parameter estimation using lsqnonlin() with unknown target values

I am going to do a gamma correction on some images. So according to these equations, I have to find unknown parameters using “ lsqnonlin ” function.

i estimated A, k with " lsqnonlin function" in eq(2).

now, I have to estimate gamma value from equation (3). but I don’t know how to use " lsqnonlin function" to solve my problem(s) with unknown target value. because i have (RGB)_out' and i initial guess of gamma values. but i don't have target values.

Any help will be appreciated. Tanx:)

[Image Analyst]

Original thread http://www.mathworks.com/matlabcentral/answers/168498-finding-non-linear-gamma-model-s-parameters-using-lsqnonlin