A tomographical reconstruction method from unknown direction projections for 2D gray-level images

This paper deals with the reconstruction of gray level images from unoriented tomographic projections as it occurs in cryo electron microscopy. For this problem, classical methods proceed in three steps, firstly angular assignation, then image reconstruction from angular information and input projections and thirdly angular assignation refinement from the reconstructed image. We propose in this paper to make the angular assignation and the image reconstruction at the same time. The main idea is to compare the input projections with the projections obtained the angular information and the image being reconstructed. A comparison with a method from the literature on a set of 2D gray-level images is done and it shows the better result of our method. Our method can be generalized to the 3D case.