Related papers: Bilevel training schemes in imaging for total-vari…
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…
In this paper, we focus on learning optimal parameters for PDE-based image regularization and decomposition. First we learn the regularization parameter and the differential operator for gray-scale image denoising using the fractional…
We present a general variational framework for the training of freeform nonlinearities in layered computational architectures subject to some slope constraints. The regularization that we add to the traditional training loss penalizes the…
We propose a new space-variant regularization term for variational image restoration based on the assumption that the gradient magnitudes of the target image distribute locally according to a half-Generalized Gaussian distribution. This…
Regularisation theory in Banach spaces, and non--norm-squared regularisation even in finite dimensions, generally relies upon Bregman divergences to replace norm convergence. This is comparable to the extension of first-order optimisation…
We consider abstract operator equations $Fu=y$, where $F$ is a compact linear operator between Hilbert spaces $U$ and $V$, which are function spaces on \emph{closed, finite dimensional Riemannian manifolds}, respectively. This setting is of…
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…
Most existing non-blind restoration methods are based on the assumption that a precise degradation model is known. As the degradation process can only be partially known or inaccurately modeled, images may not be well restored. Rain streak…
Traveltime tomography is a very effective tool to reconstruct acoustic, seismic or electromagnetic wave speed distribution. To infer the velocity image of the medium from the measurements of first arrivals is a typical example of ill-posed…
We propose a new constrained optimization approach to hyperspectral (HS) image restoration. Most existing methods restore a desirable HS image by solving some optimization problem, which consists of a regularization term(s) and a…
We give a comprehensive survey on a class of higher order variational problems which are motivated by applications in mathematical imaging. The overall aim of this note is to investigate if and in which manner results from the first…
Inverse problems are fundamental in fields like medical imaging, geophysics, and computerized tomography, aiming to recover unknown quantities from observed data. However, these problems often lack stability due to noise and…
In order to tackle the difficulty associated with the ill-posed nature of the image registration problem, regularization is often used to constrain the solution space. For most learning-based registration approaches, the regularization…
Algorithms for automatically selecting a scalar or locally varying regularization parameter for total variation models with an $L^{\tau}$-data fidelity term, $\tau\in \{1,2\}$, are presented. The automated selection of the regularization…
We study the solutions of infinite dimensional linear inverse problems over Banach spaces. The regularizer is defined as the total variation of a linear mapping of the function to recover, while the data fitting term is a near arbitrary…
The blind image deconvolution is a challenging, highly ill-posed nonlinear inverse problem. We introduce a Multiscale Hierarchical Decomposition Method (MHDM) that is iteratively solving variational problems with adaptive data and…
By the recent advances in computer technology leading to the invention of more powerful processors, the importance of creating models using data training is even greater than ever. Given the significance of this issue, this work tries to…
Overparameterized autoencoder models often memorize their training data. For image data, memorization is often examined by using the trained autoencoder to recover missing regions in its training images (that were used only in their…
We present a method for supervised learning of sparsity-promoting regularizers, a key ingredient in many modern signal reconstruction problems. The parameters of the regularizer are learned to minimize the mean squared error of…
We propose a variational regularization approach based on a multiscale representation called cylindrical shearlets aimed at dynamic imaging problems, especially dynamic tomography. The intuitive idea of our approach is to integrate a…