Multiscale Bayesian image reconstruction in positron emission tomography

Abstract

In recent years, various approaches to overcome the problems associated with iterative statistical image reconstruction methods have been investigated, including issues such as slow convergence rate, costly computational time and nonuniform correction efficiency. A multiscale Bayesian image reconstruction algorithm based on a 1-D wavelet technique is proposed. In this approach, the authors first apply a wavelet transform to the sinogram measurements, which yields a multiresolution object representation. The image is reconstructed at the corresponding grid by the Bayesian image reconstruction algorithm for each scale level in the frequency space; the backprojector is also modified to match each corresponding resolution scale. After the low-frequency components of the image have been recovered sufficiently on the coarser scale level, the resulted image is used as the starting point for the finer level at a new iteration. An important feature in the authors' new approach is that the wavelet decomposition is carried out in the sinogram space, while multiple grids are also used in the reconstructed image space.