The super resolution algorithm works as follows. It assumes
the gradient profile, which is the line crossing a zero crossing pixel in the
image in the direction the gradient is most strong, is of the form 
where 
and 
is the
gamma function.
The gradient profile is illustrated here:
(c) Is the gradient profile.
(b) Shows how the gradient profile of a specific edge pixel x0 looks like on the image.
The gradient profile traces the direction of the gradient in both direction (with and against it).
Using this assumption we can find a connection between LR
and HR images, this connection is given by 
and
. If we can find the and of the HR image
we could transform the LR gradient to the HR gradient, and since the gradient
contains all the information the image has it can be used to reconstruct the HR
image completely.
The algorithm calculates the gradient profile for a given LR image enlarged using bicubic interpolation.
After the profile is calculated and are extracted
from it. is assumed to be around 1.6 and is calculated using
the second moment of the profile. This calculation of is error prone
and so each is corrected
using its neighbors so the change in the gradient profile variance is not too
sharp. The algorithm then calculates and for the HR
image from the and of the LR image
using an empiric equation, is again
assumed to be around 1.6 with a different value given for each enlargement
factor.
After the calculation of and the gradient of
the HR image is estimated using the gradient of the enlarged LR image and the
HR image is estimated from both the LR image and the HR estimated gradient
using a minimization gradient descent algorithm.