  We develop a model independent, robust method for determining galaxy rotation
velocities across a 2D array of spaxels from an integral field spectrograph.
Simulations demonstrate the method is accurate down to lower spectral
signal-to-noise than standard methods: 99\% accurate when median $S/N=4$. We
apply it to MaNGA data to construct the galaxy velocity map and galaxy rotation
curve. We also develop a highly efficient cubic smoothing approach that is
$25\times$ faster computationally and only slightly less accurate. Such model
independent methods could be useful in studying dark matter properties without
assuming a galaxy model.
