The last week or so has been spent pouring over the various papers on multi-frame super resolution and trying to understand the approaches that have been taken in order to solve the super-resolution problem.
Having found an abundance of super-resolution papers online I have selected four papers which were written over the period of 1997 – 2004, which adopt the same approach towards solving the super-resolution problem, each of which builds on the ideas that were presented in the previous paper. The links to these papers are below, and are in chronological order.
“Restoration of a Single Superresolution Image from Several Blurred, Noisy, and Undersampled Measured Images”, Michael Elad and Arie Feuer
“A computationally efficient superresolution image reconstruction algorithm” Nhat Nguyen_, Peyman Milanfar and Gene Golub
“A Fast Super-Resolution Reconstruction Algorithm for Pure Translation Motion and Common Space-Invariant Blur” Michael Elad, Yacov Hel-Or
“Advances and Challenges in Super-Resolution”, Sina Farsiu, Dirk Robinson, Michael Elad, Peyman Milanfar
In the papers mentioned above super-resolution is defined as an inverse problem in which the formation of the low resolution images is modelled as series of successive transformations that are performed on a high resolution image. They then propose that super-resolution can be achieved by obtaining and then applying to the low resolution images the inverse of the forward transformation in order to reconstruct the original high resolution data. The forward model will be discussed below.
The forward model is the model that is used to describe the transformation from a high resolution image to a low resolution version of the same image. The low resolution image is treated as a high resolution image that has been subjected to motion (or warp), camera blur (the cameras point spread function), and down sampling (decimation) operations, the low resolution image is also treated as contained a noise component.
The model connecting the kth low resolution image to the high resolution image is shown below in a mathematical form:
Where
Yk is the kth low resolution image
Dk is the down sampling matrix
Ck is the Blurring matrix
Fk is the motion or warp matrix
X is the high resolution image
Ek is the kth noise vector
A more general model grouping the equations for all the low resolution frames into one equation is shown below:
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1 comment:
Hi tim,
how did you form the warp matrix Fk and decimation matrix Dk?
Abhijeet
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