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...

A selection of unfolding methods commonly used in High Energy Physics is compared. The methods discussed here are: bin-by-bin correction factors, matrix inversion, template fit, Tikhonov regularisation and two examples of iterative methods. Two procedures to choose the strength of the regularisation are tested, namely the L-curve scan and a scan of global correlation coefficients. The advantage...

In this paper, we consider the problem for identifying the unknown source in the Poisson equation. A modified Tikhonov regularization method is presented to deal with illposedness of the problem and error estimates are obtained with an a priori strategy and an a posteriori choice rule to find the regularization parameter. Numerical examples show that the proposed method is effective and stable....

This paper proposes a new approach for choosing the regularization parameters in multiparameter regularization methods when applied to approximate the solution of linear discrete ill-posed problems. We consider both direct methods, such as Tikhonov regularization with two or more regularization terms, and iterative methods based on the projection of a Tikhonov-regularized problem onto Krylov su...

The Tikhonov method is a famous technique for regularizing ill-posed linear problems, wherein a regularization parameter needs to be determined. This article, based on an invariant-manifold method, presents an adaptive Tikhonov method to solve ill-posed linear algebraic problems. The new method consists in building a numerical minimizing vector sequence that remains on an invariant manifold, an...

For the ill-posed linear inverse problem, we propose a hybrid regularization model, which possesses characters of Tikhonov and TV to some extent. Through transformation, is reformulated as an equivalent minimization problem. To solve present two modified iterative shrinkage-thresholding algorithms (MISTA) based on fast algorithm (FISTA) shrinkagethresholding (ISTA). The numerical experiments ar...

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...

We deve lop a met hod of 3-D magne tic anomaly inver­ sion based on traditional Tikhonov regulariza tion the­ ory. We use a minimu m support stabi lizing functional to gene rate a sharp , focused inverse image. An iterative in­ version process is const ructed in the space of weighted model parameters that accelerates the converge nce and robustness of the met hod. The weighting functions are se...

We presents a Born; iterative method, for reconstructing optical properties of turbid media by means of frequency-domain data. The approach is based on iterative solution of a linear perturbation equation, which is derived from the integral from of the Helmholtz wave equation for photon-density waves in each iteration the total field and the associated weight matrix are recalculated based on th...

Two techniques to regularize the diffuse optical tomography inverse problem were compared for a variety of simulated test domains. One method repeats the single-step Tikhonov approach until a stopping criteria is reached, regularizing the inverse problem by scaling the maximum of the diagonal of the inversion matrix with a factor held constant throughout the iterative reconstruction. The second...