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

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.