Selection of task-dependent diffusion filters for the post-processing of SPECT images

Iterative reconstruction from single photon emission computed tomography (SPECT) data requires regularization to avoid noise amplification and edge artefacts in the reconstructed image. This is often accomplished by stopping the iteration process at a relatively low number of iterations or by post-filtering the reconstructed image. The aim of this paper is to develop a method to automatically select an optimal combination of stopping iteration number and filters for a particular imaging situation. To this end different error measures between the distribution of a phantom and a corresponding filtered SPECT image are minimized for different iteration numbers. As a study example, simulated data representing a brain study are used. For postreconstruction filtering, the performance of 3D linear diffusion (Gaussian filtering) and edge preserving 3D nonlinear diffusion (Catte scheme) is investigated. For reconstruction methods which model the image formation process accurately, error measures between the phantom and the filtered reconstruction are significantly reduced by performing a high number of iterations followed by optimal filtering compared with stopping the iterative process early. Furthermore, this error reduction can be obtained over a wide range of iteration numbers. Only a negligibly small additional reduction of the errors is obtained by including spatial variance in the filter kernel. Compared with Gaussian filtering, Catte diffusion can further reduce the error in some cases. For the examples considered, using accurate image formation models during iterative reconstruction is far more important than the choice of the filter.