  Accelerated MRI protocols routinely involve a predefined sampling pattern
that undersamples the k-space. Finding an optimal pattern can enhance the
reconstruction quality, however this optimization is a challenging task. To
address this challenge, we introduce a novel deep learning framework, AutoSamp,
based on variational information maximization that enables joint optimization
of sampling pattern and reconstruction of MRI scans. We represent the encoder
as a non-uniform Fast Fourier Transform that allows continuous optimization of
k-space sample locations on a non-Cartesian plane, and the decoder as a deep
reconstruction network. Experiments on public MRI datasets show improved
reconstruction quality of the proposed AutoSamp method over the prevailing
variable density and variable density Poisson disc sampling. We demonstrate
that our data-driven sampling optimization method achieves 4.4dB, 2.0dB,
0.75dB, 0.7dB PSNR improvements over reconstruction with Poisson Disc masks for
acceleration factors of R = 5, 10, 15, 25, respectively. Furthermore, we
analyze the characteristics of the learned sampling patterns with respect to
changes in acceleration factor, measurement noise, underlying anatomy, and coil
sensitivities. We show that all these factors contribute to the optimization
result by affecting the sampling density, k-space coverage and point spread
functions of the learned sampling patterns.
