Related papers: Superiorized Regularization of Inverse Problems
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 problem of numerical differentiation can be thought of as an inverse problem by considering it as solving a Volterra equation. It is well known that such inverse integral problems are ill-posed and one requires regularization methods to…
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…
Regularization is a powerful technique for extracting useful information from noisy data. Typically, it is implemented by adding some sort of norm constraint to an objective function and then exactly optimizing the modified objective…
In this paper, we investigate iterative methods that are based on sampling of the data for computing Tikhonov-regularized solutions. We focus on very large inverse problems where access to the entire data set is not possible all at once…
The superiorization methodology can be thought of as lying conceptually between feasibility-seeking and constrained minimization. It is not trying to solve the full-fledged constrained minimization problem composed from the modeling…
The classical approach to inverse problems is based on the optimization of a misfit function. Despite its computational appeal, such an approach suffers from many shortcomings, e.g., non-uniqueness of solutions, modeling prior knowledge,…
This paper surveys an important class of methods that combine iterative projection methods and variational regularization methods for large-scale inverse problems. Iterative methods such as Krylov subspace methods are invaluable in the…
Machine learning techniques for the solution of inverse problems have become an attractive approach in the last decade, while their theoretical foundations are still in their infancy. In this chapter we want to pursue the study of…
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…
We propose the superiorization of incremental algorithms for tomographic image reconstruction. The resulting methods follow a better path in its way to finding the optimal solution for the maximum likelihood problem in the sense that they…
In this chapter we provide a theoretically founded investigation of state-of-the-art learning approaches for inverse problems from the point of view of spectral reconstruction operators. We give an extended definition of regularization…
The superiorization methodology is intended to work with input data of constrained minimization problems, that is, a target function and a set of constraints. However, it is based on an antipodal way of thinking to what leads to constrained…
Variational regularization of ill-posed inverse problems is based on minimizing the sum of a data fidelity term and a regularization term. The balance between them is tuned using a positive regularization parameter, whose automatic choice…
In this paper we consider new regularization methods for linear inverse problems of dynamic type. These methods are based on dynamic programming techniques for linear quadratic optimal control problems. Two different approaches are…
We review the superiorization methodology, which can be thought of, in some cases, as lying between feasibility-seeking and constrained minimization. It is not quite trying to solve the full fledged constrained minimization problem; rather,…
Linear superiorization (abbreviated: LinSup) considers linear programming (LP) problems wherein the constraints as well as the objective function are linear. It allows to steer the iterates of a feasibility-seeking iterative process toward…
Regularisation is commonly used in iterative methods for solving imaging inverse problems. Many algorithms involve the evaluation of the proximal operator of the regularisation term in every iteration, leading to a significant computational…
Connected with the rise of interest in inverse problems is the development and analysis of regularization methods, which are a necessity due to the ill-posedness of inverse problems. Tikhonov-type regularization methods are very popular in…
This paper discusses basic results and recent developments on variational regularization methods, as developed for inverse problems. In a typical setup we review basic properties needed to obtain a convergent regularization scheme and…