Total Generalized Variation (TGV) has recently been introduced as penalty functional for modelling images with edges as well as smooth variations [2]. It can be interpreted as a “sparse” penalization of optimal balancing from the first up to the kth distributional derivative and leads to desirable results when applied to image denoising, i.e., L-fitting with TGV penalty. The present paper studi...

The estimation of the covariance matrix is a pivotal step in several statistical tasks. In particular, the estimation becomes challenging for high dimensional representations of data when few samples are available. Using the standard Maximum Likelihood estimation (MLE) when the number of samples are lower than the dimension of the data can lead to incorrect estimation e.g. of the covariance mat...

The purpose of this study is to propose a high-accuracy and fast numerical method for the Cauchy problem of the Laplace equation. Our problem is directly discretized by the method of fundamental solutions (MFS). The Tikhonov regularization method stabilizes a numerical solution of the problem for given Cauchy data with high noises. The accuracy of the numerical solution depends on a regularizat...

We introduce a local volatility model for the valuation of options on commodity futures by using European vanilla option prices. The corresponding calibration problem is addressed within an online framework, allowing the use of multiple price surfaces. Since uncertainty in the observation of the underlying future prices translates to uncertainty in data locations, we propose a model-based adjus...

The rational function model (RFM) utilized for high resolution satellite imagery (HRSI) provides a transformation from image to object space coordinates in a geographic reference system. Compared with the rigorous model based on the collinearity condition equation or the affine model, the RFM with 80 coefficients would be over parameterized. That would result in an ill-conditioned normal equati...

Non-Fourier heat conduction model with dual phase lag wave-diffusion model was analyzed by using well-conditioned asymptotic wave evaluation (WCAWE) and finite element method (FEM). The non-Fourier heat conduction has been investigated where the maximum likelihood (ML) and Tikhonov regularization technique were used successfully to predict the accurate and stable temperature responses without t...

This paper presents a novel physics-driven spatiotemporal regularization (STRE) method for high-dimensional predictive modeling in complex healthcare systems. This model not only captures the physics-based interrelationship between time-varying explanatory and response variables that are distributed in the space, but also addresses the spatial and temporal regularizations to improve the predict...

When deriving rates of convergence for the approximations generated by the application of Tikhonov regularization to ill–posed operator equations, assumptions must be made about the nature of the stabilization (i.e., the choice of the seminorm in the Tikhonov regularization) and the regularity of the least squares solutions which one looks for. In fact, it is clear from works of Hegland, Engl a...

This paper proposes a new approach for choosing the regularization parameters in multiparameter regularization methods when applied to approximate the solution of linear discrete ill-posed problems. We consider both direct methods, such as Tikhonov regularization with two or more regularization terms, and iterative methods based on the projection of a Tikhonov-regularized problem onto Krylov su...

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 approximate solutions of the inverse problem, we propose a Tikhonov-type regularization approach coupled with a level-set framework. We prove the existence of g...