Bilevel parameter optimization for learning nonlocal image denoising models

Technical Report · Wed May 06 04:00:00 EDT 2020

DOI:https://doi.org/10.2172/1617438· OSTI ID:1617438

D'Elia, Marta ^[1]; De los Reyes, Juan Carlos ^[2]; Trujillo, Andres ^[2]

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1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2. Escuela Politécnica Nacional, Quito (Ecuador). Research Center on Mathematical Modelling (MODEMAT)

We propose a bilevel optimization approach for the estimation of parameters in nonlocal image denoising models. The parameters we consider are both the space-dependent fidelity weight and 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 trust-region algorithm in combination with a finite element discretization of the nonlocal denoising models and we introduce a computational strategy for the solution of the resulting dense linear systems. Several experiments illustrate the applicability and effectiveness 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: 1617438
• Report Number(s): SAND--2020-4564R; 685801
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING