Modified minimum cross-entropy algorithm for image reconstruction using total variation regularization

The basic mathematical problem behind PET is an inverse problem. Due to the inherent ill-posedness of this problem, the reconstructed images usually have noise and edge artifacts. How to decrease the noisy effect while preserving the edges is an open problem. In this paper, we propose a new minimum cross-entropy (MXE) image reconstruction method for PET based on the total variation (TV) norm constraint. Here, TV is presented as a regularization function in MXE based reconstruction algorithm. The use of TV is due to the fact that it can effectively reduce the noise in 2D images while preserving edges. The experimental results show that the proposed method is more effective than the common regularized MXE algorithm, especially for noisy projection data.