the grace mission has provided scientific community time-variable gravity field solutions with high precision and on a global scale. the grace mission was launched on march 2003. this mission consists of two satellites that pursue each other in their orbit. distance between two satellites in orbit is measured continuously to an accuracy of better than 1 micron using kbr system placed in satelli...

We consider the problem of finding regularized solutions to ill-posed Volterra integral equations. The method we consider is a sequential form of Tikhonov regularization that is particularly suited to problems of Volterra type. We prove that when this sequential regularization method is coupled with several standard discretizations of the integral equation (collocation, rectangular and midpoint...

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...

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...

Analogue to the ADMM method for the filter subproblem, we derive the following Algorithm 3 for solving for the sparse coefficient maps zi. However, unlike in the filter subproblem, we do not enforce consensus among the coefficient feature maps zi since there exists a distinct zi for each bi,∀i = [1 . . . N ]. In Algorithm 3, each zi update takes the form of a Tikhonov-regularized least squares ...

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 rational function model (RFM) utilized for high resolution satellite imagery (HRSI) provides a transformation from image to object space coordinates in a geographic reference system. Compared with the rigorous model based on the collinearity condition equation or the affine model, the RFM with 80 coefficients would be over parameterized. That would result in an ill-conditioned normal equati...

We consider the inverse problem of finding the nonlinear source for nonlinear Reaction-Diffusion equation whenever the initial and boundary condition are given. We investigate the numerical solution of this problem by using Adomian Decomposition Method (ADM). The approach of the proposed method is to approximate unknown coefficients by a nonlinear function whose coefficients are determined from...