{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Superresolution

Superresolution - Super Resolution Super-Resolution...

Info icon This preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
Super-Resolution Super Resolution l i ( ) i i i h 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.
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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 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 i h ddi i i d D H F h Blurring (H k ) is the additive noise and k , k , 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 ill conditioned task especially that the system is ill-conditioned
Image of page 2
Existing Super-Resolution Approaches 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)
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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 ² ³ K k k ,..., 1 , )] | log[Pr( max arg y z z Gaussian distribution for the noise and Pr(z|{y k }): ² ³ ² ³ 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 n . An iterative gradient descent minimization procedure is used to update the HR estimate as follows: f l l l z z z z z ± ´ | ) ( 1 H where H l is the step size l where is the step size
Image of page 4
Fast Two-Step (FTS) SR Algorithm [Farsiu04] Fast Two-Step SR (FTS) algorithm consists of a non-iterative data fusion step followed by an iterative gradient-descent deblurring step followed by an . Data Fusion Step: Estimated by registration followed by a median operator resulting in a blurred version of the HR frame, , where is the deblurred HR frame Z H X .
Image of page 5

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 6
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern