Benchmarking and Optimizing Techniques for Inverting Images of DIII-D Soft X-Ray Emissions

A tangential 2-D soft \hbox{x-ray} (SXR) imaging system is installed on DIII-D to directly measure the 3-D magnetic topology at the plasma edge. This diagnostic allows the study of the plasma SXR emissivity at time resolutions $\geq$\,10~ms and spatial resolutions $\sim 1$~cm. Extracting 3-D structure from the 2-D image requires the inversion of large ill-posed matrices $-$ a ubiquitous problem in mathematics. The goal of this work is to reduce the memory usage and computational time of the inversion to a point where image inversions can be processed between shots. We implement the Phillips-Tikohnov and Maximum Entropy regularization techniques on a parallel GPU processor. To optimize the memory demands of computing these matrixes, effects of reducing the inversion grid size and binning images are analyzed and benchmarked. Further benchmarking includes a characterization of the final image quality (with respect to numerical and instrumentation noise).