DECONVOLUTION AND PHASE RETRIEVAL WITH USE OF ZERO SHEETS

Recent developments in the application of zeros (of the analytically c ontinued spectrum of a compact two-dimensional image) in solving decon volution and phase retrieval problems are reviewed. New algorithms for use in the presence of noise are described and demonstrated. These in clude algorithms for deconvolution where the point-spread function is approximately known, for ensemble blind deconvolution (such as is requ ired for ensembles of astronomical speckle images), and for phase retr ieval (itself a special case of blind deconvolution). Many of the idea s embodied in the algorithms were foreshadowed by Bates et al. [J. Opt . Sec. Am. A 7, 468 (1990)]. Simulated images are employed in the exam ples shown, except for phase retrieval, where successful recovery of t he phase error in the aperture of a radio telescope is demonstrated.