A coincidence-based response matrix for correction of charge sharing spectral distortions in photon counting...

Charge sharing between pixels distorts the count and spectral information of X-ray photon counting detectors. Compensation methods for charge sharing effects are required to exploit the full potentiality of these detectors in medical diagnosis.

A statistical method is proposed to correct charge sharing effects in a pixellated photon counting detector by applying a spectral response matrix determined with a coincidence-based acquisition.

The technique is based on a preliminary calibration with a uniform irradiation and an arbitrary polychromatic spectrum, during which the number of coincidences between a pixel and its eight neighbours are collected for different combinations of energy bins. A coincidence-based response matrix (CBRM) is determined and afterwards applied to correct other spectra acquired with the same detector and conventional multi-comparator electronics. The technique was validated with Geant4 Monte Carlo simulations of a 1 mm thick CdTe detector and with data collected with a pixel hybrid detector consisting of a 300 $\mu m$ thick silicon sensor readout by a Timepix4 chip. The effect of pulse pileup was not analyzed in this study.

The response matrix restores the spectral information with a performance comparable to analog charge summing (ACS) algorithms. For example, for a simulation of a spectrum from a 120 kV X-ray tube attenuated by a solution of water and iodine and a CdTe detector with a pixel size of 200 µm, the mean absolute percentage errors (MAPE) from the comparison of the corrections with an ideal spectrum are 20.0% for the CBRM method and 22.8% for ACS. The ACS method is more sensitive to electronic noise than the CBRM correction, thus requiring a higher noise discrimination threshold. For experimental acquisitions of monochromatic spectra with the silicon sensor, the mean values and standard deviations of Gaussian fits of the restored energy peaks provide results close to those from a clustering algorithm based on 3 $\times$ 3 pixel blocks. The MAPE value from the comparison of the CBRM correction and clustering distributions for a polychromatic spectrum of an X-ray tube at 50 kV attenuated by an Ag solution is 6.2% It is also shown that a CBRM matrix determined with a fine division of the energy range can be adapted to match a lower number of energy bins employed for subsequent acquisitions without affecting the accuracy of the spectrum correction. A preliminary reconstruction of a nonuniform irradiation demonstrates the potentiality of the method to restore general spectral images.

The proposed method allows the experimental determination of a response matrix which is independent of physics models or parameterizations and is realizable with a simple coincidence electronic circuit involving a limited number of pixels in a calibration stage. With respect to ACS techniques, the application of the response matrix requires only the number of counts collected with existing readout systems with multiple comparators, without introducing additional dead-times during the acquisition.