Information Complexity-Based Regularization Parameter Selection for Solution of Ill-Conditioned Inverse Problems
نویسندگان
چکیده
We propose an information complexity-based regularization parameter selection method for solution of ill-conditioned inverse problems. The regularization parameter is selected to be the minimizer of the Kullback-Leibler (KL) distance between the unknown data-generating distribution and the fitted distribution. The KL distance is approximated by an information complexity (ICOMP) criterion developed by Bozdogan (1988, 1990, 1994, 2000). The method is not limited to the white Gaussian noise case. It can be extended to the correlated and non-Gaussian noise. It can also account for possible model misspecification. We demonstrate the performance of the proposed method on a test problem from Hansen’s (1994) Regularization Tools.
منابع مشابه
Ill-Posed and Linear Inverse Problems
In this paper ill-posed linear inverse problems that arises in many applications is considered. The instability of special kind of these problems and it's relation to the kernel, is described. For finding a stable solution to these problems we need some kind of regularization that is presented. The results have been applied for a singular equation.
متن کاملA numerical approach for solving a nonlinear inverse diusion problem by Tikhonov regularization
In this paper, we propose an algorithm for numerical solving an inverse non-linear diusion problem. In additional, the least-squares method is adopted tond the solution. To regularize the resultant ill-conditioned linear system ofequations, we apply the Tikhonov regularization method to obtain the stablenumerical approximation to the solution. Some numerical experiments con-rm the utility of th...
متن کاملImplementation of Sinc-Galerkin on Parabolic Inverse problem with unknown boundary condition
The determination of an unknown boundary condition, in a nonlinaer inverse diffusion problem is considered. For solving these ill-posed inverse problems, Galerkin method based on Sinc basis functions for space and time will be used. To solve the system of linear equation, a noise is imposed and Tikhonove regularization is applied. By using a sensor located at a point in the domain of $x$, say $...
متن کاملA Newton Root-Finding Algorithm For Estimating the Regularization Parameter For Solving Ill-Conditioned Least Squares Problems
We discuss the solution of numerically ill-posed overdetermined systems of equations using Tikhonov a-priori-based regularization. When the noise distribution on the measured data is available to appropriately weight the fidelity term, and the regularization is assumed to be weighted by inverse covariance information on the model parameters, the underlying cost functional becomes a random varia...
متن کاملAutomated Parameter Selection Tool for Solution to Ill-Posed Problems Final Report
In many applications of solving ill-posed problems there are a number of regularization methods to choose from as well as a free regularization parameter. The choice of the method and regularization can add bias if deblurred images are based on what the researcher expects. The presented project develops a tool for method choice and parameter selection by using a set of three statistical diagnos...
متن کامل