Some implications of zero sheets for blind deconvolution and phase retrieval

The insight into deconvolution and phase retrieval afforded by the concept of the zero sheet (of the spectrum of a compact image) is summarized. Difficulties associated with practical implementation of the zero-sheet concept are outlined. Possible means for overcoming these difficulties are suggested and are illustrated with selected examples for several types of deconvolution, i.e., standard, ensemble blind (i.e., blind deconvolution in Stockham’s sense), and pure blind (i.e., deconvolution of a single blurred image without prior knowledge of the point-spread function). A specialized procedure is described for blindly deconvolving a blurred image when the spectrum of the point-spread function is an unknown pure phase function. It is indicated how this procedure may facilitate phase retrieval for spectra of complex-valued images. Possible effects on Wiener filtering and on astronomical speckle imaging are discussed.