Signal separability is an important factor in the differentiation of materials in spectral computed tomography. In this work, we evaluated the separability of two such materials, iodine and gadolinium with k-edges of 33.1 keV and 50.2 keV, respectively, with an investigational photon-counting CT scanner (Siemens, Germany). A 20 cm water equivalent phantom containing vials of iodine and gadolinium was imaged. Two datasets were generated by either varying the amount of contrast (iodine – 0.125-10 mg/mL, gadolinium 0.125-12 mg/mL) or by varying the tube current (50-300 mAs). Regions of interest were drawn within vials and then used to construct multivariate Gaussian models of signal. We evaluated three separation metrics using the Gaussian models: the area under the curve (AUC) of the receiver operating characteristic curve, the mean Mahalanobis distance, and the Jaccard index. For the dataset with varying contrast, all three metrics showed similar trends by indicating a higher separability when there was a large difference in signal magnitude between iodine and gadolinium. For the dataset with varying tube current, AUC showed the least variation due to change in noise condition and had a higher coefficient of determination (0.99, 0.97) than either mean Mahalanobis distance (0.69, 0.62) or Jaccard index (0.80, 0.75) when compared to material decomposition results for iodine or gadolinium respectively.
In this work, we define a theoretical approach to characterizing the signal-to-noise ratio (SNR) of multi-channeled systems such as spectral computed tomography image series. Spectral image datasets encompass multiple near-simultaneous acquisitions that share information. The conventional definition of SNR is applicable to a single image and thus does not account for the interaction of information between images in a series. We propose an extension of the conventional SNR definition into a multivariate space where each image in the series is treated as a separate information channel thus defining a spectral SNR matrix. We apply this to the specific case of contrast-to-noise ratio (CNR). This matrix is able to account for the conventional CNR of each image in the series as well as a covariance weighted CNR (Cov-CNR), which accounts for the covariance between two images in the series. We evaluate this experimentally with data from an investigational photon-counting CT scanner (Siemens).
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