Reconstructing MRI from highly undersampled measurements is crucial for accelerating medical imaging, but is challenging due to the ill-posedness of the inverse problem. While supervised deep learning approaches have shown remarkable success, they rely on fully-sampled ground truth data, which is often impractical or impossible to obtain. Recently, numerous self-supervised methods have emerged that do not require ground truth, however, the lack of systematic comparison and standard experimental setups have hindered research. We present the first comprehensive review of loss functions from all feedforward self-supervised methods and the first benchmark on accelerated MRI reconstruction without ground truth, showing that there is a wide range in performance across methods. In addition, we propose Multi-Operator Equivariant Imaging (MO-EI), a novel framework that builds on the imaging model considered in existing methods to outperform all state-of-the-art and approaches supervised performance. Finally, to facilitate reproducible benchmarking, we provide implementations of all methods in the DeepInverse library (https://deepinv.github.io) and easy-to-use demo code at https://andrewwango.github.io/deepinv-selfsup-fastmri.

This study accelerates MR cholangiopancreatography (MRCP) acquisitions using deep learning-based (DL) reconstruction at 3T and 0.55T. Thirty healthy volunteers underwent conventional two-fold MRCP scans at field strengths of 3T or 0.55T. We trained a variational network (VN) using retrospectively six-fold undersampled data obtained at 3T. We then evaluated our method against standard techniques such as parallel imaging (PI) and compressed sensing (CS), focusing on peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) as metrics. Furthermore, considering acquiring fully-sampled MRCP is impractical, we added a self-supervised DL reconstruction (SSDU) to the evaluating group. We also tested our method in a prospective accelerated scenario to reflect real-world clinical applications and evaluated its adaptability to MRCP at 0.55T. Our method demonstrated a remarkable reduction of average acquisition time from 599/542 to 255/180 seconds for MRCP at 3T/0.55T. In both retrospective and prospective undersampling scenarios, the PSNR and SSIM of VN were higher than those of PI, CS, and SSDU. At the same time, VN preserved the image quality of undersampled data, i.e., sharpness and the visibility of hepatobiliary ducts. In addition, VN also produced high quality reconstructions at 0.55T resulting in the highest PSNR and SSIM. In summary, VN trained for highly accelerated MRCP allows to reduce the acquisition time by a factor of 2.4/3.0 at 3T/0.55T while maintaining the image quality of the conventional acquisition.

In recent years, there has been attention on leveraging the statistical modeling capabilities of neural networks for reconstructing sub-sampled Magnetic Resonance Imaging (MRI) data. Most proposed methods assume the existence of a representative fully-sampled dataset and use fully-supervised training. However, for many applications, fully sampled training data is not available, and may be highly impractical to acquire. The development and understanding of self-supervised methods, which use only sub-sampled data for training, are therefore highly desirable. This work extends the Noisier2Noise framework, which was originally constructed for self-supervised denoising tasks, to variable density sub-sampled MRI data. We use the Noisier2Noise framework to analytically explain the performance of Self-Supervised Learning via Data Undersampling (SSDU), a recently proposed method that performs well in practice but until now lacked theoretical justification. Further, we propose two modifications of SSDU that arise as a consequence of the theoretical developments. Firstly, we propose partitioning the sampling set so that the subsets have the same type of distribution as the original sampling mask. Secondly, we propose a loss weighting that compensates for the sampling and partitioning densities. On the fastMRI dataset we show that these changes significantly improve SSDU's image restoration quality and robustness to the partitioning parameters.

Self-supervised learning has shown great promise due to its capability to train deep learning 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 and the other 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 hold-out masking operation on acquired measurements to split it 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 to CG-SENSE and single-mask SSDU DL-MRI, as well as supervised DL-MRI when fully-sampled data is available. Results on knee MRI show that the proposed multi-mask SSDU outperforms SSDU and performs closely with supervised DL-MRI. A clinical reader study further ranks the multi-mask SSDU higher than supervised DL-MRI in terms of SNR and aliasing artifacts. Results on brain MRI show that multi-mask SSDU achieves better reconstruction quality compared to SSDU. Reader study demonstrates that multi-mask SSDU at R=8 significantly improves reconstruction compared to single-mask SSDU at R=8, as well as CG-SENSE at R=2.

Purpose: To investigate aspects of the validation of self-supervised algorithms for reconstruction of undersampled MR images: quantitative evaluation of prospective reconstructions, potential differences between prospective and retrospective reconstructions, suitability of commonly used quantitative metrics, and generalizability. Theory and Methods: Two self-supervised algorithms based on self-supervised denoising and neural network image priors were investigated. These methods are compared to a least squares fitting and a compressed sensing reconstruction using in-vivo and phantom data. Their generalizability was tested with prospectively under-sampled data from experimental conditions different to the training. Results: Prospective reconstructions can exhibit significant distortion relative to retrospective reconstructions/ground truth. Pixel-wise quantitative metrics may not capture differences in perceptual quality accurately, in contrast to a perceptual metric. All methods showed potential for generalization; generalizability is more affected by changes in anatomy/contrast than other changes. No-reference image metrics correspond well with human rating of image quality for studying generalizability. Compressed Sensing and learned denoising perform similarly well on all data. Conclusion: Self-supervised methods show promising results for accelerating image reconstruction in clinical routines. Nonetheless, more work is required to investigate standardized methods to validate reconstruction algorithms for future clinical use.