The removal of unknown image blurs by homomorphic filtering

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Publication Type Journal Article
School or College College of Engineering
Department Computing, School of
Creator Cole, Edwin Randolph
Title The removal of unknown image blurs by homomorphic filtering
Date 1974
Description This report describes a homomorphic method for the estimation and removal of unknown image blurs, which are presumed to have been caused by a linear stationary system. Previous methods have required a more or less perfect a priori knowledge of the identity of the blur. the method described here requires no information about the original scene which led to the blurred image, but does presently require that the blur be phaseless for best results. The estimation method uses a homomorphic mapping to map sections of the blurred image, which is a convolutional combination of the undistorted of the undistorted image and the blur, into a domain (the log spectrum) in which the components corresponding to the undistorted image and blur are added. An averaging method allows the component corresponding to the undistorted image to be estimated and subtracted, leaving an estimate of the component corresponding to the blur. This estimate is then used to generate a homomorphically estimated restoration filter. Properties of the homomorphically estimated restoration filter in the presence of additive noise are derived, and it is shown that the homomorphic filter has noise and resolution properties intermediate between those of the Weiner filter and those of the simple inverse filter. The concept of a family of filters with variable noise and resolution properties is discussed. This family is bounded by the simple inverse and Weiner filters and includes the homomorphic filter. It is shown that any member of the family of filters can be generated from the homomorphic filter and an estimate of the noise level. A homomorphic method for the treatment of multiplicative noise is presented. Finally, the limitations of the method with respect to phase are discussed and some results using real-world blurred images are presented.
Type Text
Publisher University of Utah
First Page 1
Last Page 119
Subject Homomorphic filtering; Removal; Image blurs; Blurred image
Subject LCSH Digital images; Digital images -- Editing
Language eng
Bibliographic Citation Cole, E. R. (1974). The removal of unknown image blurs by homomorphic filtering. 1-119. CSTD-74-002.
Series University of Utah Computer Science Technical Report
Rights Management ©University of Utah
Format Medium application/pdf
Format Extent 25,388,946 bytes
Identifier ir-main,16394
ARK ark:/87278/s6p84wd4
Setname ir_uspace
ID 706147
Reference URL https://collections.lib.utah.edu/ark:/87278/s6p84wd4
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