  Cone Beam CT (CBCT) is an essential imaging modality nowadays, but the image
quality of CBCT still lags behind the high quality standards established by the
conventional Computed Tomography. We propose LIRE+, a learned iterative scheme
for fast and memory-efficient CBCT reconstruction, which is a substantially
faster and more parameter-efficient alternative to the recently proposed LIRE
method. LIRE+ is a rotationally-equivariant multiscale learned invertible
primal-dual iterative scheme for CBCT reconstruction. Memory usage is optimized
by relying on simple reversible residual networks in primal/dual cells and
patch-wise computations inside the cells during forward and backward passes,
while increased inference speed is achieved by making the primal-dual scheme
multiscale so that the reconstruction process starts at low resolution and with
low resolution primal/dual latent vectors. A LIRE+ model was trained and
validated on a set of 260 + 22 thorax CT scans and tested using a set of 142
thorax CT scans with additional evaluation with and without finetuning on an
out-of-distribution set of 79 Head and Neck (HN) CT scans. Our method surpasses
classical and deep learning baselines, including LIRE, on the thorax test set.
For a similar inference time and with only 37 % of the parameter budget, LIRE+
achieves a +0.2 dB PSNR improvement over LIRE, while being able to match the
performance of LIRE in 45 % less inference time and with 28 % of the parameter
budget. Rotational equivariance ensures robustness of LIRE+ to patient
orientation, while LIRE and other deep learning baselines suffer from
substantial performance degradation when patient orientation is unusual. On the
HN dataset in the absence of finetuning, LIRE+ is generally comparable to LIRE
in performance apart from a few outlier cases, whereas after identical
finetuning LIRE+ demonstates a +1.02 dB PSNR improvement over LIRE.
