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Following their success in numerous imaging and computer vision applications, deep-learning (DL) techniques have emerged as one of the most prominent strategies for accelerated MRI reconstruction. These methods have been shown to outperform conventional regularized methods based on compressed sensing (CS). However, in most comparisons, CS is implemented with two or three hand-tuned parameters, while DL methods enjoy a plethora of advanced data science tools. In this work, we revisit ${\ell }_1$-wavelet CS reconstruction using these modern tools. Using ideas such as algorithm unrolling and advanced optimization methods over large databases that DL algorithms utilize, along with conventional insights from wavelet representations and CS theory, we show that ${\ell }_1$-wavelet CS can be fine-tuned to a level close to DL reconstruction for accelerated MRI. The optimized ${\ell }_1$-wavelet CS method uses only 128 parameters compared to >500,000 for DL, employs a convex reconstruction at inference time, and performs within <1% of a DL approach that has been used in multiple studies in terms of quantitative quality metrics. 

Self‐supervised learning has shown great promise because of its ability to train deep learning (DL) magnetic resonance imaging (MRI) reconstruction methods without fully sampled data. Current self‐supervised learning methods for physics‐guided reconstruction networks split acquired undersampled data into two disjoint sets, where one is used for data consistency (DC) in the unrolled network, while the other is used to define the training loss. In this study, we propose an improved self‐supervised learning strategy that more efficiently uses the acquired data to train a physics‐guided reconstruction network without a database of fully sampled data. The proposed multi‐mask self‐supervised learning via data undersampling (SSDU) applies a holdout masking operation on the acquired measurements to split them into multiple pairs of disjoint sets for each training sample, while using one of these pairs for DC units and the other for defining loss, thereby more efficiently using the undersampled data. Multi‐mask SSDU is applied on fully sampled 3D knee and prospectively undersampled 3D brain MRI datasets, for various acceleration rates and patterns, and compared with the parallel imaging method, CG‐SENSE, and single‐mask SSDU DL‐MRI, as well as supervised DL‐MRI when fully sampled data are available. The results on knee MRI show that the proposed multi‐mask SSDU outperforms SSDU and performs as well as supervised DL‐MRI. A clinical reader study further ranks the multi‐mask SSDU higher than supervised DL‐MRI in terms of signal‐to‐noise ratio and aliasing artifacts. Results on brain MRI show that multi‐mask SSDU achieves better reconstruction quality compared with SSDU. The reader study demonstrates that multi‐mask SSDU at R = 8 significantly improves reconstruction compared with single‐mask SSDU at R = 8, as well as CG‐SENSE at R = 2. 

PurposeTo develop a strategy for training a physics‐guided MRI reconstruction neural network without a database of fully sampled data sets. MethodsSelf‐supervised learning via data undersampling (SSDU) for physics‐guided deep learning reconstruction partitions available measurements into two disjoint sets, one of which is used in the data consistency (DC) units in the unrolled network and the other is used to define the loss for training. The proposed training without fully sampled data is compared with fully supervised training with ground‐truth data, as well as conventional compressed‐sensing and parallel imaging methods using the publicly available fastMRI knee database. The same physics‐guided neural network is used for both proposed SSDU and supervised training. The SSDU training is also applied to prospectively two‐fold accelerated high‐resolution brain data sets at different acceleration rates, and compared with parallel imaging. ResultsResults on five different knee sequences at an acceleration rate of 4 shows that the proposed self‐supervised approach performs closely with supervised learning, while significantly outperforming conventional compressed‐sensing and parallel imaging, as characterized by quantitative metrics and a clinical reader study. The results on prospectively subsampled brain data sets, in which supervised learning cannot be used due to lack of ground‐truth reference, show that the proposed self‐supervised approach successfully performs reconstruction at high acceleration rates (4, 6, and 8). Image readings indicate improved visual reconstruction quality with the proposed approach compared with parallel imaging at acquisition acceleration. ConclusionThe proposed SSDU approach allows training of physics‐guided deep learning MRI reconstruction without fully sampled data, while achieving comparable results with supervised deep learning MRI trained on fully sampled data.