Spectrally grouped total variation reconstruction for scatter imaging using ADMM

Abstract

Abstract-We consider X-ray coherent scatter imaging, where the goal is to reconstruct momentum transfer profiles (spectral distributions) at each spatial location from multiplexed measurements of scatter. Each material is characterized by a unique momentum transfer profile (MTP) which can be used to discriminate between different materials. We propose an iterative image reconstruction algorithm based on a Poisson noise model that can account for photon-limited measurements as well as various second order statistics of the data. To improve image quality, previous approaches use edge-preserving regularizers to promote piecewise constancy of the image in the spatial domain while treating each spectral bin separately. Instead, we propose spectrally grouped regularization that promotes piecewise constant images along the spatial directions but also ensures that the MTPs of neighboring spatial bins are similar, if they contain the same material. We demonstrate that this group regularization results in improvement of both spectral and spatial image quality. We pursue an optimization transfer approach where convex decompositions are used to lift the problem such that all hypervoxels can be updated in parallel and in closed-form. The group penalty introduces a challenge since it is not directly amendable to these decompositions. We use the alternating directions method of multipliers (ADMM) to replace the original problem with an equivalent sequence of sub-problems that are amendable to convex decompositions, leading to a highly parallel algorithm. We demonstrate the performance on real data.

Classifiers for material discrimination with dual modality x-ray transmission and coherent x-ray diffraction system

“…A linear array of energy-sensitive detectors (only at 60keV) are scanned to collect a 2D image of the coherent signal. A variant of the group total variation (TV) algorithm [8] is used for reconstructing the diffraction image from the scatter measurements.…”

“…A Support Vector Machine (SVM) is a supervised learning model used for classification by finding the best hyperplane separating all data points into two classes. The best hyperplane is defined as the one with the largest or maximum margin between the two classes [8] [9]. The margin is the distance that separates data points, from the two classes, that are closest to each other.…”