## 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**OSA Recommended Articles**

B. Roy Frieden

J. Opt. Soc. Am. **73**(7) 927-938 (1983)

B. Roy Frieden

Appl. Opt. **26**(9) 1755-1764 (1987)

Meredith Kathryn Whitaker, Eric Clarkson, and Harrison H. Barrett

Opt. Express **16**(11) 8150-8173 (2008)