1678 IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 30, NO. 9, SEPTEMBER 2011 Sensitivity of Photon-Counting Based -Edge Imaging in X-ray Computed Tomography Ewald Roessl*, Bernhard Brendel, Klaus-Jürgen Engel, Jens-Peter Schlomka, Axel Thran, and Roland Proksa Abstract—The feasibility of -edge imaging using energy-re- solved, photon-counting transmission measurements in X-ray computed tomography (CT) has been demonstrated by simu- lations and experiments. The method is based on probing the discontinuities of the attenuation coefficient of heavy elements above and below the -edge energy by using energy-sensitive, photon counting X-ray detectors. In this paper, we investigate the dependence of the sensitivity of -edge imaging on the atomic number of the contrast material, on the object diameter , on the spectral response of the X-ray detector and on the X-ray tube voltage. We assume a photon-counting detector equipped with six adjustable energy thresholds. Physical effects leading to a degradation of the energy resolution of the detector are taken into account using the concept of a spectral response function for which we assume four different models. As a validation of our analytical considerations and in order to investigate the influence of elliptically shaped phantoms, we provide CT simulations of an anthropomorphic Forbild–Abdomen phantom containing a gold-contrast agent. The dependence on the values of the energy thresholds is taken into account by optimizing the achievable signal-to-noise ratios (SNR) with respect to the threshold values. We find that for a given X-ray spectrum and object size the SNR in the heavy element’s basis material image peaks for a certain atomic number . The dependence of the SNR in the high- basis-material image on the object diameter is the natural, ex- ponential decrease with particularly deteriorating effects in the case where the attenuation from the object itself causes a total signal loss below the -edge. The influence of the energy-response of the detector is very important. We observed that the optimal SNR values obtained with an ideal detector and with a CdTe pixel detector whose response, showing significant tailing, has been determined at a synchrotron differ by factors of about two to three. The potentially very important impact of scattered X-ray radiation and pulse pile-up occurring at high photon rates on the sensitivity of the technique is qualitatively discussed. Index Terms—Computed tomography (CT), photon-counting, spectral -edge imaging. I. INTRODUCTION D IRECT-CONVERSION semiconductor detectors op- erated in photon-counting mode allow the selective imaging and quantification of contrast materials containing a Manuscript received December 27, 2010; revised March 28, 2011; accepted March 30, 2011. Date of publication April 15, 2011; date of current version August 31, 2011. Asterisk indicates corresponding author. *E. Roessl is with Philips Research Europe–Hamburg, D-22335 Hamburg, Germany (e-mail: ewald.roessl@philips.com). B. Brendel, J.-P. Schlomka, A. Thran, and R. Proksa are with Philips Research Europe–Hamburg, D-22335 Hamburg, Germany. K.-J. Engel is with Philips Research Europe–Aachen, D-52066 Aachen, Germany. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMI.2011.2142188 heavy element from energy-sensitive transmission measure- ments. From a basis material decomposition in the projection domain followed by a conventional filtered-back-projection reconstruction, images of the distribution of the contrast mate- rial separate from the anatomical background can be obtained. The feasibility of this imaging technique, called “ -edge imaging” in the following, has been demonstrated recently both by simulations [1] and experiments [2]. In this context it is important to investigate the method’s sensitivity in the field of X-ray computed-tomography (CT), both for applications in micro-CT and human CT. It is clear that the sensitivity of the method will strongly depend on the object size and the tube voltage setting. While the object size will determine the degree of beam-hardening in the transmitted beam, the tube voltage will determine the highest possible atomic number for which the method can be used at all. Therefore, for a given combination of object size and tube-spectrum, there will be a range of optimal atomic numbers, i.e., elements, for which the method is most sensitive. In this paper we provide estimates for the achievable signal-to-noise ratio (SNR) in the -edge basis-material im- ages in a CT environment as a function of the object size, high-voltage setting and the atomic number of the con- trast-generating element. Moreover, we study the influence of the energy resolution, or more generally the energy response, of the detection system on the -edge imaging sensitivity. We will consider only circular objects in our analytical estimation of the achievable SNR values. As a verification that our results are, with some modifications, equally applicable to medical CT, i.e., for elliptically-shaped objects, we also simulated an anthropomorphic phantom with a gold contrast insert. For this case we also verify the sensitivity as a function of tube voltage as well as the fact that by combining the entire spectral acquisition data it is always possible to recover a conventional CT image of diagnostic quality. The performance of photon-counting systems in the context of third-generation CT imaging is strongly influenced by two physical effects that were not taken into account in our consid- eration: the degrading impact of pulse pile-up and of scattered radiation on the measured X-ray spectra. Both effects are im- portant in a clinical environment, as usually very high X-ray flux rates and large coverage detectors are used in order to keep the total scanning time low. We thus emphasize that the pre- sented results could potentially be too optimistic when consid- ering third-generation CT. The structure of this paper is the following: in Section II we briefly summarize the method of -edge imaging in com- puted tomography using energy-resolved photon-counting data. 0278-0062/$26.00 © 2011 IEEE