LINEAR AND NONLINEAR APPROACHES TO SOLVE THE INVERSE PROBLEM - APPLICATIONS TO POSITRON-ANNIHILATION EXPERIMENTS

We present linear and non-linear filters to solve the ill-posed invers e problem and we use them to extract relevant information from positro n lifetime and 2D-angular correlation of the annihilation radiation of positrons in solids. A general optimal linear filter is first derived . Then a second linear approach, based on Bayes' theorem, is described . We show that these two linear approaches are indeed equivalent. Two non-linear methods are then discussed. The first is a Bayesian approac h which makes use of the maximum entropy principle. The second is an i terative method derived from the general optimal linear filter. Applic ations of these filtering techniques to positron lifetime decay curves illustrate how lifetimes shorter than the instrumental resolution can be extracted. Finally, we apply the iterative non-linear filter to th e problem of the ridge-like Fermi surface on the high temperature supe rconducting compound YBa2Cu3O7-delta. For the first time a direct meas urement of the ridge width through a Brillouin zone is obtained. It is compared with results of band structure calculations.