Abstract Tikhonov regularization with square-norm penalty for linear forward operators has been studied extensively in the literature. However, results on convergence theory are based technical proofs and sometimes difficult to interpret. It is also often not clear how those translate into discrete, numerical setting. In this paper we present a new strategy study properties of method example re...

The total least squares (TLS) method is an appropriate approach for linear systems when not only the right-hand side but also the system matrix is contaminated by some noise. For ill-posed problems regularization is necessary to stabilize the computed solutions. In this presentation we discuss two approaches for regularizing large scale TLS problems. One which is based on adding a quadratic con...

This paper is concerned with a new approach for regularizing problems with discontinuous solutions: regularization for curve representations. The idea of this approach is to represent a (discontinous) function as a curve with parameterization (a(t), b(t)). A combination with nonlinear Tikhonov regularization then yields uniform convergence of the regularized solutions. The method is applied to ...

In this paper we develop a novel criterion for choosing regularization parameters for nonsmooth Tikhonov functionals. The proposed criterion is solely based on the value function, and thus applicable to a broad range of functionals. It is analytically compared with the local minimum criterion, and a posteriori error estimates are derived. An efficient numerical algorithm for computing the minim...

In our paper, we consider Tikhonov regularization in the reproducing Kernel Hilbert Spaces. In this space we derive upper and lower bound of the interval which contains the optimal value of Tikhonov regularization parameter with respect to the sensitivity of the solution without computing the singular values of the corresponding matrix. For the case of normalized kernel, we give an explicit for...

Parameter choice is crucial to regularization-based image deblurring. In this paper, a Monte Carlo method is used to approximate the optimal regularization parameter in the sense of Stein’s unbiased risk estimate (SURE) which has been applied to image deblurring. The proposed algorithm is suitable for the exact deblurring functions as well as those of not being expressed analytically. We justif...

This paper addresses the numerical stability issue on the channelized Hotelling observer (CHO). The CHO is a well-known approach in the medical image quality assessment domain. Many researchers have found that the detection performance of the CHO does not increase with the number of channels, contrary to expectation. And to our knowledge, nobody in this domain has found the reason. We illustrat...

Inspired by Tikhonov regularization, a non-linear conjugate gradient method is proposed with the purpose of simultaneously regularizing and solving the moment matrix equation. The procedure is based on a non-quadratic conjugate gradient algorithm with exact line search, restart and rescale. Applied to the problem of TM scattering by perfectly conducting rectangular cylinders, the method is show...