For the solution of full-rank ill-posed linear systems a new approach based on the Arnoldi algorithm is presented. Working with regularized systems, the method theoretically reconstructs the true solution by means of the computation of a suitable function of matrix. In this sense the method can be referred to as an iterative refinement process. Numerical experiments arising from integral equati...

This frame work describes a computationally more efficient and adaptive threshold estimation method for image denoising in the wavelet domain based on Generalized Gaussian Distribution (GGD) modeling of subband coefficients. In this proposed method, the choice of the threshold estimation is carried out by analysing the statistical parameters of the wavelet subband coefficients like standard dev...

In the low observation noise limit particle filters become inefficient. In this paper a simple-to-implement particle filter is suggested as a solution to this well-known problem. The proposed Local Importance Sampling based particle filters draw the particles’ positions in a two-step process that makes use of both the dynamics of the system and the most recent observation. Experiments with the ...

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...

In this paper, a new meshless numerical scheme for solving inverse heat conduction problem is proposed. The numerical scheme is developed by using the fundamental solution of heat equation as basis function and treating the entire space-time domain in a global sense. The standard Tikhonov regularization technique and L-curve method are adopted for solving the resultant ill-conditioned linear sy...

Linear discrete ill-posed problems of small to medium size are commonly solved by first computing the singular value decomposition of the matrix and then determining an approximate solution by one of several available numerical methods, such as the truncated singular value decomposition or Tikhonov regularization. The determination of an approximate solution is relatively inexpensive once the s...

A constrained least squares problem in a Hilbert space H is considered. The standard Tikhonov regularization method is used. In the case where the set of the constraints is the nonempty intersection of a finite collection of closed convex subsets of H , an iterative algorithm is designed. The resulting sequence is shown to converge strongly to the unique solution of the regularized problem. The...