That was not what we were doing - It was more like weighting measurements proportional to their statistical variance, so that you penalize noisier measurements.

That was not what we were doing - It was more like weighting measurements proportional to their statistical variance, so that you penalize noisier measurements. In this process, you typically apply some sort of regularization to the objective function so that it converges to a smooth solution. There are some interactions between the weights chosen and standard regularization that creates non-uniform spatial resolution propeties, so much of the work was spent designing roughness penalties that played nice with the weightings.