  Objective: Model based deep learning (MBDL) has been challenging to apply to
the reconstruction of 3D non-Cartesian MRI acquisitions due to extreme GPU
memory demand (>250 GB using traditional backpropagation) primarily because the
entire volume is needed for data-consistency steps embedded in the model. The
goal of this work is to develop and apply a memory efficient method called
block-wise learning that combines gradient checkpointing with patch-wise
training to allow for fast and high-quality 3D non-Cartesian reconstructions
using MBDL. Approach: Block-wise learning applied to a single unroll decomposes
the input volume into smaller patches, gradient checkpoints each patch, passes
each patch iteratively through a neural network regularizer, and then rebuilds
the full volume from these output patches for data-consistency. This method is
applied across unrolls during training. Block-wise learning significantly
reduces memory requirements by tying GPU memory to user selected patch size
instead of the full volume. This algorithm was used to train a MBDL
architecture to reconstruct highly undersampled, 1.25mm isotropic, pulmonary
magnetic resonance angiography volumes with matrix sizes varying from 300-450 x
200-300 x 300-450 on a single GPU. We compared block-wise learning
reconstructions against L1 wavelet compressed reconstructions and proxy ground
truth images. Main results: MBDL with block-wise learning significantly
improved image quality relative to L1 wavelet compressed sensing while
simultaneously reducing average reconstruction time 38x. Significance:
Block-wise learning allows for MBDL to be applied to high spatial resolution,
3D non-Cartesian datasets with improved image quality and significant
reductions in reconstruction time relative to traditional iterative methods
