  Modern MRI schemes, which rely on compressed sensing or deep learning
algorithms to recover MRI data from undersampled multichannel Fourier
measurements, are widely used to reduce scan time. The image quality of these
approaches is heavily dependent on the sampling pattern. We introduce a
continuous strategy to jointly optimize the sampling pattern and network
parameters. We use a multichannel forward model, consisting of a non-uniform
Fourier transform with continuously defined sampling locations, to realize the
data consistency block within a model-based deep learning image reconstruction
scheme. This approach facilitates the joint and continuous optimization of the
sampling pattern and the CNN parameters to improve image quality. We observe
that the joint optimization of the sampling patterns and the reconstruction
module significantly improves the performance of most deep learning
reconstruction algorithms. The source code of the proposed joint learning
framework is available at https://github.com/hkaggarwal/J-MoDL.
