The "Krein" regularization method of quantum field theory is studied, inspired by the Krein space quantization and metric fluctuations. It was previously considered in one-loop approximation, this paper generalized to all orders perturbation theory. We directly recover physical results obtained starting from standard QFT imposing renormalization conditions. By applying our approach curved space...

In image processing, it is often desirable to remove noise, smooth or sharpen image features, or to otherwise enhance the image. Total Variation (TV) based regularization is a model case of geometry-driven diiusion for image processing. In our papers 14] and 15], we analyze the precise eeects of TV based regularization by analytically nding exact solutions to the TV regularization problem. In t...

Inverse scale space methods are derived as asymptotic limits of iterative regularization methods. They have proven to be efficient methods for denoising of gray valued images and for the evaluation of unbounded operators. In the beginning, inverse scale space methods have been derived from iterative regularization methods with squared Hilbert norm regularization terms, and later this concept wa...

In this paper, we study the multi-parameter Tikhonov regularization method which adds multiple different penalties to exhibit multi-scale features of the solution. An optimal error bound of the regularization solution is obtained by a priori choice of multiple regularization parameters. Some theoretical results of the regularization solution about the dependence on regularization parameters are...

In parallel imaging, the signal-to-noise ratio (SNR) of sensitivity encoding (SENSE) reconstruction is usually degraded by the ill-conditioning problem, which becomes especially serious at large acceleration factors. Existing regularization methods have been shown to alleviate the problem. However, they usually suffer from image artifacts at high acceleration factors due to the large data incon...

We consider a local regularization method for the solution of first-kind Volterra integral equations with convolution kernel. The local regularization is based on a splitting of the original Volterra operator into “local” and “global” parts, and a use of Tikhonov regularization to stabilize the inversion of the local operator only. The regularization parameters for the local procedure include t...

Abstract Local regularization methods allow for the application of sequential solution techniques for the solution of Volterra problems, retaining the causal structure of the original Volterra problem and leading to fast solution techniques. Stability and convergence of these methods was shown to hold on a large class of linear Volterra problems, i.e., the class of ν-smoothing problems for ν = ...

Electrical impedance tomography (EIT) is a technique for determining the electrical conductivity and permittivity distribution inside a medium from measurements made on its surface. The impedance distribution reconstruction in EIT is a nonlinear inverse problem that requires the use of a regularization method. The generalized Tikhonov regularization methods are often used in solving inverse pro...

Ill posed problems constitute the mathematical model of a large variety of applications. Aim of this paper is to define an iterative algorithm finding the solution of a regularization problem. The method minimizes a function constituted by a least squares term and a generally nonlinear regularization term, weighted by a regularization parameter. The proposed method computes a sequence of iterat...