Average probability of error in calculating wavelet–vaguelette coefficients while inverting the Radon transform

Image reconstruction methods based on decomposition of the image function in a special wavelet basis and subsequent thresholding of the decomposition coefficients are used to solve computational tomography problems. Their attractiveness lies in adaptation to spatial inhomogeneities of images and the possibility of reconstructing local areas of the image from incomplete projection data that is of key importance, for example, for medical applications where it is undesirable to expose a patient to an unnecessary dose of radiation. The analysis of errors of these methods is an important practical task, since it allows one to assess the quality of both the methods themselves and the equipment used. The paper considers the wavelet–vaguelette decomposition method for reconstructing tomographic images in a model with an additive Gaussian noise. The order of the loss function based on the average probability of error in calculating wavelet coefficients is estimated.