Expectation Maximization and Total Variation Based Model for Computed Tomography Reconstruction from Undersampled Data

Computerized tomography (CT) plays an important role in medical imaging, especially for diagnosis and therapy. However, higher radiation dose from CT will result in increasing of radiation exposure in the population. Therefore, the reduction of radiation from CT is an essential issue. Expectation maximization (EM) is an iterative method used for CT image reconstruction that maximizes the likelihood function under Poisson noise assumption. Total variation regularization is a technique used frequently in image restoration to preserve edges, given the assumption that most images are piecewise constant. Here, we propose a method combining expectation maximization and total variation regularization, called EM+TV. This method can reconstruct a better image using fewer views in the computed tomography setting, thus reducing the overall dose of radiation. The numerical results in two and three dimensions show the efficiency of the proposed EM+TV method by comparison with those obtained by filtered back projection (FBP) or by EM only.