5 September 2008 Iterative projection algorithms for reconstructing compact binary images
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Abstract
An algorithm is described for reconstructing compact binary images from limited Fourier amplitude data. This problem arises in macromolecular crystallography where one wishes to reconstruct the molecular envelope from crystal x-ray diffraction amplitudes using a solvent contrast series. Such data are the amplitude of the Fourier transform of an object that has a constant electron density within the boundary of the molecule and zero outside. The image is thus binary and compact, but the data are available only within a limited resolution range in Fourier space and are undersampled. The problem is solved using an iterative projection algorithm; a class of algorithm used to solve inverse problems for which the solution is subject to a number of constraints that represent a priori information and the data. Unfortunately, these algorithms experience convergence difficulties if one or more of the constraints are non-convex, which is the case for all the constraints in this problem. We solve the problem by constructing appropriate projection operators and implementing the difference map projection algorithm. Simulations are used to study convergence behaviour of the algorithm.
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V. L. Lo, V. L. Lo, R. P. Millane, R. P. Millane, } "Iterative projection algorithms for reconstructing compact binary images", Proc. SPIE 7076, Image Reconstruction from Incomplete Data V, 70760B (5 September 2008); doi: 10.1117/12.792947; https://doi.org/10.1117/12.792947
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