In this paper‎, two inverse problems of determining an unknown source term in a parabolic‎ equation are considered‎. ‎First‎, ‎the unknown source term is ‎estimated in the form of a combination of Chebyshev functions‎. ‎Then‎, ‎a numerical algorithm based on Chebyshev polynomials is presented for obtaining the solution of the problem‎. ‎For solving the problem‎, ‎the operational matrices of int...

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...

Early diagnosis of stroke type by imaging is one the most important tasks for patients. In this article, we propose a new approach to reconstruct brain image with high accuracy and quality. approach, first use Born iterative method image. Then comparing set MRI-based images, using structural similarity index measure criterion, choose best as reference Finally, distorted or along generalized Tik...

This paper considers an efficient iterative approach to solve separable nonlinear least squares problems that arise in large scale inverse problems. A variable projection GaussNewton method is used to solve the nonlinear least squares problem, and Tikhonov regularization is incorporated using an iterative Lanczos hybrid scheme. Regularization parameters are chosen automatically using a weighted...

The regularization properties of the total generalized variation (TGV) functional for the solution of linear inverse problems by means of Tikhonov regularization are studied. Considering the associated minimization problem for general symmetric tensor fields, the wellposedness is established in the space of symmetric tensor fields of bounded deformation, a generalization of the space of functio...

Electrical capacitance tomography (ECT) technology has the softfield nature and the ill-posed problems. To solve the problem of low imaging quality by standard Tikhonov regularization, a wavelet fusion algorithm based on Tikhonov regularization is proposed in this paper. Firstly, Tikhonov regularization method is used to solve ill-posed characteristic of system inverse problem, then the initial...

In the Multi Input Multi Output (MIMO) antenna system, it is known that the Linear Minimum Mean Squared Error (MMSE) receiver is equivalent to Tikhonov regularization. Given that, we develop a family of generalized receivers based on regularization with different penalty functions that penalize the received symbols outside the convex hull of the modulating constellation. For illustration purpos...

Generalized Tikhonov well-posedness is investigated for the problem of minimization of error functionals over admissible sets formed by variable-basis functions, i.e., linear combinations of a fixed number of elements chosen from a given basis without a prespecified ordering. For variablebasis functions of increasing complexity, rates of decrease of infima of error functionals are estimated. Up...

Abstract Surface heat flux estimation of high-speed aircrafts is an inverse problem and high system ill-posedness usually leading to instability low accuracy. In this study, efficient method proposed solve it stably. The identification equation established based on the superposition principle. Tikhonov regularization with parameter determined by generalized cross validation applied reduce sensi...