Regularization is used in order to obtain a reasonable estimate of the solution to an ill-posed inverse problem. One common form of regularization is to use a filter to reduce the influence of components corresponding to small singular values, perhaps using a Tikhonov least squares formulation. In this work, we break the problem into subproblems with narrower bands of singular values using spec...

Tikhonov regularization is a powerful tool for the solution of ill-posed linear systems and linear least squares problems. The choice of the regularization parameter is a crucial step, and many methods have been proposed for this purpose. However, eecient and reliable methods for large scale problems are still missing. In this paper approximation techniques based on the Lanczos algorithm and th...

When discrete ill-posed problems are analyzed and solved by various numerical regularization techniques, a very convenient way to display information about the regularized solution is to plot the norm or seminorm of the solution versus the norm of the residual vector. In particular, the graph associated with Tikhonov regularization plays a central role. The main purpose of this paper is to advo...

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...

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...

In this paper we deal with Morozov’s discrepancy principle as an aposteriori parameter choice rule for Tikhonov regularization with general convex penalty terms Ψ for non-linear inverse problems. It is shown that a regularization parameter α fulfilling the discprepancy principle exists, whenever the operator F satisfies some basic conditions, and that for this parameter choice rule holds α→ 0, ...

We describe a methodology called computed myography to qualitatively and quantitatively determine the activation level of individual muscles by voltage measurements from an array of voltage sensors on the skin surface. A finite element model for electrostatics simulation is constructed from morphometric data. For the inverse problem, we utilize a generalized Tikhonov regularization. This impose...

Recently, Sorkine et al. proposed a least squares based representation of meshes, which is suitable for compression and modeling. In this paper we look at this representation from the viewpoint of Tikhonov regularization. We show that this viewpoint yields a smoothing algorithm, which can be seen as an approximation of the shape using weighted geometry aware bases, where the weighting factor is...

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...

It is a common belief that Tikhonov scheme with ‖ · ‖L2 -penalty fails to reconstruct a sparse structure with respect to a given system {φi}. However, in this paper we present a procedure for sparsity reconstruction, which is totally based on the standard Tikhonov method. This procedure consists of two steps. At first Tikhonov scheme is used as a sieve to find the coefficients near φi, which ar...