Abstract

A longstanding problem of estimation is extraction of the signal image from a given noisy image. Here, prior knowledge in the form of a second, template image is also assumed to be present. Examples of templates are a blurred version of the signal image, the reference image used in cross-entropy minimization, or the signal power spectrum. We propose and test a method of optimally combining the data and template images to form an improved output. The output is biased, respectively, toward the template or the data image by trading off two goals: (a) minimum output probability of being successfully distinguished from the template as predicted by standard maximum likelihood theory, and (b) maximum output probability of having formed the image data. For additive Gaussian noise the estimation approach is least-squares; for Poisson noise the approach is a compromise between maximum Shannon cross entropy and maximum Burg-type entropy; and for exponential noise the approach includes maximum Burg entropy.

© 1989 Optical Society of America

Full Article  |  PDF Article
More Like This
Maximum-probable restoration of photon-limited images

B. Roy Frieden
Appl. Opt. 26(9) 1755-1764 (1987)

Minimum cross-entropy noise reduction in images

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

Unified theory for estimating frequency-of-occurrence laws and optical objects

B. Roy Frieden
J. Opt. Soc. Am. 73(7) 927-938 (1983)

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 Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica 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 Optica member, or as an authorized user of your institution.

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

Figures (5)

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

Contact your librarian or system administrator
or
Login to access Optica 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 Optica member, or as an authorized user of your institution.

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

Equations (51)

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

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

Metrics