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. Classical methods proceed in three steps: first, angular assignation, then image reconstruction from angular information and input projections and finally angular assignation refinement from the reconstructed image. We propose in this paper to perform the angular assignation and the image reconstruction at the same time. The main idea is to compare the input projections with the projections obtained from the image being reconstructed and the angular information. Our method is available for ab initio reconstruction and based on a cost optimization using the simulated annealing algorithm. A comparison with a state-of-the-art method (based on the spherical Local Linear Embedding) from the literature on a set of 2D gray-level images is done and it shows the better result of our method. The case where projections from different objects are acquired can also occur in cryo-electron microscopy (e.g. deformable molecule reconstruction). The feasibility of a reconstruction by our method in this case is shown on 2D images. Moreover our method can be generalized to the 3D case.