A simple model combining quantum noise and anatomical variation in radiographs

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Abstract
A model is presented for the detection of uniform focal lesions by means of an ideal photon dector. The difference of observed photons between an area overlyaing the embedded lesion and an adjacent reference area of equal size constitutes the signal to be detected. Application of ROC [receiver operating characteristic] analysis reveals that the exact probability distribution of this photon count difference can be approximated well by a Gaussian, on condition that modulation < 0.1 and signal-to-noise ratio (SNR) > 1. Moreover, within these constraints, SNR emerged as the more salient parameter characterizing detection performance. In the absence of anatomical variation, lesions of arbitrarily small size may be detected at any prescribed level of confidence, providing the required high photon exposure is acceptable. The effect of anatomical variation on detection performance is conveniently demonstrated in a graph of SNR vs. exposure. There, 2 global regions are identified, each characterized by an asymptote, corresponding to either photon-limited or photon-saturated imaging. Under the first condition, quantum fluctuations are dominating the noise, and thus, detection performance is influenced by the photon exposure. Under the 2nd, anatomical variations limit the SNR to an upper value, irrespective of exposure magnitude. Evidently anatomical variation is amenable to experimental measurment, and it sets the upper limit for the SNR achievable in the diagnostic task of detecting incipient carious lesions [in humans].

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