Abstract

An information divergence, such as Shannon mutual information, measures the distance between two probability-density functions (or images). A wide class of such measures, called α divergences, with desirable properties such as convexity over all space, was defined by Amari. Rényi’s information Dα is an α divergence. Because of its convexity property, the minimum of Dα is easily attained. Minimization accomplishes minimum distance (maximum resemblance) between an unknown image and a known reference image. Such a biasing effect permits complex images, such as occur in inverse synthetic-aperture-radar imaging, to be well reconstructed. The algorithm permits complex amplitudes to replace the probabilities in the Rényi form. The bias image may be constructed as a smooth version of the linear, Fourier reconstruction of the data. Examples on simulated complex image data with and without noise indicate that the Rényi reconstruction approach permits superresolution in low-noise cases and higher fidelity than ordinary, linear reconstructions in higher-noise cases.

© 1995 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Bayesian cross-entropy reconstruction of complex images

B. Roy Frieden and Anisa T. Bajkova
Appl. Opt. 33(2) 219-226 (1994)

Blind image quality assessment through anisotropy

Salvador Gabarda and Gabriel Cristóbal
J. Opt. Soc. Am. A 24(12) B42-B51 (2007)

Minimum cross-entropy noise reduction in images

Robert F. MacKinnon
J. Opt. Soc. Am. A 6(6) 739-747 (1989)

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 (11)

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 (31)

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