Future Work

In this paper I glossed over several problems. First, $\sigma$ should be a space-varying function rather than the constant I proposed. A bootstrap approach (using the model residual at one non-linear iteration as our guess at a space-varying $\sigma$) might prove effective but hasn't been tested. How to calculate $\sigma$ for the non-missing data problem is an open question. In the generic geophysical operator $\bf L$, we often don't know which model components are estimated through the data fitting goal and which are estimated by the model styling goal. Finally, I made the assumption that I was dealing with models with a normal distribution. Whether replacing $\bf v$ with another distribution or using something similar to the geostatistician's normal-score transform would be effective in correctly modeling these distributions is unknown.