  We propose and evaluate a new MRI reconstruction method named LORAKI that
trains an autocalibrated scan-specific recurrent neural network (RNN) to
recover missing k-space data. Methods like GRAPPA, SPIRiT, and AC-LORAKS assume
that k-space data has shift-invariant autoregressive structure, and that the
scan-specific autoregression relationships needed to recover missing samples
can be learned from fully-sampled autocalibration (ACS) data. Recently, the
structure of the linear GRAPPA method has been translated into a nonlinear deep
learning method named RAKI. RAKI uses ACS data to train an artificial neural
network to interpolate missing k-space samples, and often outperforms GRAPPA.
In this work, we apply a similar principle to translate the linear AC-LORAKS
method (simultaneously incorporating support, phase, and parallel imaging
constraints) into a nonlinear deep learning method named LORAKI. Since
AC-LORAKS is iterative and convolutional, LORAKI takes the form of a
convolutional RNN. This new architecture admits a wide range of sampling
patterns, and even calibrationless patterns are possible if synthetic ACS data
is generated. The performance of LORAKI was evaluated with retrospectively
undersampled brain datasets, with comparisons against other related
reconstruction methods. Results suggest that LORAKI can provide improved
reconstruction compared to other scan-specific autocalibrated reconstruction
methods like GRAPPA, RAKI, and AC-LORAKS. LORAKI offers a new deep-learning
approach to MRI reconstruction based on RNNs in k-space, and enables improved
image quality and enhanced sampling flexibility.
