A generalized approach to describing transfer of the noise power spectrum through medical imaging systems has been developed over the past several years in which image-forming processes are represented in terms of a cascade of amplified point processes. Until recently, this approach has been restricted to serial cascades only. Here we develop a generalized expression for the cross covariance of amplified point processes and an expression for the cross spectral density for wide-sense stationary conditions. These results extend the generalized transfer-theory approach to include the description of more complex image-forming processes involving parallel cascades of quantum amplification processes. This parallel-cascade approach is used to develop a theoretical expression for noise-power transfer in a simple radiographic screen that includes the effect of characteristic x-ray reabsorption. The result confirms earlier work by Metz and Vyborny, who showed that reabsorption increases image noise and decreases the detective quantum efficiency at low spatial frequencies. Use of the transfer-theory approach facilitates a straightforward generalization to many new digital imaging systems including conventional angiographic and active-matrix flat-panel systems.

Image quality in diagnostic x-ray imaging is ultimately limited by the statistical properties governing how, and where, x-ray energy is deposited in a detector. This in turn depends on the physics of the underlying x-ray interactions. In the diagnostic energy range (10-100 keV), most of the energy deposited in a detector is through photoelectric interactions. We present a theoretical model of the photoelectric effect that specifically addresses the statistical nature of energy absorption by photoelectrons, K and L characteristic x rays, and Auger electrons. A cascaded-systems approach is used that employs a complex structure of parallel cascades to describe signal and noise transfer through the photoelectric effect in terms of the modulation transfer function, Wiener noise power spectrum, and detective quantum efficiency (DQE). The model was evaluated by comparing results with Monte Carlo calculations for x-ray converters based on amorphous selenium (a-Se) and lead (Pb), representing both low and high-Z materials. When electron transport considerations can be neglected, excellent agreement (within 3%) is obtained for each metric over the entire diagnostic energy range in both a-Se and Pb detectors up to 30 cycles/mm, the highest frequency tested. The cascaded model overstates the DQE when the electron range cannot be ignored. This occurs at approximately two cycles/mm in a-Se at an incident photon energy of 80 keV, whereas in Pb, excellent agreement is obtained for the DQE over the entire diagnostic energy range. However, within the context of mammography (20 keV) and micro-computed tomography (40 keV), the effects of electron transport on the DQE are negligible compared to fluorescence reabsorption, which can lead to decreases of up to 30% and 20% in a-Se and Pb, respectively, at 20 keV; and 10% and 5%, respectively, at 40 keV. It is shown that when Swank noise is identified in a Fourier model, the Swank factor must be frequency dependent. This factor decreases quickly with frequency, and in the case of a-Se and Pb, decreases by up to a factor of 3 at five cycles/mm immediately above the K edge. The frequency-dependent Swank factor is also equivalent to what we call the "photoelectric DQE," which describes signal and noise transfer through photoelectric interactions.

Theoretical models of the detective quantum efficiency (DQE) provide insight into fundamental performance limitations and standards to which particular systems can be compared. Over the past several years, cascaded models have been developed to describe the DQE of several flat panel detectors. This article summarizes the governing principles of cascaded models, and conditions that must be satisfied to prevent misuse. It is shown how to incorporate: a) poly-energetic x rays; b) Swank noise; c) the Lubberts effect; d) reabsorption of K x rays from photo-electric interactions; e) secondary quantum noise; and, f) noise aliasing.Cascaded models involve cascading theoretical expressions of the noise-power spectrum (NPS) through multiple stages. Most expressions involve two or three terms, requiring the manipulation of algebraic expressions consisting of hundreds of terms. This practical limitation is alleviated using MATLAB's Simulink programming environment and symbolic math manipulations. It is shown that even for an "indirect" detector, noise aliasing reduces the DQE by up to 50% at the cut-off frequency. Secondary quantum noise is generally a small effect, but reabsorption can reduce the DQE by 20-25% over a wide range of spatial frequencies.

Cascaded-systems analyses have been used successfully by many investigators to describe signal and noise transfer in quantum-based x-ray detectors in medical imaging. However, the Fourier-based linearsystems approach is only valid when assumptions of linearity and shift invariance are satisfied. Digital detectors, in which a bounded image signal is spatially integrated in discrete detector elements, are not shift invariant in their response. In addition, many detectors make use of fiber optics or structured phosphors such as CsI to pass light to a photodetector both of which have a shift-variant response. These issues raise serious concerns regarding the validity of Fourier-based approaches for describing the signal and noise performance of these detectors.We have used a Monte Carlo approach to compare the image Wiener noise power spectrum (NPS) with that predicted using a Fourier-based approach when these assumptions fail. It is shown that excellent agreement is obtained between Monte Carlo results and those obtained using a Fourier-based wide-sense cyclostationary analysis, including the description of noise aliasing. A simple model of a digital detector coupled to a fiber optic bundle is described using a novel cascaded cyclostationary approach in which image quanta are integrated over fiber elements and then randomly re-distributed at the fiber output. While the image signal sometimes contains significant non-stationary beating artifacts, the Monte Carlo results generally show good agreement with Fourier models of the NPS when noise measurements are made over a sufficiently large region of interest.

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