Objective. Machine Learning methods can learn how to reconstruct magnetic resonance images (MRI) and thereby accelerate acquisition, which is of paramount importance to the clinical workflow. Physics-informed networks incorporate the forward model of accelerated MRI reconstruction in the learning process. With increasing network complexity, robustness is not ensured when reconstructing data unseen during training. We aim to embed data consistency (DC) in deep networks while balancing the degree of network complexity. While doing so, we will assess whether either explicit or implicit enforcement of DC in varying network architectures is preferred to optimize performance. Approach. We propose a scheme called Cascades of Independently Recurrent Inference Machines (CIRIM) to assess DC through unrolled optimization. Herein we assess DC both implicitly by gradient descent and explicitly by a designed term. Extensive comparison of the CIRIM to compressed sensing as well as other Machine Learning methods is performed: the End-to-End Variational Network (E2EVN), CascadeNet, KIKINet, LPDNet, RIM, IRIM, and UNet. Models were trained and evaluated on T₁-weighted and FLAIR contrast brain data, and T₂-weighted knee data. Both 1D and 2D undersampling patterns were evaluated. Robustness was tested by reconstructing 7.5× prospectively undersampled 3D FLAIR MRI data of multiple sclerosis (MS) patients with white matter lesions. Main results. The CIRIM performed best when implicitly enforcing DC, while the E2EVN required an explicit DC formulation. Through its cascades, the CIRIM was able to score higher on structural similarity and PSNR compared to other methods, in particular under heterogeneous imaging conditions. In reconstructing MS patient data, prospectively acquired with a sampling pattern unseen during model training, the CIRIM maintained lesion contrast while efficiently denoising the images. Significance. The CIRIM showed highly promising generalization capabilities maintaining a very fair trade-off between reconstructed image quality and fast reconstruction times, which is crucial in the clinical workflow.

Diffusion Tensor Imaging (DTI) group studies often require the comparison of two groups of 3D diffusion tensor fields. The total number of datasets involved in the study and the multivariate nature of diffusion tensors together make this a challenging process. The traditional approach is to reduce the six-dimensional diffusion tensor to some scalar quantities, which can be analyzed with univariate statistical methods, and visualized with standard techniques such as slice views. However, this provides merely part of the whole story due to information reduction. If to take the full tensor information into account, only few methods are available, and they focus on the analysis of a single group, rather than the comparison of two groups. Simultaneously comparing two groups of diffusion tensor fields by simple juxtaposition or superposition is rather impractical. In this work, we extend previous work by Zhang et al. [ZCH17] to visually compare two groups of diffusion tensor fields. To deal with the wealth of information, the comparison is carried out at multiple levels of detail. In the 3D spatial domain, we propose a details-on-demand glyph representation to support the visual comparison of the tensor ensemble summary information in a progressive manner. The spatial view guides analysts to select voxels of interest. Then at the detail level, the respective original tensor ensembles are compared in terms of tensor intrinsic properties, with special care taken to reduce visual clutter. We demonstrate the usefulness of our visual analysis system by comparing a control group and an HIV positive patient group.