Related papers: Bilevel Optimization, Deep Learning and Fractional…
We introduce and study a mathematical framework for a broad class of regularization functionals for ill-posed inverse problems: Regularization Graphs. Regularization graphs allow to construct functionals using as building blocks linear…
Regularization techniques are widely employed in optimization-based approaches for solving ill-posed inverse problems in data analysis and scientific computing. These methods are based on augmenting the objective with a penalty function,…
Optical diffraction tomography measures the three-dimensional refractive index map of a specimen and visualizes biochemical phenomena at the nanoscale in a non-destructive manner. One major drawback of optical diffraction tomography is poor…
Image deblurring is relevant in many fields of science and engineering. To solve this problem, many different approaches have been proposed and among the various methods, variational ones are extremely popular. These approaches are…
The use of the fractional Laplacian in image denoising and regularization of inverse problems has enjoyed a recent surge in popularity, since for discontinuous functions it can behave less aggressively than methods based on $H^1$ norms,…
For the past few years, Deep Neural Network (DNN) robustness has become a question of paramount importance. As a matter of fact, in sensitive settings misclassification can lead to dramatic consequences. Such misclassifications are likely…
A common challenge in regression is that for many problems, the degrees of freedom required for a high-quality solution also allows for overfitting. Regularization is a class of strategies that seek to restrict the range of possible…
In the context of image processing, given a $k$-th order, homogeneous and linear differential operator with constant coefficients, we study a class of variational problems whose regularizing terms depend on the operator. Precisely, the…
We address the optimization problem in a data-driven variational reconstruction framework, where the regularizer is parameterized by an input-convex neural network (ICNN). While gradient-based methods are commonly used to solve such…
We study a class of bilevel convex optimization problems where the goal is to find the minimizer of an objective function in the upper level, among the set of all optimal solutions of an optimization problem in the lower level. A wide range…
This paper introduces a novel double regularization scheme for bilevel optimization problems whose lower-level problem is composite and convex, but not necessarily strongly convex, in the lower-level variable. The analysis focuses on the…
Capturing complex high-order interactions among data is an important task in many scenarios. A common way to model high-order interactions is to use hypergraphs whose topology can be mathematically represented by tensors. Existing methods…
The emergence of deep-learning-based methods to solve image-reconstruction problems has enabled a significant increase in reconstruction quality. Unfortunately, these new methods often lack reliability and explainability, and there is a…
We propose a functional lifting-based convex relaxation of variational problems with Laplacian-based second-order regularization. The approach rests on ideas from the calibration method as well as from sublabel-accurate continuous…
Inverse problems are key issues in several scientific areas, including signal processing and medical imaging. Data-driven approaches for inverse problems aim for learning model and regularization parameters from observed data samples, and…
In this paper we present a new regularization term for variational image restoration which can be regarded as a space-variant anisotropic extension of the classical isotropic Total Variation (TV) regularizer. The proposed regularizer comes…
Recently, lower-level constrained bilevel optimization has attracted increasing attention. However, existing methods mostly focus on either deterministic cases or problems with linear constraints. The main challenge in stochastic cases with…
We consider a bilevel optimisation approach for parameter learning in higher-order total variation image reconstruction models. Apart from the least squares cost functional, naturally used in bilevel learning, we propose and analyse an…
In this work, we address the solution of both linear and nonlinear ill-posed inverse problems by developing a novel graph-based regularization framework, where the regularization term is formulated through an iteratively updated graph…
In this article, we propose a novel regularization method for a class of nonlinear inverse problems that is inspired by an application in quantitative magnetic resonance imaging (qMRI). The latter is a special instance of a general…