Journal
MULTISCALE MODELING & SIMULATION
Volume 7, Issue 3, Pages 1005-1028Publisher
SIAM PUBLICATIONS
DOI: 10.1137/070698592
Keywords
nonlocal operators; regularization; total variation; variational methods; spectral graph theory; Hamilton-Jacobi equations
Funding
- NSF [ITR ACI-0321917, DMS-0312222, DMS-0714087]
- NIH [P20 MH65166]
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We propose the use of nonlocal operators to de. ne new types of flows and functionals for image processing and elsewhere. A main advantage over classical PDE-based algorithms is the ability to handle better textures and repetitive structures. This topic can be viewed as an extension of spectral graph theory and the diffusion geometry framework to functional analysis and PDE-like evolutions. Some possible applications and numerical examples are given, as is a general framework for approximating Hamilton-Jacobi equations on arbitrary grids in high demensions, e. g., for control theory.
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