Total variation regulated EM algorithm

An iterative Bayesian reconstruction algorithm based on the total variation (TV) norm constraint is proposed. The motivation for using TV regularization is that it is extremely effective for recovering edges of images. The TV norm minimization, introduced in 1992 was shown to be effective for restoring blurred images with a Gaussian noise model and was demonstrated to be effective for noise suppression and edge preservation. The images were diffused according to a set of nonlinear anisotropic diffusion partial differential equations, which suffered from computational difficulties. This paper extends the TV norm minimization constraint to the field of SPECT image reconstruction with a Poisson noise model. The regularization norm is included in the ML-EM (maximum likelihood expectation maximization) algorithm. The partial differential equation approach is not utilized here. Reconstructions of computer simulations and patient data show that the proposed algorithm has the capacity to smooth the noise and maintain sharp edges without introducing over/under shoots and ripples around the edges