  Structured low-rank (SLR) algorithms, which exploit annihilation relations
between the Fourier samples of a signal resulting from different properties, is
a powerful image reconstruction framework in several applications. This scheme
relies on low-rank matrix completion to estimate the annihilation relations
from the measurements. The main challenge with this strategy is the high
computational complexity of matrix completion. We introduce a deep learning
(DL) approach to significantly reduce the computational complexity.
Specifically, we use a convolutional neural network (CNN)-based filterbank that
is trained to estimate the annihilation relations from imperfect (under-sampled
and noisy) k-space measurements of Magnetic Resonance Imaging (MRI). The main
reason for the computational efficiency is the pre-learning of the parameters
of the non-linear CNN from exemplar data, compared to SLR schemes that learn
the linear filterbank parameters from the dataset itself. Experimental
comparisons show that the proposed scheme can enable calibration-less parallel
MRI; it can offer performance similar to SLR schemes while reducing the runtime
by around three orders of magnitude. Unlike pre-calibrated and self-calibrated
approaches, the proposed uncalibrated approach is insensitive to motion errors
and affords higher acceleration. The proposed scheme also incorporates image
domain priors that are complementary, thus significantly improving the
performance over that of SLR schemes.
