Bilevel Parameter Optimization for Nonlocal Image Denoising Models
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
We propose a bilevel optimization approach for the determination of parameters in nonlocal image denoising. We consider both spatial weights in front of the fidelity term, as well as weights within the kernel of the nonlocal operator. In both cases we investigate the differentiability of the solution operator in function spaces and derive a first order optimality system that characterizes local minima. For the numerical solution of the problems, we propose a second-order optimization algorithm in combination with a finite element discretization of the nonlocal denoising models and a computational strategy for the solution of the resulting dense linear systems. Several experiments are run in order to show the suitability of our approach.
- Research Organization:
- Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
- Sponsoring Organization:
- USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
- DOE Contract Number:
- AC04-94AL85000; NA0003525
- OSTI ID:
- 1592945
- Report Number(s):
- SAND--2019-14566R; 682528
- Country of Publication:
- United States
- Language:
- English
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