A New Generation of Iterative Transform Algorithms for Phase Contrast Tomography

Date
2004
Journal Title
Journal ISSN
Volume Title
Publisher
Department of Mathematical Sciences
Abstract
In recent years, improvements in electromagnetic sources, detectors, optical components, and computational imaging have made it possible to achieve three-dimensional atomicscale resolution using tomographic phase-contrast imaging techniques. These greater capabilities have placed a premium on improving the efficiency and stability of phase retrieval algorithms for recovering the missing phase information in diffraction observations. In some cases, . so called direct methods suffice, but for large macromolecules and nonperiodic 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 convex 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 effectiveness of the newer generation of algorithms compared to the current state of the art.
Description
Keywords
tomographic phase-contrast imaging techniques, iterative phase retrieval, theory of convex optimisation, three-dimensional atomicscale resolution
Citation