Computational engine for development of complex cascaded models of signal and noise in X-ray imaging systems

Abstract

The detective quantum efficiency (DQE) is generally accepted as the primary metric of signal-to-noise performance in medical X-ray imaging systems. Simple theoretical models of the Wiener noise power spectrum (NPS) and DQE can be developed using a cascaded-systems approach to assess particular system designs and establish operational benchmarks. However, the cascaded approach is often impractical for the development of comprehensive models due to the complexity and extremely large number of algebraic terms that must be manipulated to describe signal and noise transfer. We have developed a computational engine that overcomes this limitation. Using a predefined library of elementary physical processes, complex models are assembled and input-output relationships established using a graphical interface. A novel recursive algorithm is described that allows the signal and noise analyses of models with arbitrary complexity including the use of multiple parallel cascades. Symbolic mathematics is used to develop analytic expressions for the NPS and DQE. The algorithm is validated by manual calculation for simple models and by Monte Carlo calculation for complex models. We believe our approach enables the use of complex cascaded models to design better detectors with improved image quality.

Optimal Frequency-Based Weighting for Spectral X-Ray Projection Imaging

“…APPENDIX Below, we summarize the general formulations in continuous Fourier integrals of the DQE, NEQ, and detectability index based on an optimal Hotelling observer, followed by the resulting expressions for projection imaging using a multiple-bin photon counting detector. Listing all the contributors to the unified framework for system evaluation is not in the scope of this work but interested readers are referred to the work of Cunningham and Shaw [27] for a historical exposition and general overview, as well as to the introduction by Sattarivan and Cunningham [28] on how to estimate the DQE via the MTF and noise power spectrum (NPS) by cascading elementary processes.…”

“…3) Optimally Weighted Projection Image: Using the general (17), optimal frequency-based weights can be calculated for the system described in Sections III-B1 and III-B2. Each entry in the 1 vector is denoted , and the 1 sub-vector of is equal to (28) Since is block diagonal (29) using and as defined in Sections III-B1 and III-B2. The upper limit on the (squared) SDNR, i.e., Hotelling SDNR or detectability index , is then equal to…”

Single-shot dual-energy x-ray imaging with a flat-panel sandwich detector for preclinical imaging

“…In general, statistical correlations may exist between parallel cascades requiring the use of cross terms in the noise variance [25,26]. However, in this model each hexagon represents a quantum branch process and the cross terms are all zero [26].…”

“…However, in this model each hexagon represents a quantum branch process and the cross terms are all zero [26]. This happens because incident x-ray quanta are all statistically independent and the signal from any one x-ray photon does not contribute to more than one path.…”

Statistical characterization of radiological images: basic principles and recent progress

“…13 There is probably no field of imaging for which the statistics of the measurement noise have been so thoroughly investigated and are so fully understood as in digital radiography. A recent publication that illustrates the state of the art and discusses practical computational issues is Satarivand et al 14 …”