The purpose of this study is to propose a high-accuracy and fast numerical method for the Cauchy problem of the Laplace equation. Our problem is directly discretized by the method of fundamental solutions (MFS). The Tikhonov regularization method stabilizes a numerical solution of the problem for given Cauchy data with high noises. The accuracy of the numerical solution depends on a regularizat...

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 A. This method replaces the given problem by a penalized least-squares problem. The present paper discusses measuring the residual error (discrepancy) in Tikhonov regularization with a seminorm that uses a fractional power of ...

Many numerical methods for the solution of linear ill-posed problems apply Tikhonov regularization. This paper presents a modification of a numerical method proposed by Golub and von Matt for quadratically constrained least-squares problems and applies it to Tikhonov regularization of large-scale linear discrete ill-posed problems. The method is based on partial Lanczos bidiagonalization and Ga...

Model-based elastography is fraught with problems owing to the ill-posed nature of the inverse elasticity problem. To overcome this limitation, we have recently developed a novel inversion scheme that incorporates a priori information concerning the mechanical properties of the underlying tissue structures, and the variance incurred during displacement estimation in the modulus image reconstruc...

Discrete coefficients filter banks reduce the computational complexity for subband image coding system. A new time domain formulation is proposed for the design of near-perfect reconstruction filter banks with discrete coefficients. It can be shown that the proposed design method yields l 2 optimal solution which is considered to be practical in image coding applications. In addition, special e...

conclusions parasitic contamination of fresh herbs sold in izeh may pose a health risk to consumers if eaten as unwashed or improperly washed. results parasitic pollution was detected in 3.5% of the examined samples, including cryptosporidium spp. oocyst (1.5%), giardia spp. cyst (1%), blastocystis spp. cyst (0.5%) and taenia spp. egg (0.5%). materials and methods four hundred samples of fresh ...

L-filters are very successful at restoration of signals corrupted by noise. However, their on-line design in real-time applications is practically impossible, since the computation of optimal L-filter coefficients with the existing methods based on numerical approximations are extremely time consuming. In this paper, we present a new design methodology for L-filters. Our approach allows one to ...

This paper is concerned with the solution of large-scale linear discrete ill-posed problems. The determination of a meaningful approximate solution of these problems requires regularization. We discuss regularization by the Tikhonov method and by truncated iteration. The choice of regularization matrix in Tikhonov regularization may significantly affect the quality of the computed approximate s...