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
Original Manuscript: November 14, 1994
Revised Manuscript: April 11, 1995
Manuscript Accepted: April 12, 1995
Published: September 1, 1995
P. J. Bones, C. R. Parker, B. L. Satherley, and R. W. Watson, "Deconvolution and phase retrieval with use of zero sheets," J. Opt. Soc. Am. A 12, 1842-1857 (1995)