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.

© 1994 Optical Society of America

Full Article  |  PDF Article
Related Articles
Phase retrieval for a complex-valued object by using a low-resolution image

J. R. Fienup and A. M. Kowalczyk
J. Opt. Soc. Am. A 7(3) 450-458 (1990)

Restoration of images degraded by atmospheric turbulence and detection noise

Xiaotian Shi and Rabab K. Ward
J. Opt. Soc. Am. A 9(3) 364-370 (1992)

References

You do not have subscription access to this journal. Citation lists with outbound citation links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Figures (9)

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Equations (34)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Metrics

You do not have subscription access to this journal. Article level metrics are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription