Rajbhandary PL, Hsieh SS, Pelc NJ. Segmented targeted least squares estimator for material decomposition in multibin photon-counting detectors.
J Med Imaging (Bellingham) 2017;
4:023503. [PMID:
28560242 DOI:
10.1117/1.jmi.4.2.023503]
[Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/23/2017] [Accepted: 04/25/2017] [Indexed: 11/14/2022] Open
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 [Formula: see text]. Using the same protocol, the MLE showed variance within 1.9% of the CRLB ratio and average absolute error of [Formula: see text] 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 [Formula: see text] 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.
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