Over-Complete Dictionary Methods for Structural Materials Characterization by High Energy X-ray Diffraction Microscopy

Abstract

High energy x-ray diffraction (HEXD) data collected during loading experiments permits probing crystal structure of a plastically deforming material sample. An elastoplastic deformation is associated with heterogeneity in both crystal orientation and lattice spacing—manifesting as azimuthal broadening and radial broadening of diffraction peaks respectively. Quantifying the spreading effect is challenging, especially when individual Bragg peaks merge and overlap. In this thesis, we develop over-complete dictionary models to evaluate signal spread in HEXD data.

We begin by modeling the intensity signal in the vicinity of a diffraction ring as a sparse, nonnegative superposition of Gaussian basis functions drawn from an over-complete dictionary. By formulating a convex optimization problem and solving it using non-negative fast iterative soft thresholding, we arrive at a sparse representation that we use to compute scalar features of radial and azimuthal broadening for the peaks of a diffraction ring. We show that analysis of diffraction peak shape information from an aluminum alloy 7075 T651 sample provides insight into the origin of material state.

To model high temporal resolution diffraction measurements captured during a dynamic in situ experiment with the mixed-mode pixel array detector (MM-PAD), we develop a temporally coupled model that penalizes differences in the distribution of dictionary entries used in time. We use the solution of the resulting coupled convolutional sparse coding problem to compute a feature indicative of signal spread in a manner that is correlated with plastic deformation of the sample.

To further improve data representation we bolster both the dictionary model and the model of coefficients in time. First, we formulate the dictionary to be learned from the data and generate dictionary entries at multiple scales by decimating or interpolating the learned dictionary entries. Second, we derive an objective term from the optical flow constraint equation to model the coefficients in time. The coefficients are encouraged to follow trajectories mapped by optical flow velocities as they move through shift/scale space to represent the translating and broadening diffraction peaks. We recover the true dictionary in simulated data and demonstrate the technique on a HEXD time series captured by the MM-PAD.