Related papers: Convergence analysis of Tikhonov regularization fo…
It is common to have to process signals or images whose values are cyclic and can be represented as points on the complex circle, like wrapped phases, angles, orientations, or color hues. We consider a Tikhonov-type regularization model to…
We study multi-parameter regularization (multiple penalties) for solving linear inverse problems to promote simultaneously distinct features of the sought-for objects. We revisit a balancing principle for choosing regularization parameters…
Learning kernels in operators from data lies at the intersection of inverse problems and statistical learning, providing a powerful framework for capturing non-local dependencies in function spaces and high-dimensional settings. In contrast…
In this paper we the formulation of inverse problems as constrained minimization problems and their iterative solution by gradient or Newton type. We carry out a convergence analysis in the sense of regularization methods and discuss…
We provide theoretical analysis of the statistical and computational properties of penalized $M$-estimators that can be formulated as the solution to a possibly nonconvex optimization problem. Many important estimators fall in this…
Many inverse problems can be described by a PDE model with unknown parameters that need to be calibrated based on measurements related to its solution. This can be seen as a constrained minimization problem where one wishes to minimize the…
We consider the efficient minimization of a nonlinear, strictly convex functional with $\ell_1$-penalty term. Such minimization problems appear in a wide range of applications like Tikhonov regularization of (non)linear inverse problems…
We consider a misspecified optimization problem that requires minimizing a function f(x;q*) over a closed and convex set X where q* is an unknown vector of parameters that may be learnt by a parallel learning process. In this context, We…
We consider choice of the regularization parameter in Tikhonov method if the noise level of the data is unknown. One of the best rules for the heuristic parameter choice is the quasi-optimality criterion where the parameter is chosen as the…
We investigate a level-set type method for solving ill-posed problems, with the assumption that the solutions are piecewise, but not necessarily constant functions with unknown level sets and unknown level values. In order to get stable…
In this paper, we propose a Tikhonov-like regularization for dynamical systems associated with non-expansive operators defined in closed and convex sets of a Hilbert space. We prove the well-posedness and the strong convergence of the…
The problem of object restoration in the case of spatially incoherent illumination is considered. A regularized solution to the inverse problem is obtained through a probabilistic approach, and a numerical algorithm based on the statistical…
We consider a class of inexact Newton regularization methods for solving nonlinear inverse problems in Hilbert scales. Under certain conditions we obtain the order optimal convergence rate result.
Neural networks have emerged as effective tools for solving ill-posed inverse problems. In many scientific applications, however, observational training data are insufficient, and learned inverse operators must instead be trained on…
We deal with the shape reconstruction of inclusions in elastic bodies. For solving this inverse problem in practice, data fitting functionals are used. Those work better than the rigorous monotonicity methods from [5], but have no…
This paper focuses on scattered data fitting problems on spheres. We study the approximation performance of a class of weighted spectral filter algorithms, including Tikhonov regularization, Landaweber iteration, spectral cut-off, and…
A space-time interface-fitted approximation of an inverse source problem for the advection-diffusion equation with moving subdomains is investigated. The problem is reformulated as an optimization problem using Tikhonov regularization. A…
Problems in machine learning (ML) can involve noisy input data, and ML classification methods have reached limiting accuracies when based on standard ML data sets consisting of feature vectors and their classes. Greater accuracy will…
We investigate Tikhonov regularization methods for nonlinear ill-posed problems in Banach spaces, where the penalty term is described by Bregman distances. We prove convergence and stability results. Moreover, using appropriate source…
We provide estimators for a large class of inverse problems, including nonlinear inverse problems. Using complexity regularization technics we provide adaptive estimators achieving the best rate over the collection of models.