RECONSTRUCTION OF PHOTON-LIMITED STELLAR IMAGES BY GENERALIZED PROJECTIONS WITH USE OF THE SELF-CROSS SPECTRUM

TitleRECONSTRUCTION OF PHOTON-LIMITED STELLAR IMAGES BY GENERALIZED PROJECTIONS WITH USE OF THE SELF-CROSS SPECTRUM
Publication TypeJournal Article
Year of Publication1994
AuthorsSHI, X. T., and R. K. Ward
JournalJournal of the Optical Society of America A-Optics Image Science and Vision
Volume11
Pagination1589-1598
Date PublishedMAY
Type of ArticleArticle
ISSN0740-3232
Abstract

We define self-cross correlation as the cross correlation between an image and a truncated part of it. A new method for finding tight object-support bounds by use of the self-cross-correlation information is addressed. These bounds are used in the generalized-projection method to reconstruct photon-limited atmosphere-degraded images. The iterative Fourier-transform algorithm and the generalized-projection method, with use of the autocorrelation function only, have not been preferred to the Knox-Thompson and the triple-correlation methods for phase-retrieval problems, because the use of the autocorrelation function only usually does not give tight object-support bounds. The tight-object-support-bounds constraint is crucial for the uniqueness of phase retrieval by generalized projections. We find that the information contained in the average self cross correlation gives the required tight object-support bounds. The advantage of our method over the triple-correlation method lies in the speed of computation.

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