On model-space and data-space regularization:
A tutorial

Sergey Fomel

sergey@sep.stanford.edu

ABSTRACT

Constraining ill-posed inverse problems often requires regularized optimization. I describe two alternative approaches to regularization. The first approach involves a column operator and an extension of the data space. The second approach constructs a row operator and expands the model space. In large-scale problems, when the optimization is incomplete, the two methods of regularization behave differently. I illustrate this fact with simple examples and discuss its implications for geophysical problems.