David you likely do not need the answer anymore but everyone else:
I decided to code this out : http://www.mathworks.com/matlabcentral/fileexchange/54944-calculate-blur-kernel-from-original-and-blurry-images
my old comment: This seems like a perfect task for SVDor QR factorization or least square means (an over-contrained system of equations).
esentially : blurredImg = sharpImg**Kernel Kernel is what you are trying to find.
Kernel = a matrix of mxn unknown doubles .
'**' = convolution = moving sum of dot product between Kernel and the pixels of the image in batches of size(mxn).
you can rewrite that entire mess into a series of many many equations which are along the lines of...
blurredImg(i,j) = Kernel.*sharpImg( i-m/2:i+m/2,j-n/2:j+n/2); % This will only work for odd size Kernel.
for each i,j you can write an equation like that. Let's call the sharpImg( i-m/2:i+m/2,j-n/2:j+n/2) the constants of the euqations such that
constants(:,i,j) =reshape(sharpImg( i-m/2:i+m/2,j-n/2:j+n/2),[1,1,m*n]));
least square mean solvers take in a set of equations writen in matrix form ( going back to the linear algebra basics of writing a system of equations as a matrix equation).
blurredImg(:,1) = (Kernel(:)'*constants(:,:,1))';
The simplest way to solve for kernels is QR factorization although there are other solvers available.
good luck
*The above was meant to be easy to understand , but at the cost of extremely inefficient and sub-optimal code.
