In this work we analyze ill{posed problems modelled by rst kind Fred-holm integral equations with non degenerate kernel. We survey the main properties of the least{squares solutions and derive the regularized solutions in the cases of Truncated Singular Value Decomposition, Tikhonov method and Conjugate Gradient regularization method. Numerical results are reported in the case of medical imagin...

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 analysis of high spectral resolution Fourier Transform infrared (FTIR) solar absorption spectra is an important issue in remote sensing. If this is done carefully, one can obtain information, not only about the total column abundances, but also about the vertical distribution of various constituents in the atmosphere. This work introduces the application of the information operator approach...

Lanczos-hybrid regularization methods have been proposed as effective approaches for solving largescale ill-posed inverse problems. Lanczos methods restrict the solution to lie in a Krylov subspace, but they are hindered by semi-convergence behavior, in that the quality of the solution first increases and then decreases. Hybrid methods apply a standard regularization technique, such as Tikhonov...

In sensitivity encoding reconstruction, the issue of ill conditioning becomes serious and thus the signal-to-noise ratio becomes poor when a large acceleration factor is employed. Total variation (TV) regularization has been used to address this issue and shown to better preserve sharp edges than Tikhonov regularization but may cause blocky effect. In this article, we study nonlocal TV regulari...

This paper presents a systematic and computable method for choosing the regularization parameter appearing in Tikhonov-type regularization based on non-quadratic regularizers. First, we extend the notion of the L-curve, originally defined for quadratically regularized problems, to the case of non-quadratic functions. We then associate the optimal value of the regularization parameter for these ...

This paper studies iterative learning control (ILC) for under-determined and over-determined systems, i.e., systems for which the control action to produce the desired output is not unique, or for which exact tracking of the desired trajectory is not feasible. For both cases we recommend the use of the pseudoinverse or its approximation as a learning operator. The Tikhonov regularization techni...