In this paper we describe a new approach to shar p boundary geophy sical inversion. We demon strate that regularized inversion with a minimum support stabilizer can be implemented by using a specially designed nonl inear parametrization of the mode l parameters . Thi s parametrization plays the same role as transformation into the space of the weighted model parameters, introd uced in the origi...

In this work, a new iterative method is proposed for obtaining the approximate solution of a class of Hammerstein type Integral Equations System. The main structure of this method is based on the Richardson iterative method for solving an algebraic linear system of equations. Some conditions for existence and unique solution of this type equations are imposed. Convergence analysis and error bou...

Inverse source problems arise often in real-world applications, such as localizing unknown groundwater contaminant sources. Being different from Tikhonov regularization, the quasi-boundary value method has been studied an effective way for regularizing inverse problems, which was shown to achieve optimal order convergence under suitable assumptions. However, fast direct or iterative solvers res...

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...

Estimating the generalization performance of learning algorithms is one of the main purposes of machine learning theoretical research. The previous results describing the generalization ability of Tikhonov regularization algorithm are almost all based on independent and identically distributed (i.i.d.) samples. In this paper we go far beyond this classical framework by establishing the bound on...

‎In this paper‎, ‎we consider an inverse boundary value problem for two-dimensional heat equation in an annular domain‎. ‎This problem consists of determining the temperature on the interior boundary curve from the Cauchy data (boundary temperature and heat flux) on the exterior boundary curve‎. ‎To this end‎, ‎the boundary integral equation method is used‎. ‎Since the resulting system of linea...

Images in fluorescence microscopy are inherently blurred due to the limit of diffraction of light. The purpose of deconvolution microscopy is to compensate numerically for this degradation. Deconvolution is widely used to restore fine details of 3D biological samples. Unfortunately, dealing with deconvolution tools is not straightforward. Among others, end users have to select the appropriate a...

The present paper is concerned with developing tensor iterative Krylov subspace methods to solve large multi-linear equations. We use the T-product for two tensors define tubal global Arnoldi and Golub-Kahan bidiagonalization algorithms. Furthermore, we illustrate how tensor-based approaches can be exploited ill-posed problems arising from recovering blurry multichannel (color) images videos, u...