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Structured low-rank (SLR) algorithms, which exploit annihilation relationsbetween the Fourier samples of a signal resulting from different properties, isa powerful image reconstruction framework in several applications. This schemerelies on low-rank matrix completion to estimate the annihilation relationsfrom the measurements. The main challenge with this strategy is the highcomputational 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 thatis trained to estimate the annihilation relations from imperfect (under-sampledand noisy) k-space measurements of Magnetic Resonance Imaging (MRI). The mainreason for the computational efficiency is the pre-learning of the parametersof the non-linear CNN from exemplar data, compared to SLR schemes that learnthe linear filterbank parameters from the dataset itself. Experimentalcomparisons show that the proposed scheme can enable calibration-less parallelMRI; it can offer performance similar to SLR schemes while reducing the runtimeby around three orders of magnitude. Unlike pre-calibrated and self-calibratedapproaches, the proposed uncalibrated approach is insensitive to motion errorsand affords higher acceleration. The proposed scheme also incorporates imagedomain priors that are complementary, thus significantly improving theperformance over that of SLR schemes.

Deep Generalization of Structured Low-Rank Algorithms (Deep-SLR)