Multivariate signal-to-noise ratio as a metric for characterizing spectral computed tomography

Objective.With the introduction of spectral CT techniques into the clinic, the imaging capacities of CT were expanded to multiple energy levels. Due to a variety of factors, the acquired signal in spectral CT datasets is shared between these images. Conventional image quality metrics assume independence between images which is not preserved within spectral CT datasets, limiting their utility for characterizing energy selective images. The purpose of this work was to develop a metrology to characterize energy selective images by incorporating the shared information between images within a spectral CT dataset.Approach.The signal-to-noise ratio (SNR) was extended into a multivariate space where each image within a spectral CT dataset was treated as a separate information channel. The general definition was applied to the specific case of contrast to define a multivariate contrast-to-noise ratio (CNR). The matrix contained two types of terms: a conventional CNR term which characterized image quality within each image in the spectral CT dataset and covariance weighted CNR (Covar-CNR) which characterized the contrast in each image relative to the covariance between images. Experimental data from an investigational photon-counting CT scanner was used to demonstrate the insight of this metrology. A cylindrical water phantom containing vials of iodine and gadolinium (2, 4, and 8 mg ml^-1) was imaged under conditions of variable tube current, tube voltage, and energy threshold. Two image series (threshold and bin images) containing two images each were defined based upon the contribution of photons to reconstructed images. Analysis of variance (ANOVA) was calculated between CNR terms and image acquisition variables. A multivariate regression was then fitted to experimental data.Main Results.Image type had a major difference on how Covar-CNR values were distributed. Bin images had a slightly higher mean and wider standard deviation (Covar-CNR_lo: 3.38 ±17.25, Covar-CNR_hi: 5.77 ± 30.64) compared to threshold images (Covar-CNR_lo: 2.08 ±1.89, Covar-CNR_hi: 3.45 ± 2.49) across all conditions. ANOVA found that each acquisition variable had a significant relationship with both Covar-CNR terms. The multivariate regression model suggested that material concentration had the largest impact on all CNR terms.Signficance.In this work, we described a theoretical framework to extend the SNR to a multivariate form that is able to characterize images independently and also provide insight regarding the relationship between images. Experimental data was used to demonstrate the insight that this metrology provides about image formation factors in spectral CT.