This article is cited in 3 papers

Asymptotic properties of risk estimate in the problem of reconstructing images with correlated noise by inverting the Radon transform

A. A. Eroshenko^a, O. V. Shestakov<sup>ba

a</sup> Faculty of Computational Mathematics and Cybernetics, M. V. Lomonosov MoscowStateUniversity, 1-52 Leninskiye Gory, GSP-1, Moscow 119991, Russian Federation
^b Institute of Informatics Problems, Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation

Abstract: In recent years, wavelet methods based on the decomposition of projections in a special basis and the following thresholding procedure became widely used for solving the problems of tomographic image reconstruction. These methods are easily implemented through fast algorithms; so, they are very appealing in practical situations. Besides, they allow the reconstruction of local parts of the images using incomplete projection data, which is essential, for example, for medical applications, where it is not desirable to expose the patient to the redundant radiation dose. Wavelet thresholding risk analysis is an important practical task, because it allows determining the quality of techniques themselves and the equipment which is used. The present paper considers the problem of estimating the function by inverting the Radon transform in the model of data with correlated noise. The asymptotic properties of mean-square risk estimate of wavelet-vaguelette thresholding technique are studied. The conditions under which the unbiased risk estimate is asymptotically normal are given.

Keywords: wavelets; linear homogeneous operator; Radon transform; thresholding; unbiased risk estimate; correlated noise; asymptotic normality.

Received: 29.09.2014

DOI: 10.14357/19922264140404

Bibliographic databases:

•