Sufficient statistics as a generalization of binning in spectral X-ray imaging.

Departments of Electrical Engineering and Radiology, Stanford University, Stanford, CA 94305, USA.
IEEE transactions on medical imaging 01/2011; 30(1):84-93. DOI: 10.1109/TMI.2010.2061862
Source: PubMed

ABSTRACT It is well known that the energy dependence of X-ray attenuation can be used to characterize materials. Yet, even with energy discriminating photon counting X-ray detectors, it is still unclear how to best form energy dependent measurements for spectral imaging. Common ideas include binning photon counts based on their energies and detectors with both photon counting and energy integrating electronics. These approaches can be generalized to energy weighted measurements, which we prove can form a sufficient statistic for spectral X-ray imaging if the weights used, which we term μ-weights, are basis attenuation functions that can also be used for material decomposition. To study the performance of these different methods, we evaluate the Cramér-Rao lower bound (CRLB) of material estimates in the presence of quantum noise. We found that the choice of binning and weighting schemes can greatly affect the performance of material decomposition. Even with optimized thresholds, binning condenses information but incurs penalties to decomposition precision and is not robust to changes in the source spectrum or object size, although this can be mitigated by adding more bins or removing photons of certain energies from the spectrum. On the other hand, because μ-weighted measurements form a sufficient statistic for spectral imaging, the CRLB of the material decomposition estimates is identical to the quantum noise limited performance of a system with complete energy information of all photons. Finally, we show that μ-weights lead to increased conspicuity over other methods in a simulated calcium contrast experiment.

  • [Show abstract] [Hide abstract]
    ABSTRACT: The in-depth photon counting x-ray detector (PCXD) is a multi-layer detector arrangement which has been introduced to tackle photon count rate limitations of current systems. The capability of resolving photon detections along the detector's depth direction enables multiple measurements in a single scan with energy information that could be potentially utilized for x-ray spectral imaging. The benefit of this depth information has not been explored. We conducted a simulation study to evaluate the performance of in-depth PCXDs for dual material decomposition and compared it against single layer detectors. Common semiconductor materials (Si, GaAs and CdTe) were assessed, with imperfect energy response modeled. We demonstrate that depth information is useful if spectral distortion is present. The benefits depend on how the detector is segmented in the depth direction.
    2014 IEEE 11th International Symposium on Biomedical Imaging (ISBI 2014); 04/2014
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: The validation of a previous work on the optimization of material discrimination in spectral x-ray imaging is reported. Using Monte Carlo simulations based on the BEAMnrc package, material decomposition was performed on the projection images of phantoms containing up to three materials. The simulated projection data was first decomposed into material basis images by minimizing the z-score between expected and simulated counts. Statistical analysis was performed for the pixels within the region-of-interest consisting of contrast material(s) in the BEAMnrc simulations. With the consideration of scattered radiation and a realistic scanning geometry, the theoretical optima of energy bin borders provided by the algorithm were shown to have an accuracy of $\pm$2 keV for the decomposition of 2 and 3 materials. Finally, the signal-to-noise ratio predicted by the theoretical model was also validated. The counts per pixel needed for achieving a specific imaging aim can therefore be estimated using the validated model.
    Journal of Instrumentation 02/2014; 9(08). · 1.53 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: Dual energy imaging enables material decomposition and requires attenuation measurements with at least two different energies. Today's clinically available implementations use two separate exposures, at a low and high tube voltage (dual kV). Photon counting x-ray detectors (PCXDs) are an alternative technology that takes advantage of an x-ray source's broad spectrum by counting the number of transmitted photons at each energy from a single exposure. The richness of the information contained in these measurements can depend heavily on the detector's energy response, itself dependent on count rate. We compare the material decomposition precision of dual kV with energy integrating detectors to that of realistic PCXDs. We model the three primary effects that degrade PCXD performance: count rate limitations, energy resolution, and spectrum tailing. For example, the high flux rates required for clinical imaging pose a serious challenge for PCXDs. The Cram´er-Rao Lower Bound is used to predict the best possible material decomposition variance as a function of these detector imperfections. For dual kV and photon counting, we determined the optimal kV, mAs, and filtration for a broad range of imaging tasks, subject to dose and tube power constraints. We found that a well-optimized dual kV protocol performs on par with the estimated performance of today's PCXDs. For dual kV protocols, it is helpful to increase the energy separation between the spectra by increasing the kV separation and adding filtration. For PCXDs, the detector's count rate capabilities must be increased and the spectrum tailing reduced for photon counting to become a competitive technology at the high intensities of clinical imaging.
    Proceedings of SPIE - The International Society for Optical Engineering 02/2012; · 0.20 Impact Factor

Full-text (2 Sources)

Available from
Sep 3, 2014

Adam S Wang