Abstract

Although it is generally believed that the information at the zeros of the transfer function is lost and cannot be recovered, this is not true: the information can be recovered, even in the presence of noise, because the lost information is coded into intermediate points where the transfer function is not zero. We extend our previous one-dimensional treatment [ Can. J. Phys. 49: 1865 ( 1971)] to two dimensions and apply the results to the restoration of images degraded by noise and by linear filtering, such as movement blurring. The filter used is an honest filter in the sense that in the absence of noise, it yields a perfect restoration, including frequencies at the zeros of the transfer function. It is shown that the method considerably improves the restoration of linearly degraded real images.

© 1991 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Deconvolution and phase retrieval with use of zero sheets

P. J. Bones, C. R. Parker, B. L. Satherley, and R. W. Watson
J. Opt. Soc. Am. A 12(9) 1842-1857 (1995)

Systematic approach to two-dimensional blind deconvolution by zero-sheet separation

D. C. Ghiglia, L. A. Romero, and G. A. Mastin
J. Opt. Soc. Am. A 10(5) 1024-1036 (1993)

Two-dimensional modulation transfer functions of image scanning systems

R. M. Simonds
Appl. Opt. 20(4) 619-622 (1981)

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 (3)

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

Tables (1)

You do not have subscription access to this journal. Article tables 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 (23)

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