Article

# 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: DBLP

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.

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Available from: Norbert J Pelc, Sep 03, 2014
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• ", m materials. Given the linear dependency of the material attenuation functions, only two materials can be decomposed, if the imaging object does not present any k-edges within the energies considered [11] [12]. However, a third material with a k-edge within the detected x-ray spectrum can be discriminated with 3 or more spectroscopic measurements. "
##### Article: Monte Carlo validation of optimal material discrimination using spectral x-ray imaging
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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). DOI:10.1088/1748-0221/9/08/T08003 · 1.40 Impact Factor
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• "PECTRAL computed tomography (CT) refers to methods whereby measurements at different effective X-ray energies are performed in order to make better use of the energy dependence of linear attenuation coefficients (LACs). The additional information gained from energy sensitive measurements can be used in a variety of ways, but the applications fall broadly in one of the following four main categories: 1) increasing the contrast-to-noise ratio (CNR), [1]–[6], [8]–[11]; 2) removing beam hardening artifacts, [3], [12]–[14]; 3) improving tissue segmentation and quantification, and [15]–[21]; 4) improving contrast agent quantification. [22]–[24], [26]–[28]. "
##### Article: Theoretical Comparison of the Iodine Quantification Accuracy of Two Spectral CT Technologies
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ABSTRACT: We compare the theoretical limits of iodine quantification for the photon counting multibin and dual energy technologies. Dual energy systems by necessity have to make prior assumptions in order to quantify iodine. We explicitly allow the multibin system to make the same assumptions and also allow them to be wrong. We isolate the effect of technology from imperfections and implementation issues by assuming both technologies to be ideal, i.e. without scattered radiation, unity detection efficiency and perfect energy response functions, and by applying the Cram´er-Rao lower bound methodology to assess the quantification accuracy. When priors are wrong the maximum likelihood estimates will be biased and the mean square error of the quantification error is a more appropriate figure of merit. The evaluation assumes identical x-ray spectra for both methodologies and for that reason a sensitivity analysis is performed with regard to the assumed x-ray spectrum. We show that when iodine is quantified over regions of interest larger than 6 cm2, multibin systems benefit by independent estimation of three basis functions. For smaller regions of interest multibin systems can increase quantification accuracy by making the same prior assumptions as dual energy systems.
11/2013; 33(2). DOI:10.1109/TMI.2013.2290198
• ##### Conference Paper: Multidimensional Data Processing Methods for Material Discrimination Using an Ideal X-Ray Spectrometric Photon Counting Detector
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ABSTRACT: Development at LETI of X-ray photon counting detectors based on CdTe/CZT architecture has shown many improvements in counting abilities and in energy resolution for fast digital imaging modalities. In this context, this study aims at quantifying contribution of these technologies associated to new data processing methods for radiographic material recognition in homeland security. An ideal spectrometric detector was simulated and three non-layered homogeneous materials at millimetric thicknesses were investigated as potential hazardous materials to identify. A criterion quantifying material separability was developed and appears applicable to various systems of detection. Two methods for exploiting spectrometric information were analyzed. The first one, named “channel binning method”, is based on spectrum data summation before the calculation of the attenuation coefficients. The second one, “linear method”, corresponds to a summation of the attenuation function after the log calculation, making the obtained data directly linear to material thickness. Both methods provide N data exploitable with the criterion of separability. Thresholds of the summation windows were optimized for N = 2 to 5 and, for N≥5, windows were selected equally distributed over the energy range of the spectrum. As reference, performances supplied by both methods were compared to an ideal integrating sandwich technology with an optimized geometry. Compared to sandwich detector performances, criterion values are increased by more than 50% using the “linear method” and the “channel binning method” with only two optimized summation windows (N=2). And, for an increasing number of summation windows, performances of both methods are enhanced. In the optimal configuration with windows width of 1 keV, both methods are identical, linear with material thickness and supply a gain of about 80% relatively to the sandwich detector, providi- - ng then higher performances than existing integrating technologies.
Nuclear Science Symposium Conference Record (NSS/MIC), 2010 IEEE; 12/2010