Abstract

Recent developments in the application of zeros (of the analytically continued spectrum of a compact two-dimensional image) in solving deconvolution and phase retrieval problems are reviewed. New algorithms for use in the presence of noise are described and demonstrated. These include algorithms for deconvolution where the point-spread function is approximately known, for ensemble blind deconvolution (such as is required for ensembles of astronomical speckle images), and for phase retrieval (itself a special case of blind deconvolution). Many of the ideas embodied in the algorithms were foreshadowed by Bates et al. [ J. Opt. Soc. Am. A 7, 468 ( 1990)]. Simulated images are employed in the examples shown, except for phase retrieval, where successful recovery of the phase error in the aperture of a radio telescope is demonstrated.

© 1995 Optical Society of America

Some implications of zero sheets for blind deconvolution and phase retrieval

R. H. T. Bates, B. K. Quek, and C. R. Parker
J. Opt. Soc. Am. A 7(3) 468-479 (1990)

Blind deconvolution and phase retrieval from point zeros

Pi-tung Chen, M. A. Fiddy, C.-W. Liao, and D. A. Pommet
J. Opt. Soc. Am. A 13(7) 1524-1531 (1996)

Iterative blind deconvolution algorithm applied to phase retrieval

J. H. Seldin and J. R. Fienup
J. Opt. Soc. Am. A 7(3) 428-433 (1990)

Systematic approach to two-dimensional blind deconvolution by zero-sheet separation

D. C. Ghiglia, L. A. Romero, and G. A. Mastin
J. Opt. Soc. Am. A 10(5) 1024-1036 (1993)

Zero tracks for blind deconvolution of blurred ensembles

B. L. Satherley and P. J. Bones
Appl. Opt. 33(11) 2197-2205 (1994)