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

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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Scopus citations


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.

Original languageEnglish (US)
Title of host publicationMedical Imaging 2014
Subtitle of host publicationPhysics of Medical Imaging
ISBN (Print)9780819498267
StatePublished - 2014
EventMedical Imaging 2014: Physics of Medical Imaging - San Diego, CA, United States
Duration: Feb 17 2014Feb 20 2014

Publication series

NameProgress in Biomedical Optics and Imaging - Proceedings of SPIE
ISSN (Print)1605-7422


OtherMedical Imaging 2014: Physics of Medical Imaging
Country/TerritoryUnited States
CitySan Diego, CA


  • Photon-counting x-ray detectors (PCXDs)
  • material decomposition
  • over-determined solution
  • spectral CT

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Atomic and Molecular Physics, and Optics
  • Radiology Nuclear Medicine and imaging
  • Biomaterials


Dive into the research topics of 'Segmented targeted least squares estimator for material decomposition in multi bin PCXDs'. Together they form a unique fingerprint.

Cite this