Multi‐energy inter‐pixel coincidence counters for charge sharing correction and compensation in photon counting detectors

Abstract

Purpose: Smaller pixel sizes of x-ray photon counting detectors (PCDs) are advantageous for count rate capabilities but disadvantageous for charge sharing. With charge sharing, the energy of an x-ray photon may be split and one photon may produce two or more counts at adjacent pixels, both at lower energies than the incident energy. This "double-counting" increases noise variance and degrades the spectral response. Overall, it has a significantly negative impact on the performance of PCD-based computed tomography (CT). Charge sharing is induced by the detection physics and occurs regardless of count rates; thus, it is impossible to avoid. We propose in this paper a method that has a potential to address both noise and bias added by charge sharing. Methods: We propose applying a multi-energy inter-pixel coincidence counter (MEICC) technique, which uses energy-dependent coincidence counters, keeps the book of charge sharing events during data acquisition, and provides the exact number of charge sharing occurrences, which can be used to either correct or compensate for them after the acquisition is completed. MEICC does not interfere with the primary counting process; therefore, PCDs with MEICC will remain as fast as those without MEICC. MEICC can be implemented using current electronics technology because its inter-pixel coincidence counters used to handle digital data are rather simple. We evaluated Cram er-Rao lower bound (CRLB) of PCDs with and without MEICC using a Monte Carlo simulation. Results: When the number of energy windows was four or larger and eight neighboring pixels were used, the CRLBs of 225-µm PCD with MEICC normalized by those of the current PCD with the same number of windows were 0.361-0.383 for water density images of two basis functions, which was only 5.7-16.4% worse than those of a PCD without charge sharing (which were at 0.329-0.358). In contrast, the normalized CRLBs of the PCD with one coincidence counter were 0.466-0.499, which were 37.3-45.6% worse than the PCD without charge sharing. The use of eight neighboring pixels provided~10% better CRLB values than four neighboring pixels for MEICC. With four energy windows, decreasing the number of coincidence counters from 16 to 9 only slightly increased the CRLB from 0.255 to 0.269 (which corresponded to as little as a 5.5% change). The normalized CRLBs of MEICC for K-edge imaging (gold) were 0.295-0.426, while those of the one coincidence counter were 0.926-0.959 and the ideal PCDs were 0.126-0.146. Conclusions:The proposed MEICC provides spectral information that can be used to address charge sharing problems in PCDs and is expected to satisfy the requirements for clinical x-ray CT. MEICC is very effective, especially for K-edge imaging, which requires accurate spectral information.

Assessment of Multienergy Interpixel Coincidence Counters (MEICC) for Charge Sharing Correction or Compensation for Photon Counting Detectors With Boxcar Signals

“…In this case, a count is also added to a coincidence counter of the corresponding neighbor pixel, CC XY , as the circuitry for MEICC in each pixel processes coincidences with its own neighboring pixels independently and in parallel. This figure is from [34]. Fig.…”

“…We used the following three different physics tasks with different dimensionality that are relevant to three clinical applications in this study: 1) the line integral estimation of water for the conventional CT imaging; 2) water thickness estimation for water-bone material density imaging; and 3) gold thickness estimation for K-edge imaging with water-bone-gold material decomposition. Note that the conventional CT imaging is a 1-D estimation problem and is different from monochromatic CT imaging used in [34] that is a 2-D estimation problem The lines and spheres are X-rays and electronic charge clouds; those in blue and red are generated with conditions 1 and 2, respectively. Numbers are the number of counts produced at the POI.…”

“…Hsieh [32], [33] proposed a reading-based post-acquisition scheme with a use of one coincidence counter (which we call "1CC" in this article) to record the number of doublecounting events with neighboring pixels with no energy information. Being inspired by Hsieh's 1CC, we recently proposed another scheme for reading-based post-acquisition correction/compensation called MEICC for multienergy interpixel coincidence counter [34]. We will explain MEICC in Section II-A; briefly, MEICC records the spectral information of CS events, while 1CC saves the intensity information.…”

“…The performance of MEICC was assessed using a Monte Carlo (MC) simulation and Cramér-Rao lower bound (CRLB) in the previous study [34]. The study found that the CRLBs of PCDs with MEICC were close to those of a PCD without CS.…”

CdTe Based Energy Resolving, X-ray Photon Counting Detector Performance Assessment: The Effects of Charge Sharing Correction Algorithm Choice

“…A wide range of CSCAs have been proposed [13][14][15][16]; however, this work will focus on those implemented on chip. These CSCAs can broadly be divided into online techniques and offline techniques.…”