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Restoring Images Degraded by Spatially-Variant Blur

dc.contributor.authorNagy, James G.en_US
dc.contributor.authorO'Leary, Dianne P.en_US
dc.description.abstractRestoration of images that have been blurred by the effects of a Gaussian blurring function is an ill-posed but well-studied problem. Any blur that is spatially invariant can be expressed as a convolution kernel in an integral equation. Fast and effective algorithms then exist for determining the original image by preconditioned iterative methods. If the blurring function is spatially variant, however, then the problem is more difficult. In this work we develop fast algorithms for forming the convolution and for recovering the original image when the convolution functions are spatially variant but have a small domain of support. This assumption leads to a discrete problem involving a banded matrix. We devise an effective preconditioner and prove that the preconditioned matrix differs from the identity by a matrix of small rank plus a matrix of small norm. Numerical examples are given, related to the Hubble Space Telescope Wide-Field / Planetary Camera. The algorithms that we develop are applicable to other ill-posed integral equations as well. (Also cross-referenced as UMIACS-TR-95-26)en_US
dc.format.extent3127951 bytes
dc.relation.ispartofseriesUM Computer Science Department; CS-TR-3426en_US
dc.relation.ispartofseriesUMIACS; UMIACS-TR-95-26en_US
dc.titleRestoring Images Degraded by Spatially-Variant Bluren_US
dc.typeTechnical Reporten_US
dc.relation.isAvailableAtDigital Repository at the University of Marylanden_US
dc.relation.isAvailableAtUniversity of Maryland (College Park, Md.)en_US
dc.relation.isAvailableAtTech Reports in Computer Science and Engineeringen_US
dc.relation.isAvailableAtUMIACS Technical Reportsen_US

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