  Deep-neural-network-based image reconstruction has demonstrated promising
performance in medical imaging for under-sampled and low-dose scenarios.
However, it requires large amount of memory and extensive time for the
training. It is especially challenging to train the reconstruction networks for
three-dimensional computed tomography (CT) because of the high resolution of CT
images. The purpose of this work is to reduce the memory and time consumption
of the training of the reconstruction networks for CT to make it practical for
current hardware, while maintaining the quality of the reconstructed images.
  We unrolled the proximal gradient descent algorithm for iterative image
reconstruction to finite iterations and replaced the terms related to the
penalty function with trainable convolutional neural networks (CNN). The
network was trained greedily iteration by iteration in the image-domain on
patches, which requires reasonable amount of memory and time on mainstream
graphics processing unit (GPU). To overcome the local-minimum problem caused by
greedy learning, we used deep UNet as the CNN and incorporated separable
quadratic surrogate with ordered subsets for data fidelity, so that the
solution could escape from easy local minimums and achieve better image
quality.
  The proposed method achieved comparable image quality with state-of-the-art
neural network for CT image reconstruction on 2D sparse-view and limited-angle
problems on the low-dose CT challenge dataset.
