Extremal regularization

William W. Symes

ABSTRACT

Extremal regularization finds a model fitting the data to a specified tolerance, and additionally minimizing an auxiliary criterion. It provides relative model/data space weights when no statistical information about the model or data is available other than an estimate of noise level. A version of the Moré-Hebden algorithm using conjugate gradients to solve the various linear systems implements extremal regularization for large scale inverse problems. A deconvolution application illustrates the possibilities and pitfalls of extremal regularization in the linear case.