Image Restoration Using A Norm Of Maximum Information

B. Roy Frieden

doi:10.1117/12.7972512

1 June 1980 Image Restoration Using A Norm Of Maximum Information

B. Roy Frieden

Author Affiliations +

Optical Engineering, Vol. 19, Issue 3, 193290 (June 1980). https://doi.org/10.1117/12.7972512

Abstract

Image interpreters often express the desire to extract a "maximum of information" from a given picture. We have devised a new norm of restoration that, in fact, realizes this aim. The image data are forced to contain a maximum of information about the object, through variation of the object estimate. This maximum information (MI) norm restores the ideal object which, had it existed, would have maximized the throughput of information from object to image planes. Or, the object estimate achieves the "channel capacity" of the image-forming medium. The following simple model for image formation is used. The imaging system is regarded as a transducer of photon position, from x in the object plane toy in the image plane. Then the conditional probability p(y1 x) is just s(y-x), the point spread function for the imagery, plus an unknown noise probability law n(y) independent of x (signal) for those transitions to y that are due to noise. The average information per photon transition x-y may then be calculated, using the correspondence of probability law p(x) with the object and p(y) with the image. When the image law p(y) is constrained to equal the data, the only set of unknowns remaining is the object, which may be varied to maximize the information. Restorations by this method are compared with corresponding ones by maximum entropy and show some advantage over the latter.

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B. Roy Frieden "Image Restoration Using A Norm Of Maximum Information," Optical Engineering 19(3), 193290 (1 June 1980). https://doi.org/10.1117/12.7972512

Published: 1 June 1980

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