Exploiting Sparsity While Extracting Morphological Diversity in Physics and Technology

Bedros Afeyan
Polymath Research, Inc.

Modern techniques from the worlds of harmonic analysis, multiresolution analysis, and the detection of coherent structures in noise, clutter and chaos, are making an impact in applied physics and technology. We will show instances
of this by highlighting rich applications in inertial confinement fusion (ICF) research. An attractive source of energy for the future, ICF faces many challenges such as the requirement for very smooth and well polished target
surfaces and uniform interiors, to a very high degree of radiation symmetry imploding a target, to the accurate tracking of the implosion itself in computer simulations when highly complicated nonlinear structures are born and interact
due to laser-plasma interaction caused instabilities which degrade target coupling, and hydrodynamic instabilities which can tear the targets apart before fusion energy is released.

Separating target surface defects on the tens of nanometer amplitude scale that are global (of the order of 100's of microns to a mm) from local bumps (micron to sub micron scale), when both are immersed in texture like artifacts due to
the detection and recording instruments on a spherical shell will a prime example. Various techniques of characterizing the target surface nonuniformities will be presented which result in spherical 3D data (atomic force microscopy),
to patches which are 2D (spherical diffractive phase shift interferometry), and 16 channel X ray transmission data which are 1D but can detect the fractal nature or voids and bumps throughout the CH or Be shells, and not just o their
surfaces. Methods of feature separation which exploit sparsity in large redundant libraries and iteratively home in on morphologically diverse
components, succeed in this context as will be shown.

Detecting, estimating and characterizing sub-percent level radiation asymmetry
in very noisy images will also be shown which rely on multiresolution analysis techniques which have sparsity and redundant libraries as their primary tools. Throughout this presentation, practical considerations and mathematical precision will be made to coexist harmoniously.

Back to Short Course: Sparse Representations and High Dimensional Geometry : In conjunction with the AMS 2007 Von Neumann Symposium