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dc.contributor.advisorFredo Durand
dc.contributor.authorLevin, Anaten_US
dc.contributor.authorNadler, Boazen_US
dc.contributor.authorDurand, Fredoen_US
dc.contributor.authorFreeman, William T.en_US
dc.contributor.otherComputer Graphicsen
dc.date.accessioned2012-07-31T17:45:08Z
dc.date.available2012-07-31T17:45:08Z
dc.date.issued2012-10-07
dc.identifier.urihttp://hdl.handle.net/1721.1/71919
dc.description.abstractImage restoration tasks are ill-posed problems, typically solved withpriors. Since the optimal prior is the exact unknown density of natural images,actual priors are only approximate and typically restricted to small patches. Thisraises several questions: How much may we hope to improve current restorationresults with future sophisticated algorithms? And more fundamentally, even withperfect knowledge of natural image statistics, what is the inherent ambiguity ofthe problem? In addition, since most current methods are limited to finite supportpatches or kernels, what is the relation between the patch complexity of naturalimages, patch size, and restoration errors? Focusing on image denoising, we makeseveral contributions. First, in light of computational constraints, we study the relation between denoising gain and sample size requirements in a non parametricapproach. We present a law of diminishing return, namely that with increasingpatch size, rare patches not only require a much larger dataset, but also gain littlefrom it. This result suggests novel adaptive variable-sized patch schemes for denoising. Second, we study absolute denoising limits, regardless of the algorithmused, and the converge rate to them as a function of patch size. Scale invarianceof natural images plays a key role here and implies both a strictly positive lowerbound on denoising and a power law convergence. Extrapolating this parametriclaw gives a ballpark estimate of the best achievable denoising, suggesting thatsome improvement, although modest, is still possible.en_US
dc.format.extent23 p.en_US
dc.relation.ispartofseriesMIT-CSAIL-TR-2012-022
dc.rightsCreative Commons Attribution-NonCommercial-NoDerivs 3.0 Unporteden
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/
dc.titlePatch complexity, finite pixel correlations and optimal denoisingen_US
dc.identifier.citationsupplemental material for conference paper at ECCV 2012 (European Conf. on Computer Vision)en_US


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