Edge detection attempts to reconstruct 3-D physical edges from a 2-D image. It is therefore an ill-posed problem, and a regularization procedure is required to convert it into a well-posed problem. This procedure introduces a regularization parameter for adjusting the extent of the regularization eeect: the larger the value of is, the stronger the regularization eeect. Therefore, could be inter...

In this paper we derive a generalizing concept of G-norms, which we call G-sets, which is used to characterize minimizers of non-differentiable regularization functionals. Moreover, the concept is closely related to the definition of slopes as published in a recent book by Ambrosio, Gigli, Savaré. A paradigm of regularization models fitting in this framework is robust bounded variation regulari...

in this paper the inversion of gravity data using l1–norm stabilizer is considered. the inversion is an important step in the interpretation of data. in gravity data inversion, the goal is to estimate density and geometry of the unknown subsurface model from a set of known observation measured on the surface. commonly, rectangular prisms are used to model the subsurface under the survey area. t...

For dimensions close to D = 4, the Feynman integrals in momentum space derived in Chapter 4 do not converge since their integrands fall off too slowly at large momenta. Divergences arising from this short-wavelength region of the integrals are called ultraviolet (UV)-divergences. For massive fields, these are the only divergences of the integrals. In the zero-mass limit relevant for critical ph...

The generalized singular value decomposition (GSVD) often is used to solve Tikhonov regularization problems with a regularization matrix without exploitable structure. This paper describes how the standard methods for the computation of the GSVD of a matrix pair can be simplified in the context of Tikhonov regularization. Also, other regularization methods, including truncated GSVD, are conside...

Large linear discrete ill-posed problems with contaminated data are often solved with the aid of Tikhonov regularization. Commonly used regularization matrices are finite difference approximations of a suitable derivative and are rectangular. This paper discusses the design of square regularization matrices that can be used in iterative methods based on the Arnoldi process for large-scale Tikho...

This paper proposes a novel regularization approach for Extreme Learning Machines. Regularization is performed using a priori spacial information expressed by an affinity matrix. We show that the use of this type of a priori information is similar to perform Tikhonov regularization. Furthermore, if a parameter free affinity matrix is used, like the cosine similarity matrix, regularization is pe...

In this paper we establish a regularization method for Radon measures. Motivated from sparse L regularization we introduce a new regularization functional for the Radon norm, whose properties are then analyzed. We, furthermore, show well-posedness of Radon measure based sparsity regularization. Finally we present numerical examples along with the underlying algorithmic and implementation detail...