87 citations · 197 across the 13 of their papers we have counts for
13 papers · 1 filter
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…
Bilevel parameter learning for higher-order total variation regularisation models
J. C. De los Reyes, C. -B. Schönlieb, T. Valkonen
We consider a bilevel optimisation approach for parameter learning in higher-order total variation image reconstruction models. Apart from the least squares cost functional, natura…
Bilevel approaches for learning of variational imaging models
Luca Calatroni, Cao Chung, Juan Carlos De Los Reyes +2
We review some recent learning approaches in variational imaging, based on bilevel optimisation, and emphasize the importance of their treatment in function space. The paper covers…
The structure of optimal parameters for image restoration problems
Juan Carlos De Los Reyes, Carola-Bibiane Schönlieb, Tuomo Valkonen
We study the qualitative properties of optimal regularisation parameters in variational models for image restoration. The parameters are solutions of bilevel optimisation problems…
Second-order orthant-based methods with enriched Hessian information for sparse -optimization
J. C. De los Reyes, E. Loayza, P. Merino
We present a second order algorithm, based on orthantwise directions, for solving optimization problems involving the sparsity enhancing -norm. The main idea of our method…
Strong stationarity conditions for a class of optimization problems governed by variational inequalities of the 2nd kind
Juan-Carlos De Los Reyes, Christian Meyer
We investigate optimality conditions for optimization problems constrained by a class of variational inequalities of the second kind. Based on a nonsmooth primal-dual reformulation…
Dynamic sampling schemes for optimal noise learning under multiple nonsmooth constraints
Luca Calatroni, Juan Carlos De Los Reyes, Carola-Bibiane Schönlieb
We consider the bilevel optimisation approach proposed by De Los Reyes, Schönlieb (2013) for learning the optimal parameters in a Total Variation (TV) denoising model featuring for…
Image denoising: learning noise distribution via PDE-constrained optimization
Juan-Carlos De los Reyes, Carola-Bibiane Schönlieb
We propose a PDE-constrained optimization approach for the determination of noise distribution in total variation (TV) image denoising. An optimization problem for the determinatio…