Iterative methods in large field electron microscope tomography

Electron tomography (ET) is a powerful technology allowing the three-dimensional (3D) imaging of cellular ultrastructure. These structures are reconstructed from a set of micrographs taken at different sample orientations, the final volume being the solution of a general inverse problem. Two different approaches are used in this context: iterative methods and filtered backprojection. Iterative methods are known to provide high-resolution 3D reconstructions for ET under noisy and incomplete data conditions. However, all previous implementations have been restricted to the straight-line projection models. This is not accurate since electron trajectories in electron microscopes do not follow the straight-line optics assumed for X-rays, and biological samples may warp as a result of being exposed to an electron beam. Compensation for curvilinear trajectories, nonlinear electron optics, and sample warping constitutes a major advance in large-field ET and has made possible resolution down to the molecular level in reconstructions of whole cells. At present these advances are limited to filtered backprojection and have been implemented in the software package TxBR. As the next step in this development, we have modified the ASART method in conjunction with a 3D model. By employing alignment based on general curvilinear trajectories we have been able to show that further improvements can be achieved with iterative methods. We also discuss a unified treatment of the alignment and reconstruction problems within the framework of iterative methods, and the relationship between formulas employed in the update step and cross-validation methods.