Name
Title | ||
|---|---|---|
Regularization with Metric Double Integrals of Functions with Values in a Set of Vectors |
Abstract | ||
|---|---|---|
We present an approach for variational regularization of inverse and imaging problems for recovering functions with values in a set of vectors. We introduce regularization functionals, which are derivative-free double integrals of such functions. These regularization functionals are motivated from double integrals, which approximate Sobolev semi-norms of intensity functions. These were introduced in Bourgain et al. (Another look at Sobolev spaces. In: Menaldi, Rofman, Sulem (eds) Optimal control and partial differential equations-innovations and applications: in honor of professor Alain Bensoussan’s 60th anniversary, IOS Press, Amsterdam, pp 439–455, 2001). For the proposed regularization functionals, we prove existence of minimizers as well as a stability and convergence result for functions with values in a set of vectors. |
Year | DOI | Venue |
|---|---|---|
2019 | 10.1007/s10851-018-00869-6 | Journal of Mathematical Imaging and Vision |
Keywords | Field | DocType |
Regularization, Manifold-valued data, Non-convex, Metric, Double integral, Fractional Sobolev space, Bounded variation | Convergence (routing),Applied mathematics,Inverse,Discrete mathematics,Optimal control,Sobolev space,Partial derivative,Regularization (mathematics),Multiple integral,Mathematics | Journal |
Volume | Issue | ISSN |
61 | 6 | 0924-9907 |
Citations | PageRank | References |
0 | 0.34 | 17 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| R. Ciak | 1 | 7 | 0.83 |
| Melanie Hirzmann | 2 | 0 | 0.34 |
| Otmar Scherzer | 3 | 346 | 52.10 |