We propose minimal linear networks (MLN) for MR image reconstruction that employ complex-valued, axis-dependent and fully- and neighborhood-connected layers with shared and independent weights, Their topology is restricted to the minimum required by the MR-physics, without nonlinear activation layers. The suggested MLN perform well in reconstructing imaging data acquired under challenging real-world imaging conditions, specifically an Arterial Spin Labeling perfusion experiment with spiral sampling at 7 Tesla. Despite the strong B0 field inhomogeneities at 7T, artifact-free images are obtained that are capable of resolving the minute perfusion signal changes. The results show that even without nonlinear activation and higher-order image manifold description as used by others, deep-learning algorithms and framework, and learning from large realistic datasets, can play a significant role in the success of image reconstruction.
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