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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 58, Iss. 9 — Sep. 1, 1968
  • pp: 1272–1275

Optimum, Nonlinear Processing of Noisy Images

B. Roy FRIEDEN  »View Author Affiliations


JOSA, Vol. 58, Issue 9, pp. 1272-1275 (1968)
http://dx.doi.org/10.1364/JOSA.58.001272


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Abstract

It has been traditional to constrain image processing to linear operations upon the image. This is a realistic limitation of analog processing. In this paper, we find the optimum restoration of a noisy image by the criterion that expectation 〈θj-θ¯|K.〉 be a minimum. Subscript j denotes the spatial frequency ωj at which the unknown object spectrum is to be restored, θ¯ denotes the optimum restoration by this criterion, and K is any positive number at the user’s discretion. In general, such processing is nonlinear and requires the use of an electronic computer. Processor θ¯ uses the presence of known, Markov-image statistics to enhance the restoration quality and permits the image-forming phenomenon to obey an arbitrary law Ij = £(τj, θj, Nj). Here, τj denotes the intrinsic system characteristic (usually the optical transfer function), and Nj represents a noise function. When restored values θ¯j, j= 1, 2, …, are used as inputs to the band-unlimited restoration procedure (derived in a previous paper), the latter is optimized for the presence of noise. The optimum θ¯j is found to be the root of a finite polynomial. When the particular value K=2 is used, the root θ¯j is known analytically. Particular restorations θ¯j are found for the case of additive, independent, gaussian detection noise and a white object region. These restorations are graphically compared with that due to conventional, linear processing.

Citation
B. Roy FRIEDEN, "Optimum, Nonlinear Processing of Noisy Images," J. Opt. Soc. Am. 58, 1272-1275 (1968)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-58-9-1272

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