Several numerical methods for the solution of large linear ill-posed problems combine Tikhonov regularization with an iterative method based on partial Lanczos bidiagonalization of the operator. This paper discusses the determination of the regularization parameter and the dimension of the Krylov subspace for this kind of methods. A method that requires a Krylov subspace of minimal dimension is...

In this paper, we study and analyze the regularized weighted total least squares (RWTLS) formulation. Our regularization of the weighted total least squares problem is based on the Tikhonov regularization. Numerical examples are presented to demonstrate the effectiveness of the RWTLS method.

Computation of perfusion parameters by deconvolution from contrast-enhanced time-resolved CT or MR perfusion data sets is an ill-conditioned problem. Thus, adequate regularization and determination of corresponding regularization parameters is required. We present a novel method for Tikhonov regularization for perfusion imaging to locally adapt parameters to the SNR level by using a regression ...

without (a) and with (b) the proposed regularization. Noise level = 5%. (c) RMSE vs. regularization factor at various noise levels. λopt is defined in Eqn. (5). Fig. 1 RMSE for GRAPPA images with different Tikhonov regularization factors (a) and additive noise level in the ACS region (b). λopt and σopt are defined in Eqn. (5) and (6), respectively. Image matrix 256 x 256, reduction factor R = 4...

This paper introduces a new approach to computing an approximate solution of Tikhonov-regularized large-scale ill-posed problems with a general nonlinear regularization operator. The iterative method applies a sequence of projections onto generalized Krylov subspaces using a semi-implicit approach to deal with the nonlinearity in the regularization term. A suitable value of the regularization p...

This review provides a comprehensive understanding of regularization theory from different perspectives, emphasizing smoothness and simplicity principles. Using the tools of operator theory and Fourier analysis, it is shown that the solution of the classical Tikhonov regularization problem can be derived from the regularized functional defined by a linear differential (integral) operator in the...

one of the main steps within the geoid computation methodology without applying the stokes formula is downward continuation of the harmonic residual observables from the surface of the earth down to the surface of the reference ellipsoid. this downward continuation is done via the abel-poisson integral and its derivatives. this integral in which the unknowns, i.e. harmonic residual potential va...

Inversion of ill-posed problem from measurement data have been proposed use: i) Conjugate gradient projection method with regularization; ii) Conditional gradient method with regularization; iii) SVD with constraints with regularization method and iv) The method for solving two-dimensional integral equation of convolution type for vector functions using DFT method for Tikhonov functional. The p...

Although the residual method, or constrained regularization, is frequently used in applications, a detailed study of its properties is still missing. This sharply contrasts the progress of the theory of Tikhonov regularization, where a series of new results for regularization in Banach spaces has been published in the recent years. The present paper intends to bridge the gap between the existin...

Abstract. This note addresses possible applications of the Tikhonov regularization to image reconstruction of gravitational lens systems. Several modifications of the regularization algorithm are discussed. Our illustrative example is the close quadruple gravitational lens QSO 2237+0305 (Einstein Cross). The restored image of the lens is decomposed into two parts – the quasar components and the...