Segmented targeted least squares estimator for material decomposition in multibin photon-counting detectors

Paurakh L. Rajbhandary; Scott S. Hsieh; Norbert J. Pelc

doi:10.1117/1.JMI.4.2.023503

18 May 2017 Segmented targeted least squares estimator for material decomposition in multibin photon-counting detectors

Paurakh L. Rajbhandary, Scott S. Hsieh, Norbert J. Pelc

Author Affiliations +

Journal of Medical Imaging, Vol. 4, Issue 2, 023503 (May 2017). https://doi.org/10.1117/1.JMI.4.2.023503

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) is an improvement of a previously described A-table method by incorporating dynamic weighting that allows the variance 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, compared with Cartesian segmentation, the average-energy method requires fewer segments to achieve similar performance. We compare the average-energy TLSE to other proposed estimators—including the gold standard maximum likelihood estimator (MLE) and the A-table—in terms of variance, bias, and computational efficiency. The variance and bias were simulated in the range of 0 to 6 cm of aluminum and 0 to 50 cm of water with Monte Carlo methods. The Average-energy TLSE achieves an average variance within 2% of the CRLB and mean absolute error of 3.68±0.06×10−6 cm. Using the same protocol, the MLE showed variance within 1.9% of the CRLB ratio and average absolute error of 3.10±0.06×10−6 cm but was 50 times slower in our implementations. Compared with the A-table method, TLSE gives a more homogenously optimal variance-to-CRLB ratio in the operating region. We show that variance in basis material estimates for TLSE is lower than that of the A-table method by as much as ∼36% in the peripheral region of operating range (thin or thick objects). The TLSE is a computationally efficient and fast method for material separation with PCXDs, with accuracy and precision comparable to the MLE.

Citation Download Citation

Paurakh L. Rajbhandary, Scott S. Hsieh, and Norbert J. Pelc "Segmented targeted least squares estimator for material decomposition in multibin photon-counting detectors," Journal of Medical Imaging 4(2), 023503 (18 May 2017). https://doi.org/10.1117/1.JMI.4.2.023503

Received: 23 January 2017; Accepted: 25 April 2017; Published: 18 May 2017

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