This paper presents a regularized least squares algorithm for the restoration and reconstruction of images. A whitening filter of short length provides the regularization function. An adaptive version of the algorithm is developed by matching a weighting function to the regularization function. The adaptive regularization simultaneously leads to proper noise suppression and enhanced resolution ...

Gravity data inversion is one of the important steps in the interpretation of practical gravity data. The inversion result can be obtained by minimization of the Tikhonov objective function. The determination of an optimal regularization parameter is highly important in the gravity data inversion. In this work, an attempt was made to use the active constrain balancing (ACB) method to select the...

In this paper we present a regularization of an H2-minimization based LPV-model generation algorithm. Our goal is to take care of uncertainties in the data, and obtain more robust models when we have few data. We give an interpretation of the regularization, which shows that the regularization has connections to robust optimization and worst-case approaches. We present how to effectively calcul...

We propose a locally regularized snake based on smoothing-spline filtering. The proposed algorithm associates a regularization process with a force equilibrium scheme leading the snake’s deformation. In this algorithm, the regularization is implemented with a smoothing of the deformation forces. The regularization level is controlled through a unique parameter that can vary along the contour. I...

An adjustment scheme for the regularization parameter of a Moreau-Yosida-based regularization, or relaxation, approach to the numerical solution of pointwise state constrained elliptic optimal control problems is introduced. The method utilizes error estimates of an associated finite element discretization of the regularized problems for the optimal selection of the regularization parameter in ...

In a recent paper [24] an algorithm for large-scale Tikhonov regularization in standard form called GKB-FP was proposed and numerically illustrated. In this paper, further insight into the convergence properties of this method is provided and extensions to general-form Tikhonov regularization are introduced. In addition, as alternative to Tikhonov regularization, a preconditioned LSQR method co...

Gated 4D cardiac imaging with C-arm CT scanners suffers from insufficient image quality due to strong angular undersampling. To deal with this problem, we suggest an iterative reconstruction method with spatial and temporal total variation regularization based on an established framework which controls the relative contributions of raw data error minimization and regularization. This new method...

In this paper, several boundary element regularization methods, such as iterative, conjugate gradient, Tikhonov regularization and singular value decomposition methods, for solving the Cauchy problem associated to the Helmholtz equation are developed and compared. Regularizing stopping criteria are developed and the convergence, as well as the stability, of the numerical methods proposed are an...

Generalized Cross Validation (GCV) is a popular approach to determining the regularization parameter in Tikhonov regularization. The regularization parameter is chosen by minimizing an expression, which is easy to evaluate for small-scale problems, but prohibitively expensive to compute for large-scale ones. This paper describes a novel method, based on Gauss-type quadrature, for determining up...

Usually when determining parameters with an inverse method, it is assumed that parameters or properties, other than those being sought, are known exactly. When such known parameters are uncertain, the inverse solution can be very sensitive to the degree of uncertainty. The stochastic regularization method can be modi ed to reduce this sensitivity. This paper presents such a modi cation. In addi...