Model and Standard Operating Procedures Supporting Signal Variation Flow Graph Analysis

Abstract

This document will describe the principles of the Signal Variation Flow Technique, and the uncertainty models generated using it. We focus on the capture of the variation between the ideal signal and the measured signal. The ideal signal is defined to represent the signal output of a system whose full state behavior is known, with no variation in environment or during operation, and whose photons trajectories are not modified by the object. A CT uncertainty analysis is the result of two main steps. First, the radiography regime extends from the source to the collected image, which is 2D in the case of standard CT. This maps all upstream uncertainties into the variation observed on the radiograph and captures all variation in the physical domain. Second, the reconstruction regime extends from the captured images to the reconstructed 3D image. This regime is purely in the mathematical domain and corrects reconstruction algorithm artifacts/anomalies. The present work focuses on building the model through the radiography regime. The reconstruction regime is expected to be largely a study of algorithmic sensitivity, requiring the definition of a range of standardized tests through which the algorithms would be run. Radiographic variation would then be mapped through reconstruction sensitivities to predict the signal variation in the final image. An incomplete list for the reconstructed image variation output basis includes voxel density, edge blur and length variation, in analogous fashion to the basis functions presented in this work. The signal variation occurs in several forms at the radiograph. These forms are gathered into a complete basis set of functions describing all variation on the radiograph. The scale of each basis function is calculated independently via a specific SVFG. This includes 0D pixel noise (0DI), 0D energy noise (0DE), 1D blur (1DB), 1D length (1DL) or 2D position (2DP). These models are orthogonal in that they each explore a space in the signal variation domain that cannot be reached by the other basis functions. The variation basis functions, and associated SVFG models are split by output dimensionality, a term loosely used for categorization, and explained further below.