Random projections and the optimization of an algorithm for phase retrieval

Abstract

Iterative phase retrieval algorithms typically employ projections onto constraint subspaces to recover the unknown phases in the Fourier transform of an image, or, in the case of x-ray crystallography, the electron density of a molecule. For a general class of algorithms, where the basic iteration is specified by the difference map, solutions are associated with fixed points of the map, the attractive character of which determines the effectiveness of the algorithm. The behavior of the difference map near fixed points is controlled by the relative orientation of the tangent spaces of the two constraint subspaces employed by the map. Since the dimensionalities involved are always large in practical applications, it is appropriate to use random matrix theory ideas to analyze the average-case convergence at fixed points. Optimal values of the gamma parameters of the difference map are found which differ somewhat from the values previously obtained on the assumption of orthogonal tangent spaces.

15 pages

Cited by in corpus (5)

• Sub-wavelength coherent imaging of periodic samples using a 13.5 nm tabletop high harmonic light source
• Sparsity assisted solution to the twin image problem in phase retrieval
• Phase retrieval with complexity guidance
• Deconstructing the energy landscape: new algorithms for folding heteropolymers
• Robust phase retrieval with complexity-guidance for coherent X-ray imaging