Learning Optical Flow for Fast MRI Reconstruction
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Reconstructing high-quality magnetic resonance images from undersampled raw data is of great interest from both mathematical and clinical point of views. However, it is still an open issue due to the severely ill-posed problem involved and the computational constraints imposed. Whilst a number of techniques have been presented to improve image reconstruction, they only account for spatial regularisation, which shows its limitations in several relevant scenarios including dynamic data. In this work, we propose a new mathematical model for the reconstruction of high-quality medical MR images from few measurements. Our proposed approach combines - in a multi-task and hybrid model - the traditional compressed sensing formulation for the reconstruction of dynamic MRI with motion compensation by learning an optical flow approximation. We propose our optical flow to be encoded in a sparse representation over a learnt dictionary, with the enormous advantage that ground truth data is not required. Furthermore, we present an efficient optimisation scheme to tackle the non-convex problem based on an alternating splitting method. We demonstrate the potentials of our approach through an extensive set of visuals and numerical results using different datasets and acceleration factors. Our combined approach reaches and outperforms several state of the art techniques. Finally, we show the ability of our technique to transfer phantom based knowledge to real datasets.
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