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Unformatted text preview: Supe Resolution Super Resolution SuperResolution (SR) image reconstruction is the process of combining the information from multiple LowResolution (LR) aliased and noisy frames of the Low Resolution (LR) aliased and noisy frames of the same scene to estimate a HighResolution (HR) un aliased and sharp/deblurred image. SR Observation Mode SR Observation Model The values of the pixels in the kth low resolution frame Y of the sequence can be Warping (F k ) resolution frame Y k of the sequence can be expressed in matrix notation as: K k k k k k k ,..., 1 , . . . n z F H D y Blurring H where y k and z are, respectively, the lexicographic form of Y k and the undegraded HR image Z , n k Blurring (H k ) is the additive noise and D k , H k , F k are the downsampling, blurring, & subpixel warping matrices. Y k : N 1 N 2 pixels; Z : rN 1 x rN 2 , where r is the Downsampling (D k ) magnification factor. Inverting ( D k . H k . F k ) to obtain z is not a trivial task especially that the system is il conditioned task especially that the system is illconditioned Existing Supe Resolution Approache Existing Super Resolution Approaches Iterative SR methods Projection onto convex sets (POCS) [Stark et al 1989 Projection onto convex sets (POCS) [Stark et al., 1989] Leastsquare error minimization [Schultz et al., 1996] Regularized maximum a Posteriori (MAP) methods Regularized maximum a Posteriori (MAP) methods [Hardie et al., 1997] FusionRestoration (FR) SR methods (also known as two Fusion Restoration (FR) SR methods (also known as two step methods) [Elad et al., 2001; Farsiu et al., 2004; Hardie et al., 2007]  Noniterative fusion step followed by a restoration step. More computationally efficient Perceptualbased SuperResolution (Karam et al., 2011) MAPBased SR Algorithm [Hardie et al. 97] The HR image estimate can be computed by maximizing the a posteriori probability, Pr(X{Y k }), or by maximizing the loglikelihood function: This results in the following cost function to be minimized assuming a K k k ,..., 1 , )]  log[Pr( max arg y z z Gaussian distribution for the noise and Pr(z{y k }): z z Wz y Wz y z 1 2 2 1 2 1 ) ( C f T T V where y is a vector concatenating all the LR observations y k , k=1,..,K, V n is the noise standard deviation and C is the covariance matrix of z, W is the degradation matrix 2 2 n V degradation matrix . An iterative gradient descent minimization procedure is used to update the HR estimate as follows: f z z z z  ) ( 1 H where H is the step size l l l l z z 1 where H l is the step size Fast TwoStep (FTS) SR Algorithm [Farsiu04 [Farsiu04] Fast TwoStep SR (FTS) algorithm consists of a noniterative data fusion step followed by an iterative gradien descent deblurring step followed by an iterative gradientdescent deblurring step ....
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This document was uploaded on 03/11/2012.
 Fall '09

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