Calibrationless Parallel MRI using Model based Deep Learning (C-MODL)

We introduce a fast model based deep learning approach for calibrationless parallel MRI reconstruction. The proposed scheme is a non-linear generalization of structured low rank (SLR) methods that self learn linear annihilation filters from the same subject. It pre-learns non-linear annihilation relations in the Fourier domain from exemplar data. The pre-learning strategy significantly reduces the computational complexity, making the proposed scheme three orders of magnitude faster than SLR schemes. The proposed framework also allows the use of a complementary spatial domain prior; the hybrid regularization scheme offers improved performance over calibrated image domain MoDL approach. The calibrationless strategy minimizes potential mismatches between calibration data and the main scan, while eliminating the need for a fully sampled calibration region

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

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