This paper introduces a new approach to computing an approximate solution of Tikhonov-regularized large-scale ill-posed problems with a general nonlinear regularization operator. The iterative method applies a sequence of projections onto generalized Krylov subspaces using a semi-implicit approach to deal with the nonlinearity in the regularization term. A suitable value of the regularization p...

where f ∈ L2(Ω); it is well known that problems (1.1) and (1.2) admit a unique solution (see [3]). The aim of this paper is to develop a regularization method for solving a nondifferentiable minimization problem that is equivalent to problems (1.1) and (1.2). The idea of the regularization method is to approximate the nondifferentiable term by a sequence of differentiable ones depending on (ε ≥...

This paper describes an efficient edge-preserved regularization algorithm for downward continuation of magnetic data in detection of unexploded ordnance (UXO). The magnetic anomalies arising from multi-source UXO can overlap at a height over the ground surface, while causative sources may not be readily separated due to low level of signal-to-noise ratio of the observed data. To effectively the...

The generalized singular value decomposition (GSVD) often is used to solve Tikhonov regularization problems with a regularization matrix without exploitable structure. This paper describes how the standard methods for the computation of the GSVD of a matrix pair can be simplified in the context of Tikhonov regularization. Also, other regularization methods, including truncated GSVD, are conside...

In this paper we establish a regularization method for Radon measures. Motivated from sparse L regularization we introduce a new regularization functional for the Radon norm, whose properties are then analyzed. We, furthermore, show well-posedness of Radon measure based sparsity regularization. Finally we present numerical examples along with the underlying algorithmic and implementation detail...

Regularization is an well-known technique for obtaining stable solution of ill-posed inverse problems. In this paper we establish a key relationship among the regularization methods with an edge-preserving noise filtering method which leads to an efficient adaptive regularization methods. We show experimentally the efficiency and superiority of the proposed regularization methods for some inver...

In this paper, we proposed a new model with nuclear-norm and L1-norm regularization for image reconstruction in aerospace remote sensing. The curvelet based L1-norm regularization promotes sparse reconstruction, while the low-rank based nuclear-norm regularization leads to a principle component solution. Split Bregman method is used to solve this problem. Numerical experiments show the proposed...

In this paper a simple and convenient new regularization method for solving backward heat equation— Fourier regularization method is given. Meanwhile, some quite sharp error estimates between the approximate solution and exact solution are provided. A numerical example also shows that the method works effectively. © 2006 Elsevier Inc. All rights reserved.

Abstract. A new parameter choice method for Tikhonov regularization of discrete ill-posed problems is presented. Some of the regularized solutions of a discrete ill-posed problem are less sensitive than others to the perturbations in the right-hand side vector. This method chooses one of the insensitive regularized solutions using a certain criterion. Numerical experiments show that the new met...