 10.1137/19M1239210 | SIAM JOURNAL ON IMAGING SCIENCES |
Keywords | DocType | Volume |
anisotropic total variation,higher-order total variation,variational model | Journal | 13 |
Issue | ISSN | Citations |
1 | 1936-4954 | 0 |
PageRank | References | Authors |
0.34 | 0 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Simone Parisotto | 1 | 1 | 1.36 |
| Simon Masnou | 2 | 124 | 9.26 |
| Carola-Bibiane Schönlieb | 3 | 334 | 39.39 |