Wavelets, Curvelets and Multiresolution Analysis Techniques in Fast Z Pinch Research

TL;DR

This paper applies wavelet, curvelet, and multiresolution analysis techniques to improve the analysis of X-ray imaging data from Z pinches, enabling better quantification of implosion dynamics and non-uniformities.

Contribution

It introduces the use of advanced multiresolution techniques to analyze Z pinch images, particularly for quantifying shell deformations and density distributions.

Findings

Curvelet transform outperforms wavelets in denoising.

Undecimated wavelet decompositions are more effective than decimated ones.

Legendre polynomial decomposition quantifies non-uniformities in shell density.

Abstract

Z pinches produce an X ray rich plasma environment where backlighting imaging of imploding targets can be quite challenging to analyze. What is required is a detailed understanding of the implosion dynamics by studying snapshot images of its in flight deformations away from a spherical shell. We have used wavelets, curvelets and multiresolution analysis techniques to address some of these difficulties and to establish the Shell Thickness Averaged Radius (STAR) of maximum density, r*(N, {\theta}), where N is the percentage of the shell thickness over which we average. The non-uniformities of r*(N, {\theta}) are quantified by a Legendre polynomial decomposition in angle, {\theta}, and the identification of its largest coefficients. Undecimated wavelet decompositions outperform decimated ones in denoising and both are surpassed by the curvelet transform. In each case, hard thresholding based on noise modeling is used.