最新topic-14_image_restoration-ii 图像复原教学讲义ppt课件.ppt

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1、topic-14_image_restoration-ii图像复原OutlineRestorationProblemUnconstrainedRestorationInverseFilterConstrainedRestorationDeterministicRegularizationStochasticRegularizationWienerFilterRestorationforSignalDependentNoiseGeometricRestoration1EECE-5626:Image

2、Restoration-2DeterministicRegularizationTheclassofproblemsinvolvinginversefiltersarecalled“Ill-Conditioned”problems.Ingeneralrestorationisanill-conditionedproblem.Itisevidentthattheinversefilterisnotanattractivepracticalapproachbecauseithasunconstrai

3、nedsolution.Wehavetoconstraintheoptimizationsolutioninordertoavoidstabilityproblemsassociatedwiththeinversefilter.ThisisalsoknownasaRegularizationapproach.Therearetwoapproachestothisconstrainedoptimization:Deterministicregularization:Weimposeconstrai

4、ntsbasedonimageparametersforstabilization.Stochasticregularization:Weuseimageandnoiserandomfieldspectraldensityfunctionsforstabilization.2EECE-5626:ImageRestoration-2DeterministicRegularization(5)Comments:(continued)Letusanalyzetherestorationerrornor

5、m:(inthefollowingdevelopment,wedroptheargumentsortoconsetoconservespace).UsingParseval’srelation,wehave6EECE-5626:ImageRestoration-2DeterministicRegularization(6)Comments:(continued)ErrorAnalysis:ForafixedIfIf7EECE-5626:ImageRestoration-2Determinist

6、icRegularization(7)Comments:(continued)ErrorAnalysis:IfIfThusthetotalrestorationerrorisaminimumforsome.ErrorNorm8EECE-5626:ImageRestoration-2DeterministicRegularization(8)Comments:(continued)SelectionofthestabilizingoperatorInthehighsignal-to-noisera

7、tio(SNR)region,i.e.,whenthentheregularizationshouldhaveverylittleeffect(sodeconvolutionhavesharpentheimage).HencewechooseInthelowSNRregion,i.e.,whenthenthereshouldbeastrongregularizationtoavoidinstability.Hencewechoose9EECE-5626:ImageRestoration-2Det

8、erministicRegularization(9)Comments:(continued)Basedonthechoicesgivenonthepreviousslide,thefrequencyresponseofthestabilizingoperatormaylooklike:Apopularchoiceforisthewell-known2-DLaplacianoperator:Magnitude10EECE-5626:ImageRestoration-2DeterministicR