  Ultra sparse-view computed tomography (CT) algorithms can reduce radiation
exposure of patients, but those algorithms lack an explicit cycle consistency
loss minimization and an explicit log-likelihood maximization in testing. Here,
we propose X2CT-FLOW for the maximum a posteriori (MAP) reconstruction of a
three-dimensional (3D) chest CT image from a single or a few two-dimensional
(2D) projection images using a progressive flow-based deep generative model,
especially for ultra low-dose protocols. The MAP reconstruction can
simultaneously optimize the cycle consistency loss and the log-likelihood. The
proposed algorithm is built upon a newly developed progressive flow-based deep
generative model, which is featured with exact log-likelihood estimation,
efficient sampling, and progressive learning. We applied X2CT-FLOW to
reconstruction of 3D chest CT images from biplanar projection images without
noise contamination (assuming a standard-dose protocol) and with strong noise
contamination (assuming an ultra low-dose protocol). With the standard-dose
protocol, our images reconstructed from 2D projected images and 3D ground-truth
CT images showed good agreement in terms of structural similarity (SSIM, 0.7675
on average), peak signal-to-noise ratio (PSNR, 25.89 dB on average), mean
absolute error (MAE, 0.02364 on average), and normalized root mean square error
(NRMSE, 0.05731 on average). Moreover, with the ultra low-dose protocol, our
images reconstructed from 2D projected images and the 3D ground-truth CT images
also showed good agreement in terms of SSIM (0.7008 on average), PSNR (23.58 dB
on average), MAE (0.02991 on average), and NRMSE (0.07349 on average).
