AdvanTopics in CSInverse Problems in Imaging
AdvanTopics in CSInverse Problems in Imaging CSC 790
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This 7 page Class Notes was uploaded by Melyssa Aufderhar on Wednesday October 28, 2015. The Class Notes belongs to CSC 790 at Wake Forest University taught by Staff in Fall. Since its upload, it has received 18 views. For similar materials see /class/230726/csc-790-wake-forest-university in ComputerScienence at Wake Forest University.
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Date Created: 10/28/15
rt 1 V iiiii iii mgi qii L V PaL39JI Pauca Department of Computer Science Wake Forest University CSC 790 Computational Imaging October 2008 Components 0 The system H o The input Xm7 n o The output ym7n Ym n HXm7 7 Examples 0 HXmv quot1 3Xm7 n 15 o HXmv quot1 mzr12xm7 n O Hmm quot1 2m in Xu v 1700 voo A system H is linear it and only it any linear combination of two inputs produces the same combination of their respective outputs Ha1x1mna2x2m7 i a1HX1m7 ia2HX2m7n a1y1mna2Y2m7 o lsHXm n mzr12Xm 17 linear Ha1X1m7 7 32X2m7 7 quot72 2a1X1m7 a2X2m7 a1mznzx1m n azmzn2X2m a1HX1m7 n a2HX2m7 quot1 Yes 0 lsHXm n 3Xm n 15 linear A system H is spatially invariant or shift invariant it a translation of the input causes the same translation of the output It Xm 7 k n 7 6 implies ym 7 k n 7 Z o lsHXm n mzr12Xm n shift invariant Denote the translation of the input by k 6 as rm n Xm 7 k n7 6 Then Hrm n mznzrm n 7 mznzxm7 k n7 6 The translation of the output of HXm n ym n mzr12Xm n by k 6 is ym7 k n7 z m7 k2n7 2Xm7 k n7 a No