Tikhonov regularization is a popular and effective method for the approximate solution of illposed problems, including Fredholm equations of the first kind. The Tikhonov method works well when the solution of the equation is well-behaved, but fails for solutions with irregularities, such as jump discontinuities. In this paper we develop a method that overcomes the limitations of the standard Ti...

Given a compact operator G, we consider the ill-posed problem, given y , solve Gφ = y (approximately). Typically, in the presence of noise y / ∈ Range(G). We consider the iterated Tikhonov method for this problem. The method selects a regularization parameter based on stability and corrects several times to increase accuracy. We show that it gives a higher accuracy approximation to the noise-fr...

This report develops and studies a new family of NSE-regularizations, Tikhonov Leray Regularization with Time Relaxation Models. This new family of turbulence models is based on a modification (consistent with the large scales) of Tikhonov-Lavrentiev regularization. With this approach, we obtain an approximation of the unfiltered solution by one filtering step. We introduce the modified Tikhono...

Total variation-penalized Tikhonov regularization is a popular method for the restoration of images that have been degraded by noise and blur. The method is particularly effective, when the desired noiseand blur-free image has edges between smooth surfaces. The method, however, is computationally expensive. We describe a hybrid regularization method that combines a few steps of the GMRES iterat...

In this work, we analyze the behavior of the active-set method for the nonnegative regularization of discrete ill-posed problems. In many applications, the solution of a linear ill-posed problem is known to be nonnegative. Standard Tikhonov regularization often provides an approximated solution with negative entries. We apply the activeset method to find a nonnegative approximate solution of th...

In a recent paper [24] an algorithm for large-scale Tikhonov regularization in standard form called GKB-FP was proposed and numerically illustrated. In this paper, further insight into the convergence properties of this method is provided and extensions to general-form Tikhonov regularization are introduced. In addition, as alternative to Tikhonov regularization, a preconditioned LSQR method co...

The problem of convergence of a special form of the generalized pulsespectrum technique (GPST) for solving inverse problems of one-dimensional diffusion equations in space-time domain is considered. Under the assumptions that a Tikhonov regularized solution exists and the derivative operator of the regularized forward problem at the regularized solution is invertible, the iterative solutions of...

in this paper the 3d inversion of gravity data using two different regularization methods, namely tikhonov regularization and truncated singular value decomposition (tsvd), is considered. the earth under the survey area is modeled using a large number of rectangular prisms, in which the size of the prisms are kept fixed during the inversion and the values of densities of the prisms are the mode...