Robust `1 Approaches to Computing the Geometric Median and Principal and Independent Components

Abstract. Robust measures are introduced for methods to determine statistically uncorrelated or also statistically independent components spanning data measured in a way that does not permit direct separation of these underlying components. Because of the nonlinear nature of the proposed methods, iterative primal-dual based methods are presented for the optimization of merit functions, and convergence of these methods is proved. Illustrative examples are presented to demonstrate the benefits of the robust approaches, including an application to the processing of dynamic medical imaging.