31 citations · 33 across the 5 of their papers we have counts for
7 papers
Analysis of Four-Dimensional Variational Data Assimilation Problems in Low Regularity Spaces
Paula Castro, Juan Carlos De los Reyes, Ira Neitzel
We carry out a rigorous analysis of four-dimensional variational data assimilation (-VAR) problems for linear and semilinear parabolic partial differential equations. Continuit…
Optimal control of a nonsmooth PDE arising in the modeling of shear-thickening fluids
Juan Carlos De los Reyes, Paola Quiloango
This paper focuses on the analysis of an optimal control problem governed by a nonsmooth quasilinear partial differential equation that models a stationary incompressible shear-thi…
Bilevel Imaging Learning Problems as Mathematical Programs with Complementarity Constraints: Reformulation and Theory
Juan Carlos De los Reyes
We investigate a family of bilevel imaging learning problems where the lower-level instance corresponds to a convex variational model involving first- and second-order nonsmooth sp…
Bilevel parameter learning for nonlocal image denoising models
M. D'Elia, J. C. De los Reyes, A. Miniguano-Trujillo
We propose a bilevel optimization approach for the estimation of parameters in nonlocal image denoising models. The parameters we consider are both the fidelity weight and weights…
Infimal convolution of data discrepancies for mixed noise removal
Luca Calatroni, Juan Carlos De Los Reyes, Carola-Bibiane Schönlieb
We consider the problem of image denoising in the presence of noise whose statistical properties are a combination of two different distributions. We focus on noise distributions t…
Learning optimal spatially-dependent regularization parameters in total variation image restoration
C. Chung, J. C. De los Reyes, C. B. Schoenlieb
We consider a bilevel optimization approach in function space for the choice of spatially dependent regularization parameters in TV image restoration models. First- and second-orde…