In many image restoration/resolution enhancement applications, the blurring process, i.e., point spread function (PSF) of the imaging system, is not known or is known only to within a set of parameters. We estimate these PSF parameters for this ill-posed class of inverse problem from raw data, along with the regularization parameters required to stabilize the solution, using the generalized cro...

The objective of this paper is to estimate the period and the light curve (or periodic function) of a variable star. Previously, several methods have been proposed to estimate the period of a variable star, but they are inaccurate especially when a data set contains outliers. We use a smoothing spline regression to estimate the light curve given a period and then find the period which minimizes...

This paper concerns the asymptotic properties of a class of criteria for model selection in linear regression models, which covers the most well known criteria as e.g. MALLOWS' Cp, CV (cross-validation), GCV ( generalized cross-validation), AKAIKE's AIC and FPE as well as SCHWARZ' BIC. These criteria are shown to be consistent in the sense of selecting the true or larger models, assuming i.i.d....

To apply the Generalized Cross-Validation (GCV) as a stopping rule for an iterative method, we must estimate the trace of the so-called influence matrix which appears in the denominator of the GCV function. In the case of conjugate gradient, unlike what happens with stationary iterative methods, the regularized solution has a nonlinear dependence on the noise which affects the data of the probl...

In this paper, we propose a numerical algorithm for filtering and robust signal differentiation. The numerical procedure is based on the solution of a simplified linear optimization problem. A compromise between smoothing and fidelity with respect to the measurable data is achieved by the computation of an optimal regularization parameter that minimizes the Generalized Cross Validation criterio...

Inverse problems are usually ill-posed in such a way that it is necessary to use some method to reduce their deficiencies. The method that we choose is the regularization by derivative matrices. There is a crucial problem in regularization, which is the selection of the regularization parameter λ. In this work we use generalized cross validation (GCV) as a tool for the selection of λ. GCV was p...

The selection of significant components in a sparse vector, directly observed with i.i.d. observational noise, typically proceeds by thresholding the observations. The objective in this paper is to choose the threshold that minimizes the risk (expected squared prediction error) of the estimator with respect to the noise-free sparse vector. The risk as a function of the model size (or, equivalen...