Wavelets, Curvelets and Multiresolution Analysis Techniques Applied to ICF and Z Pinch Research

Summary form only given. We will show, through a number of diverse applications, how multiresolution analysis (MRA) can have a strong impact in inertial confinement fusion (ICF) and Z pinch research. We will start with the characterization of ICF target surface roughness and imperfections using wavelets and curvelets on the sphere contrasting their advantages over spherical harmonics at finer scales of the MRA. We will then show Be ICF layer deposition dynamics characterization by denoising and deblurring a sequence of time lapse photographic images. We will then consider rad-hydro simulation data of ICF implosions in order to contrast the wavelet decomposition and information compression characteristics of uniform and igniting targets vs those with strong Rayleigh-Taylor nonlinear growth using (1+1)D wavelet decompositions in these highly anisotropic (r,thetas) data sets. In Z pinches, we will focus on three separate applications: (1) the characterization of the radiation asymmetry of double Z pinch hohlraums from noisy X ray backlighting images using curvelets and undecimated wavelet transforms. (2) In nested wire array implosions, denoising X ray backlighting images so that the individual wire MHD instabilities can be identified and contrasted with collective wire array MHD modes. (3) Characterization of astrophysical radiation jets and K-H rolls emulated in the laboratory using Z pinches. The unifying themes throughout these applications, will be denoising and pattern detection using optimal phase space tiling techniques such as wavelets and curvelets for signals (1D), images (2D) and hyperspectral (3D) data sets. Whether it is spectroscopy or imaging in noisy environments, ICF research can benefit greatly by the adoption of these techniques where proper statistical analysis plays a key role