Robust ℓ1 Approaches to Computing the Geometric Median and Principal and Independent Components

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 me...

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Bibliographic Details
Published in:Journal of mathematical imaging and vision 2016-09, Vol.56 (1), p.99-124
Main Authors: Keeling, Stephen L., Kunisch, Karl
Format: Article
Language:English
Subjects:
Applications of Mathematics
Computer Science
Image Processing and Computer Vision
Mathematical Methods in Physics
Signal,Image and Speech Processing
Online Access:Get full text
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Summary: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 methods are presented for the optimization of merit functions, and local 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.
ISSN:0924-9907
1573-7683
DOI:10.1007/s10851-016-0637-9