Nuclear Inst. and Methods in Physics Research, A 897 (2018) 1–7 Contents lists available at ScienceDirect Nuclear Inst. and Methods in Physics Research, A journal homepage: www.elsevier.com/locate/nima Pile-up correction algorithm based on successive integration for high count rate medical imaging and radiation spectroscopy Mohammad-Reza Mohammadian-Behbahani, Shahyar Saramad * Department of Energy Engineering and Physics, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran ARTICLE INFO Keywords: Bi-exponential pulse model Pile-up correction Scintillation detector Successive integration method ABSTRACT In high count rate radiation spectroscopy and imaging, detector output pulses tend to pile up due to high interaction rate of the particles with the detector. Pile-up effects can lead to a severe distortion of the energy and timing information. Pile-up events are conventionally prevented or rejected by both analog and digital electronics. However, for decreasing the exposure times in medical imaging applications, it is important to maintain the pulses and extract their true information by pile-up correction methods. The single-event reconstruction method is a relatively new model-based approach for recovering the pulses one-by-one using a fitting procedure, for which a fast fitting algorithm is a prerequisite. This article proposes a fast non-iterative algorithm based on successive integration which fits the bi-exponential model to experimental data. After optimizing the method, the energy spectra, energy resolution and peak-to-peak count ratios are calculated for different counting rates using the proposed algorithm as well as the rejection method for comparison. The obtained results prove the effectiveness of the proposed method as a pile-up processing scheme designed for spectroscopic and medical radiation detection applications. 1. Introduction Pulse pile-up phenomenon occurs in high-count-rate radiation detec- tion experiments where two or more subsequent electric pulses overlap due to finite resolving time of the detector [1,2]. The pile-up effect not only deteriorates the energy [3] and timing [4] resolution, but can also distort the spatial resolution in nuclear medicine imaging modalities like Positron Emission Tomography (PET) and Single Photon Emission Computed Tomography (SPECT) [5]. Different strategies exist to solve this problem such as rejection methods (discarding all pile- up events) [6–8], prevention methods (optimally shaping the pulses to minimize their probability of overlapping [9,10]) and correction algorithms (separating the piled-up pulses [1,11,12]). Since the rejection methods may lead to a substantial decrease of the detector throughput at higher rates, the data acquisition time must be increased to obtain an acceptable count with tolerable statistical noise [13]. However, a longer exposure time means a higher radiation dose for patients in medical imaging procedures. A shaping method mainly aims to reshape the slow decaying pulses of the preamplifier for removing their long tails in order to avoid the pile- up effect [14]. Although digital triangular and trapezoidal shapers are now frequently implemented and used [15–17], the shaping methods * Corresponding author. E-mail address: ssaramad@aut.ac.ir (S. Saramad). may fail to preserve the original pulse amplitude (energy information) at high counting rates, resulting in degradation of the energy resolution and Signal-to-Noise Ratio (SNR) [18]. Pile-up correction approaches are relatively recent, especially fa- cilitated by the advent of digital processing modules [19,20]. Most of the correction methods consider the pile-up pulse waveform as a linear combination of single events with a determined pulse model but unknown amplitudes and times of arrival [1,11,21,22]. However, for further simplifying the problem, the time of arrival is usually obtained by a popular method like leading edge detection [5,23] or constant fraction discrimination [24]. Pulse model can be determined experimentally by inspecting a set of detector output pulses [21,25]; or can be a mathematical description of the physical processes of the pulse formation and collection [1,5,22,26], for instance the so-called bi-exponential model [19,22]. The main drawbacks of pile-up correction strategies are: (a) their high complexity and computational costs for high order pile-up cases, and (b) the need for determining model parameters beforehand, except for the amplitudes which must be computed. Although the fixed prede- termined parameters may be admissible for all pulses of a scintillator, they may drastically change for the detectors with large variations in charge collection time (due to different depths of interaction), resulting https://doi.org/10.1016/j.nima.2018.04.028 Received 25 January 2018; Received in revised form 14 April 2018; Accepted 15 April 2018 Available online 22 April 2018 0168-9002/© 2018 Published by Elsevier B.V.