  Purpose: To propose a wave-encoded model-based deep learning (wave-MoDL)
strategy for highly accelerated 3D imaging and joint multi-contrast image
reconstruction, and further extend this to enable rapid quantitative imaging
using an interleaved look-locker acquisition sequence with T2 preparation pulse
(3D-QALAS).
  Method: Recently introduced MoDL technique successfully incorporates
convolutional neural network (CNN)-based regularizers into physics-based
parallel imaging reconstruction using a small number of network parameters.
Wave-CAIPI is an emerging parallel imaging method that accelerates the imaging
speed by employing sinusoidal gradients in the phase- and slice-encoding
directions during the readout to take better advantage of 3D coil sensitivity
profiles. In wave-MoDL, we propose to combine the wave-encoding strategy with
unrolled network constraints to accelerate the acquisition speed while
enforcing wave-encoded data consistency. We further extend wave-MoDL to
reconstruct multi-contrast data with controlled aliasing in parallel imaging
(CAIPI) sampling patterns to leverage similarity between multiple images to
improve the reconstruction quality.
  Result: Wave-MoDL enables a 47-second MPRAGE acquisition at 1 mm resolution
at 16-fold acceleration. For quantitative imaging, wave-MoDL permits a 2-minute
acquisition for T1, T2, and proton density mapping at 1 mm resolution at
12-fold acceleration, from which contrast weighted images can be synthesized as
well.
  Conclusion: Wave-MoDL allows rapid MR acquisition and high-fidelity image
reconstruction and may facilitate clinical and neuroscientific applications by
incorporating unrolled neural networks into wave-CAIPI reconstruction.
