lsqnonlin time optimization of matrix

Dear all

I have a 551*551 matrix with RGB values. I need to optimize these values to "normal conditions" with calibration functions of the form D = a+(b/(x-c)) with each separate a, b and c constants and x the color value.

I rescale the RGB values to something known and "normal" (I remove component that doesn't need to influence the RGB values accoriding to calibration conditions).

So i need to perform (D_red-D_blue)²+(D_blue-D_green)²+(D_green-D_red)²=0 with D_color = a+(b/((x*rescaling_factor)-c)).

This function works:

%first vectorized the matrix tot 1:551*551
%and with a RGB to optical density conversion (10.^-(X*factor))
parfor i=1:(551*551)
f=@(factor) [(aR+(bR/((10.^-(R(i)*factor))-cR)))-(aB+(bB/((10.^-(B(i)*factor))-cB)));...
                (aB+(bB/((10.^-(B(i)*factor))-cB)))-(aG+(bG/((10.^-(G(i)*factor))-cG)));...
                (aG+(bG/((10.^-(G(i)*factor))-cG)))-(aR+(bR/((10.^-(R(i)*factor))-cR)))]
output(i)=lsqnonlin(f,factor,lb,ub,options);
end

But it takes aprox. 300s to perform on a 551*551 matrix.

My knowledge of matlab isn't great, so I would like to know is there a much faster way to calculate this with the same results? Is the use of Jacobian possible here and will it give a performance boost? Maybe mex file?

Thank you for your help!!

Dominique