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If I understand you well, you are trying to fit some arbitrary basis function to your data and want to find a (possibly local) maximum of that function.

A blunt and computationally expensive way of doing that is to select an environment of the maximum you are interested in, compute the 2D fourier transform, possibly remove some high frequencies from that to your taste, and transform back at higher resolution (scale your transform appropriately). Then, you can find the maximum of the regridded smoothed function, which may or may not have anything to do with your original data.

There are many choices of basis functions possible. Use a priori knowledge of the sampled data as much as you can to choose your basis.