Approximating filtered scale-variant signals
We develop theorems that place limits on the point-wise approximation of the responses of filters, both linear shift invariant (LSI) and linear shift variant (LSV), to input signals and images that are LSV in the following sense: they can be expressed as the outputs of systems with LSV impulse respo...
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Published in | IEEE transactions on image processing Vol. 14; no. 1; pp. 23 - 35 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
New York, NY
IEEE
01.01.2005
Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
Subjects | |
Online Access | Get full text |
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Summary: | We develop theorems that place limits on the point-wise approximation of the responses of filters, both linear shift invariant (LSI) and linear shift variant (LSV), to input signals and images that are LSV in the following sense: they can be expressed as the outputs of systems with LSV impulse responses, where the shift variance is with respect to the filter scale of a single-prototype filter. The approximations take the form of LSI approximations to the responses. We develop tight bounds on the approximation errors expressed in terms of filter durations and derivative (Sobolev) norms. Finally, we find application of the developed theory to defoveation of images, deblurring of shift-variant blurs, and shift-variant edge detection. |
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Bibliography: | ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23 ObjectType-Article-1 ObjectType-Feature-2 |
ISSN: | 1057-7149 1941-0042 |
DOI: | 10.1109/TIP.2004.838696 |