| It was in the spirit of “reuniting divergent trends by clarifying the common features and interconnections of many distinct and diverse scientific facts” that Courant and Hilbert published their book Methods of Mathematical Physics [43]. This thesis is written in the same spirit and with the same goal. We focus our attention on the problem of wavefront reconstruction and deconvolution in adaptive optics. This is an ill-posed, non-linear inverse problem that touches on the theory of harmonic analysis, variational analysis, signal processing, nonconvex optimization, regularization, statistics and probability. Numerical solutions rely on spectral and operator-splitting methods as well as limited memory and multi-resolution techniques. We introduce novel methods for wavefront reconstruction and compare our results against common techniques. Previous work on this problem is reviewed and unified in a non-parametric, analytic framework. |
