QC 351 A7 no. 72 / The problem of inferring some unknown distribution (object) from measurements of physical quantities (image data) occurs frequently in scientific investigation. This study is concerned with the numerical estimation of a continuous object distribution from a finite set of noisy image data, where the transformation (degradation) between the object and the noiseless portion of the data is assumed known. So defined, the restoration problem is inherently a statistical one, requiring a priori information to define the "most probable" object and noise associated with a given set of data. With a random particle model, the problem of implementing complex statistical and analytical foreknowledge (positive and bounded objects, signal - dependent noise, multiple -stage imaging, spatial correlation, etc.) is reduced to a few simple restoring formulas. For linear problems, noise impedes the ability to restore those object modes (statistically orthogonal components) that have a low power transmission through the imaging process. Linear applications of Fourier transform techniques are dis- cussed, where modifications to the standard Wiener filter are required for under - sampling a bandlimited image. The use of nonlinear object formulas tends to reduce the effects of noise and may extend restored resolution to well beyond the Rayleigh limit. This enhancement occurs in relatively isolated regions in an extended object, where the average restored information can never exceed that in the image. Particular attention is given to developing numerical algorithms for efficient use in digital computers. A positive or bounded object estimate is found through a series of linear matrix solutions, with an example of "superresolving" two impulses separated by half the Rayleigh limit. For 2 -D problems with stationary imaging, a purely iterative algorithm is developed, based on a series of Fourier transform operations. For restoring a 64 X 64 data array with nonlinear constraints, computation time may require only seconds (CDC 6600) as compared with hours using direct matrix methods. The iterative transform method is then applied to experimental absorption spectra, resulting in considerable resolution enhancement. Included are brief discussions of restoring photon -limited images, multiple -stage imaging problems, estimation of the imaging response, use of a finite object extent, the problem of systematic errors, and possible applications of the restoring techniques.
| Identifer | oai:union.ndltd.org:arizona.edu/oai:arizona.openrepository.com:10150/621676 |
| Date | 12 1900 |
| Creators | Hershel, Ronald S. |
| 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 72 |
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