Abstract
We present a fast, noise-efficient, and accurate estimator for material separation using photon-counting x-ray detectors
(PCXDs) with multiple energy bin capability. The proposed targeted least squares estimator (TLSE) improves a
previously proposed A-Table method by incorporating dynamic weighting that allows noise to be closer to the Cramér-
Rao Lower Bound (CRLB) throughout the operating range. We explore Cartesian and average-energy segmentation of
the basis material space for TLSE, and show that iso-average-energy contours require fewer segments compared to
Cartesian segmentation to achieve similar performance. We compare the iso-average-energy TLSE to other proposed
estimators - including the gold standard maximum likelihood estimator (MLE) and the A-Table1 - in terms of variance,
bias and computational efficiency. The variance and bias of this estimator between 0 to 6 cm of aluminum and 0 to 50
cm of water is simulated with Monte Carlo methods. Iso-average energy TLSE achieves an average variance within 2%
of CRLB, and mean of absolute error of (3.68 ± 0.06) x 10-6 cm. Using the same protocol, MLE showed variance-to-
CRLB ratio and average bias of 1.0186 ± 0.0002 and (3.10 ± 0.06) x 10-6 cm, respectively, but was 50 times slower in
our simulation. Compared to the A-Table method, TLSE gives a more homogenous variance-to-CRLB profile in the
operating region. We show that variance-to-CRLB for TLSE is lower by as much as ~36% than A-Table method in the
peripheral region of operation (thin or thick objects). The TLSE is a computationally efficient and fast method for
implementing material separation technique in PCXDs, with performance parameters comparable to the MLE.