Related papers: Analysis of regularization methods for the solutio…

This paper is concerned with topology optimization based on a level set method using (doubly) nonlinear diffusion equations. Topology optimization using the level set method is called level set-based topology optimization, which is possible…

In this paper, we study the inverse problem for a class of abstract ultraparabolic equations which is well-known to be ill-posed. We employ some elementary results of semi-group theory to present the formula of solution, then show the…

It's well-known that inverse problems are ill-posed and to solve them meaningfully one has to employ regularization methods. Traditionally, the most popular regularization approaches are Variational-type approaches, i.e.,…

These lecture notes evolve around mathematical concepts arising in inverse problems. We start by introducing inverse problems through examples such as differentiation, deconvolution, computed tomography and phase retrieval. This then leads…

In this paper, we introduce a new class of optimization problems whose objective functions are weakly homogeneous relative to the constraint sets. By using the normalization argument in asymptotic analysis, we prove two criteria for the…

In this paper we extend a recent idea of formulating and regularizing inverse problems as minimization problems, so without using a forward operator, thus avoiding explicit evaluation of a parameter-to-state map. We do so by rephrasing…

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…

The main goal of this paper is to present the application of a superiorization methodology to solution of variational inequalities. Within this framework a variational inequality operator is considered as a small perturbation of a convex…

In this paper we propose a novel regularization strategy for the local discontinuous Galerkin method to solve the Hamilton-Jacobi equation in the context of level-set reinitialization. The novel regularization idea works in analogy to…

A new understanding of the notion of regularizer is proposed. It is argued that this new notion is more realistic than the old one and better fits the practical computational needs. An example of the regularizer in the new sense is given. A…

In this paper, we develop a regularized higher-order Taylor based method for solving composite (e.g., nonlinear least-squares) problems. At each iteration, we replace each smooth component of the objective function by a higher-order Taylor…

In this paper we discuss a deterministic form of ensemble Kalman inversion as a regularization method for linear inverse problems. By interpreting ensemble Kalman inversion as a low-rank approximation of Tikhonov regularization, we are able…

Regularizing a linear ill-posed operator equation can be achieved by manipulating the spectrum of the operator's pseudo-inverse. Tikhonov regularization and spectral cutoff are well-known techniques within this category. This paper…

Diverse inverse problems in imaging can be cast as variational problems composed of a task-specific data fidelity term and a regularization term. In this paper, we propose a novel learnable general-purpose regularizer exploiting recent…

We shall investigate randomized algorithms for solving large-scale linear inverse problems with general regularizations. We first present some techniques to transform inverse problems of general form into the ones of standard form, then…

We study the inverse conductivity problem with discontinuous conductivities. We consider, simultaneously, a regularisation and a discretisation for a variational approach to solve the inverse problem. We show that, under suitable choices of…

We introduce an algorithm to solve linear inverse problems regularized with the total (gradient) variation in a gridless manner. Contrary to most existing methods, that produce an approximate solution which is piecewise constant on a fixed…

This paper is concerned with the numerical solution of a class of variational inequalities of the second kind, involving the $p$-Laplacian operator. This kind of problems arise, for instance, in the mathematical modelling of non-Newtonian…

In this paper, we address the problem of approximating solutions of ill-posed problems using mollification. We quickly review existing mollification regularization methods and provide two new approximate solutions to a general ill-posed…

This paper focuses on the regularization of backward time-fractional diffusion problem on unbounded domain. This problem is well-known to be ill-posed, whence the need of a regularization method in order to recover stable approximate…