A regularization method based on the non-extensive maximum entropy principle is devised. Special emphasis is given to the q = 1=2 case. We show that, when the residual principle is considered as constraint, the q = 1=2 generalized distribution of Tsallis yields a regularized solution for bad-conditioned problems. The so devised regularized distribution is endowed with a component which correspo...

This paper proposes an iterative computation of sparse representations of functions defined on Rd , which exploits a formulation of the sparsification problem equivalent to Support Vector Machine and based on Tikhonov regularization. Through this equivalent formulation, the sparsification reduces to an approximation problem with a Tikhonov regularizer, which selects the null coefficients of the...

Methods: This study relies solely on simulations of a transmit-array head coil at 7T. The coil consisted of 8 stripline dipoles distributed every 40degrees on a cylindrical surface of 27.6-cm diameter, leaving an open space in front of the patient’s eyes. An eight-anatomical structure human head model (provided by Aarkid, East Lothian, Scotland) was placed at the centre of the coil. The same he...

We investigate the use of Tikhonov regularization with the minimum support stabilizer for underdetermined 2-D inversion of gravity data. This stabilizer produces models with nonsmooth properties which is useful for identifying geologic structures with sharp boundaries. A very important aspect of using Tikhonov regularization is the choice of the regularization parameter that controls the trade ...

Tikhonov regularization is one of the most popular approaches to solving linear discrete ill-posed problems. The choice of regularization matrix may significantly affect the quality of the computed solution. When the regularization matrix is the identity, iterated Tikhonov regularization can yield computed approximate solutions of higher quality than (standard) Tikhonov regularization. This pap...

Abstract. The χ-principle generalizes the Morozov discrepancy principle to the augmented residual of the Tikhonov regularized least squares problem. For weighting of the data fidelity by a known Gaussian noise distribution on the measured data and, when the stabilizing, or regularization, term is considered to be weighted by unknown inverse covariance information on the model parameters, the mi...

Tikhonov regularization is one of the most popular methods for solving linear systems of equations or linear least-squares problems with a severely ill-conditioned matrix and an error-contaminated data vector (right-hand side). This regularization method replaces the given problem by a penalized least-squares problem. It is well known that Tikhonov regularization in standard form may yield appr...

This paper is concerned with the uniqueness of the Maximum a Posteriori estimate for restoration problems of data corrupted by Poisson noise, when we have to minimize a combination of the generalized Kullback–Leibler divergence and a regularization penalty function. The aim of this paper is to prove the uniqueness result for 2D and 3D problems for several penalty functions, such as an edge pres...