  Compressed sensing (CS) in Magnetic resonance Imaging (MRI) essentially
involves the optimization of 1) the sampling pattern in k-space under MR
hardware constraints and 2) image reconstruction from the undersampled k-space
data. Recently, deep learning methods have allowed the community to address
both problems simultaneously, especially in the non-Cartesian acquisition
setting. This paper aims to contribute to this field by tackling some major
concerns in existing approaches.Regarding the learning of the sampling pattern,
we perform ablation studies using parameter-free reconstructions like the
density compensated (DCp) adjoint operator of the nonuniform fast Fourier
transform (NUFFT) to ensure that the learned k-space trajectories actually
sample the center of k-space densely. Additionally we optimize these
trajectories by embedding a projected gradient descent algorithm over the
hardware MR constraints. Later, we introduce a novel hybrid learning approach
that operates across multiple resolutions to jointly optimize the
reconstruction network and the k-space trajectory and present improved image
reconstruction quality at 20-fold acceleration factor on T1 and T2-weighted
images on the fastMRI dataset with SSIM scores of nearly 0.92-0.95 in our
retrospective studies.
