QC 351 A7 no. 23 / 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, the calculus of variations is used to find the optimum,
generally non - linear, processor of a noisy image. In general, such processing
requires the use of an electronic computer. The criterion of optimization
is that expectation (10. - (5j1K) be a minimum. Subscript j denotes the
spatial frequency w. at which the unknown object spectrum 0 is to be re-
stored, 0 denotes the optimum restoration by this criterion, and K is an
even power at the user's discretion. A further generality is to allow the
image- forming phenomenon to obey an arbitrary law I. = L(T., O., N.). Here,
J J J
T. denotes the intrinsic system characteristic (usually the optical transfer
function), and N. represents a noise function. The optimum Oj is found to
be the root of a finite polynomial. When the particular value K = 2 is
used, the root O. is known analytically, along with the expected, mean -square,
minimal error due to its use. When K = 2, processor O. has the added significance of minimizing the total mean -square restoration error over the spatial
object. This error may be further minimized by choice of an optimal processing bandwidth. Particular processors O. are found for the "image recognition"
problem and for the case of a "white" object region. The latter case is
numerically simulated.
| Identifer | oai:union.ndltd.org:arizona.edu/oai:arizona.openrepository.com:10150/621616 |
| Date | 06 March 1968 |
| Creators | Frieden, B. Roy |
| Publisher | Optical Sciences Center, University of Arizona (Tucson, Arizona) |
| Source Sets | University of Arizona |
| Language | en_US |
| Detected Language | English |
| Type | Technical Report |
| Rights | Copyright © Arizona Board of Regents |
| Relation | Optical Sciences Technical Report 23 |
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