Efficient, Non-Iterative Estimator for Imaging Contrast Agents With Spectral X-Ray Detectors

An estimator to image contrast agents and body materials with x-ray spectral measurements is described. The estimator is usable with the three or more basis functions that are required to represent the attenuation coefficient of high atomic number materials. The estimator variance is equal to the Cramèr-Rao lower bound (CRLB) and it is unbiased. Its parameters are computed from measurements of a calibration phantom with the clinical x-ray system and it is non-iterative. The estimator is compared with an iterative maximum likelihood estimator. The estimator first computes a linearized maximum likelihood estimate of the line integrals of the basis set coefficients. Corrections for errors in the initial estimates are computed by interpolation with calibration phantom data. The final estimate is the initial estimate plus the correction. The performance of the estimator is measured using a Monte Carlo simulation. Random photon counting with pulse height analysis data are generated. The mean squared errors of the estimates are compared to the CRLB. The random data are also processed with an iterative maximum likelihood estimator. Previous implementations of iterative estimators required advanced physics instruments not usually available in clinical institutions. The estimator mean squared error is essentially equal to the CRLB. The estimator outputs are close to those of the iterative estimator but the computation time is approximately 180 times shorter. The estimator is efficient and has advantages over alternate approaches such as iterative estimators.