Expectation maximization (EM) algorithms using polar symmetries for computed tomography (CT) image reconstruction

We suggest a symmetric-polar pixellation scheme which makes possible a reduction of the computational cost for expectation maximization (EM) iterative algorithms. The proposed symmetric-polar pixellation allows us to deal with 3D images as a whole problem without dividing the 3D problem into 2D slices approach. Performance evaluation of each approach in terms of stability and image quality is presented. Exhaustive comparisons between all approaches were conducted in a 2D based image reconstruction model. From these 2D approaches, that showing the best performances were finally implemented and evaluated in a 3D based image reconstruction model. Comparison to 3D images reconstructed with FBP is also presented. Although the algorithm is presented in the context of computed tomography (CT) image reconstruction, it can be applied to any other tomographic technique as well, due to the fact that the only requirement is a scanning geometry involving measurements of an object under different projection angles. Real data have been acquired with a small animal (CT) scanner to verify the proposed mathematical description of the CT system.