Segmented targeted least squares estimator for material decomposition in multi bin PCXDs

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

doi:10.1117/12.2043198

19 March 2014 Segmented targeted least squares estimator for material decomposition in multi bin PCXDs

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

Proceedings Volume 9033, Medical Imaging 2014: Physics of Medical Imaging; 903319 (2014) https://doi.org/10.1117/12.2043198
Event: SPIE Medical Imaging, 2014, San Diego, California, United States

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.

Citation Download Citation

Paurakh L. Rajbhandary, Scott S. Hsieh, and Norbert J. Pelc "Segmented targeted least squares estimator for material decomposition in multi bin PCXDs", Proc. SPIE 9033, Medical Imaging 2014: Physics of Medical Imaging, 903319 (19 March 2014); https://doi.org/10.1117/12.2043198

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