Multivariate SNR in spectral computed tomography

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).