SNR Spectra as a Quantitative Model for Image Quality in Polychromatic X-Ray Imaging

In polychromatic x-ray imaging for nondestructive testing, material science or medical applications, image quality is usually a problem of detecting sample structure in noisy data. This problem is typically stated this way: As many photons as possible need to be detected to get a good image quality. We instead propose to use the concept of signal detection, which is more universal. In signal detection, it is the sample properties which are detected. Photons play the role of information carriers for the signal. Signal detection for example allows modeling the effects which polychromaticity has on image quality. $\mathit{SNR}$ spectra (= spatial $\mathit{SNR}$) are used as a quantity to describe if reliable signal detection is possible. They include modulation transfer and phase contrast in addition to noisiness effects. $\mathit{SNR}$ spectra can also be directly measured, which means that theoretical predictions can easily be tested. We investigate the effects of signal and noise superposition on the $\mathit{SNR}$ spectrum and show how selectively not detecting photons can increase the image quality.