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Empirical optimization of energy bin weights for compressing measurements with realistic photon counting x-ray
Yirong Yang1,2, Sen Wang2, Debashish Pal3
1Department of Electrical Engineering, Stanford University, Stanford, California, USA.
Background:
Photon counting detectors (PCDs) provide higher spatial resolution, improved contrast-to-noise ratio (CNR), and energy discriminating capabilities. However, the greatly increased amount of projection data in photon counting computed tomography (PCCT) systems becomes challenging to transmit through the slip ring, process, and store.
Purpose:
This study proposes and evaluates an empirical optimization algorithm to obtain optimal energy weights for energy bin data compression. This algorithm is universally applicable to spectral imaging tasks including 2 and 3 material decomposition (MD) tasks and virtual monoenergetic images (VMIs). This method is simple to implement while preserving spectral information for the full range of object thicknesses and is applicable to different PCDs, for example, silicon detectors and CdTe detectors.
Methods:
We used realistic detector energy response models to simulate the spectral response of different PCDs and an empirical calibration method to fit a semi-empirical forward model for each PCD. We numerically optimized the optimal energy weights by minimizing the average relative Cramér-Rao lower bound (CRLB) due to the energy-weighted bin compression, for MD and VMI tasks over a range of material area density (0-40 g/cm2 water, 0-2.16 g/cm2 calcium). We used Monte Carlo simulation of a step wedge phantom and an anthropomorphic head phantom to evaluate the performance of this energy bin compression method in the projection domain and image domain, respectively.
Results:
The results show that for 2 MD, the energy bin compression method can reduce PCCT data size by 75% and 60%, with an average variance penalty of less than 17% and 3% for silicon and CdTe detectors, respectively. For 3 MD tasks with a K-edge material (iodine), this method can reduce the data size by 62.5% and 40% with an average variance penalty of less than 12% and 13% for silicon and CdTe detectors, respectively.
Conclusions:
We proposed an energy bin compression method that is broadly applicable to different PCCT systems and object sizes, with high data compression ratio and little loss of spectral information.
