A NEW GENERATION OF ITERATIVE TRANSFORM ALGORITHMS FOR PHASE CONTRAST TOMOGRAPHY

In recent years, improvements in electromagnetic sources, detectors, optical components, and computational imaging have made it possible to achieve three-dimensional atomic-scale resolution using tomographic phase-contrast imaging techniques. These greater capabilities have placed a pre-mium on improving the efficiency and stability of phase re-trieval algorithms for recovering the missing phase informa-tion in diffraction observations. In some cases, so called di-rect methods suffice, but for large macromolecules and non-periodic structures one must rely on numerical techniques for reconstructing the missing phase. This is the principal motivation of our work. We report on recent progress in algorithms for iterative phase retrieval. The theory of con-vex optimisation is used to develop and to gain insight into counterparts for the nonconvex problem of phase retrieval. We propose a relaxation of averaged alternating reflectors and determine the fundamental mathematical properties of the related operator in the convex case. Numerical studies support our theoretical observations and demonstrate the ef-fectiveness of the newer generation of algorithms compared to the current state of the art. 1