Superresolution

Superresolution - Supe -Resolution Super Resolution...

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Unformatted text preview: Supe -Resolution Super Resolution Super-Resolution (SR) image re-construction is the process of combining the information from multiple Low-Resolution (LR) aliased and noisy frames of the Low Resolution (LR) aliased and noisy frames of the same scene to estimate a High-Resolution (HR) un- aliased and sharp/de-blurred image. SR Observation Mode SR Observation Model The values of the pixels in the k-th 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, & sub-pixel 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 ill-conditioned 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]- Least-square error minimization [Schultz et al., 1996] Regularized maximum a Posteriori (MAP) methods- Regularized maximum a Posteriori (MAP) methods [Hardie et al., 1997] Fusion-Restoration (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] - Non-iterative fusion step followed by a restoration step.- More computationally efficient Perceptual-based Super-Resolution (Karam et al., 2011) MAP-Based 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 log-likelihood 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 Two-Step (FTS) SR Algorithm [Farsiu04 [Farsiu04] Fast Two-Step SR (FTS) algorithm consists of a non-iterative data fusion step followed by an iterative gradien descent deblurring step followed by an iterative gradient-descent deblurring step ....
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This document was uploaded on 03/11/2012.

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Superresolution - Supe -Resolution Super Resolution...

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