For one reason or another I started to estimate histograms of gradients of natural images.
Let us assume that I want to try to fit a function of the exponential family to this data.
For example $$f(t) = C \exp\left(-\sum_{\forall i}\left(\frac{{|t|}}{b_i}\right)^{a_i}\right)$$
To data where we have measured pairs $(t_k,\hat f(t_k)), k = 1,2,\cdots,n$ and we want to estimate $C,a_i,b_i$
So my question is, how can I find some method to try and optimize
$$\min_{C,a_i,b_i}\left\{\sum_{\forall k} (f(t_k) - \hat f(t_k))^2\right\}$$