Development of a separability index for task specific characterization of spectral computed tomography

Purpose: In this work, we define a signal detection based metrology to characterize the separability of two different multi-dimensional signals in spectral CT acquisitions. Method: Signal response was modelled as a random process with a deterministic signal and stochastic noise component. A linear Hotelling observer was used to estimate a scalar test statistic distribution that predicts the likelihood of an intensity value belonging to a signal. Two distributions were estimated for two materials of interest and used to derive two metrics separability: a separability index (s′) and the area under the curve of the test statistic distributions. Experimental and simulated data of photon-counting CT scanners were used to evaluate each metric. Experimentally, vials of iodine and gadolinium (2, 4, 8 mg/mL) were scanned at multiple tube voltages, tube currents and energy thresholds. Additionally, a simulated dataset with low tube current (10–150 mAs) and material concentrations (0.25–4 mg/mL) was generated. Results: Experimental data showed that conditions favorable for low noise and expression of k-edge signal produced the highest separability. Material concentration had the greatest impact on separability. The simulated data showed that under more difficult separation conditions, difference in material concentration still had the greatest impact on separability. Conclusion: The results demonstrate the utility of a task specific metrology to measure the overlap in signal between different materials in spectral CT. Using experimental and simulated data, the separability index was shown to describe the relationship between image formation factors and the signal responses of material.