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least squares on images
Posted:
Mar 22, 2014 6:16 PM


I'm trying to use least squares to minimise expression (9) http://infoscience.epfl.ch/record/188639/files/ImageDehazing_icip2013.pdf :
(J,t) = argmin  tJ+(1t)AIrgb^2
where t is a single channel image array (mxn), J is an RGB image (mxnx3), and Irgb is a 3channel image (mxnx3) A is a 3x1 vector.
I'm ignoring the gradient terms in the equation from the original paper for now.
J and t can change, but Irgb and A are constant.
I'm really struggling to formulate this into a format that I can use a least squares method with.
J can be calculated from t and Irgb, so I guess I can reduce the input to just t.
This is what I've tried
I rearranged the expression above to :
 t(JA)  (Irgb + A) ^2
now If I set my input x to equal JA, and y = (Irgb+A), I would expect y\x to return an estimate of t?
the expression is now in the form: axy, where a=t, x=(JA) and y=Irgb+A;
I've listed the inputs so x=[Jr(:)A(1) Jg(:)A(2) Jr(:)A(3)]; and y=[I_R(:)+A(1) I_G(:)+A(2) I_B(:)+A(3)];
where I_R=I(:,:,1), I_G=I(:,:,2) and I_B=I(:,:,2)
y\x is actually giving me a 3x3 matrix and I'm sure my formulating must be wrong somewhere, because I can't multiply my Nx1 vector x by the 3x3 matrix
If anybody can see where I've messed up it would be great if they can let me know.
Thanks Adam



