A convolutional neural network approach for reconstructing polarization information of photoelectric X-ray polarimeters

This paper presents a data processing algorithm with machine learning for polarization extraction and event selection applied to photoelectron track images taken with X-ray polarimeters. The method uses a convolutional neural network (CNN) classification to predict the azimuthal angle and 2-D position of the initial photoelectron emission from a 2-D track image projected along the X-ray incident direction. Two CNN models are demonstrated with data sets generated by a Monte Carlo simulation: one has a commonly used loss function calculated by the cross entropy and the other has an additional loss term to penalize nonuniformity for an unpolarized modulation curve based on the $H$-test, which is used for periodic signal search in X-ray/$\gamma$-ray astronomy. The modulation curve calculated by the former model with unpolarized data has several irregular features, which can be canceled out by unfolding the angular response or simulating the detector rotation. On the other hand, the latter model can predict a flat modulation curve with a residual systematic modulation down to $\lesssim1$%. Both models show almost the same modulation factors and position accuracy of less than 2 pixel (or 240 $\mu$m) for all four test energies of 2.7, 4.5, 6.4, and 8.0 keV. In addition, event selection is performed based on probabilities from the CNN to maximize the polarization sensitivity considering a trade-off between the modulation factor and signal acceptance. The developed method with machine learning improves the polarization sensitivity by 10-20%, compared to that determined with the image moment method developed previously.