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eee508_Restoration_Part1

# eee508_Restoration_Part1 - Image Restoration age esto at o...

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Image Restoration Basic idea: assume the source of the distortion is known; use this information and possibly info about the image to reconstruct the image . degradation image restoration x r ( n 1 , n 2 ) x ( n 1 , n 2 ) Example: digitizer distortion recorder distortion additive random noise blurring x d ( n 1 , n 2 ) image h restoration? x ( n 1 , n 2 ) + ± ² 2 1 , , 2 1 n n m m Ș ( n 1 , n 2 ) Systems modeling distortion, e.g. blur point spread function ± ² 2 1 , ± n n x r x ( n 1 , n 2 ) = original undistorted input m a random field wide-sense stationary (WSS). x d ( n 1 , n 2 ) = distorted image. h ( n 1 , n 2 ) = point-spread function (impulse response of system modeling distortion process). Ș ( n 1 , n 2 ) = noise assumed to be zero-mean white noise, WSS random field. 1 EEE 508

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Image Restoration ¾ Assumption: x and Ș are uncorrelated ±² ± ² ± ²± ² 2 1 2 1 2 1 2 1 2 1 , , , ; , , 12 n n m m x m m n n h n n x nn d K ³ ¦¦ Time varying point spread function in genera ¾ But, in several cases, it is sufficient to treat the PSF as a Linear Time-Invariant (LTI) system ´ much simpler to work with. Time-varying point spread function in general ¾ Since it is simpler to work with LTI systems ´ typically, LTI system model used for simplicity. n n n n n n h n n ³ µ µ ± ² ± ² ± ² ± ² 2 1 2 1 2 1 2 1 , , , , x x d EEE 508 2
Image Restoration ¾ Want to find also an LTI system for the image restoration: h ( n 1 , n 2 ) g ( n 1 , n 2 ) + Ș ( n 1 , n 2 ) x ( n 1 , n 2 ) x d ( n 1 , n 2 ) ± ² 2 1 , ± n n x ¾ In frequency domain: ± ² ± ² ± ² 2 1 2 1 2 1 , , , ± n n x n n g n n x d ³ ³ ¾ We could solve for X ( Ȧ 1 , Ȧ 2 ) ±² ± ² ± ²± ² 2 1 2 1 2 1 2 1 , , , , Z K ´ X H X d ± ² ± ² 2 1 2 1 2 1 2 1 2 1 , , , , , H H X X d µ EEE 508 3

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Image Restoration ¾ If noise small (or no noise), we can approximate X ( Ȧ 1 , Ȧ 2 ) by so ±² ± ² 2 1 2 1 2 1 2 1 2 1 , , , , , Z d d r X G H X X 2 1 1 , H G Inverse filter solution ¾ Problem: G ( Ȧ 1 , Ȧ 2 ) will not be defined if H ( Ȧ 1 , Ȧ 2 ) has zeros ³ inverse not stable.
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eee508_Restoration_Part1 - Image Restoration age esto at o...

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