We present a method for enhancing the sensitivity of X-ray telescopic observations with imaging polarimeters, with a focus on the gas pixel detectors (GPDs) to be flown on the Imaging X-ray Polarimetry Explorer (IXPE). Our analysis determines photoelectron directions, X-ray absorption points and X-ray energies for 1-9 keV event tracks, with estimates for both the statistical and model (reconstruction) uncertainties. We use a weighted maximum likelihood combination of predictions from a deep ensemble of ResNet convolutional neural networks, trained on Monte Carlo event simulations. We define a figure of merit to compare the polarization bias-variance trade-off in track reconstruction algorithms. For power-law source spectra, our method improves on the current planned IXPE analysis (and previous deep learning approaches), providing ~45% increase in effective exposure times. For individual energies, our method produces 20-30% absolute improvements in modulation factor for simulated 100% polarized events, while keeping residual systematic modulation within 1 sigma of the finite sample minimum. Absorption point location and photon energy estimates are also significantly improved. We have validated our method with sample data from real GPD detectors.
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