Conclusion

Extremal regularization appears to be practical for large scale problems, as the Moré-Hebden algorithm with conjugate gradient inner solves either converges in a reasonable number of steps or doesn't converge when the constraint (target noise level) forces too many small singular values into the act. All of these terms are relative - small, doesn't converge, etc. Modulo floating point arithmetic, the algorithm will always work if enough effort is expended. The issue of course is reasonable level of effort, and that is in some sense a translation of the concept of ``noise level'' - it's the misfit between the data and what you can achieve with an easily computable model, no more.

Thus extremal regularization as implemented in this report appears to give a reasonable approach to relative weighting in model and data space when an independent estimate of noise level is somehow available. This is the case for example in the examples mentioned in the introduction. Maybe quiet parts of seismic traces furnish pure noise series which might give a usable estimate of noise level - provided that the modeling operator is sophisticated enough to fit the rest!