Physics of Medical Imaging

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

[+] Author Affiliations
Paurakh L. Rajbhandary

Stanford University, Department of Radiology, Palo Alto, California, United States

Stanford University, Department of Electrical Engineering, Stanford, California, United States

Scott S. Hsieh

Stanford University, Department of Radiology, Palo Alto, California, United States

Norbert J. Pelc

Stanford University, Department of Radiology, Palo Alto, California, United States

Stanford University, Department of Electrical Engineering, Stanford, California, United States

Stanford University, Department of Bioengineering, Stanford, California, United States

J. Med. Imag. 4(2), 023503 (May 18, 2017). doi:10.1117/1.JMI.4.2.023503
History: Received January 23, 2017; Accepted April 25, 2017
Text Size: A A A

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±0.06×106  cm. Using the same protocol, the MLE showed variance within 1.9% of the CRLB ratio and average absolute error of 3.10±0.06×106  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.

Figures in this Article
© 2017 Society of Photo-Optical Instrumentation Engineers

Citation

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


Access This Article
Sign in or Create a personal account to Buy this article ($20 for members, $25 for non-members).

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging & repositioning the boxes below.

Related Book Chapters

Topic Collections

Advertisement
  • Don't have an account?
  • Subscribe to the SPIE Digital Library
  • Create a FREE account to sign up for Digital Library content alerts and gain access to institutional subscriptions remotely.
Access This Article
Sign in or Create a personal account to Buy this article ($20 for members, $25 for non-members).
Access This Proceeding
Sign in or Create a personal account to Buy this article ($15 for members, $18 for non-members).
Access This Chapter

Access to SPIE eBooks is limited to subscribing institutions and is not available as part of a personal subscription. Print or electronic versions of individual SPIE books may be purchased via SPIE.org.