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We address the problem of reconstructing high quality images fromundersampled MRI data. This is a challenging task due to the highly ill-posednature of the problem. In particular, in dynamic MRI scans, the interactionbetween the target structure and the physical motion affects the acquiredmeasurements leading to blurring artefacts and loss of fine details. In thiswork, we propose a framework for dynamic MRI reconstruction framed under a newmulti-task optimisation model called Compressed Sensing Plus Motion (CS+M).Firstly, we propose a single optimisation problem that simultaneously computesthe MRI reconstruction and the physical motion. Secondly, we show our model canbe efficiently solved by breaking it up into two more computationally tractableproblems. The potentials and generalisation capabilities of our approach aredemonstrated in different clinical applications including cardiac cine, cardiacperfusion and brain perfusion imaging. We show, through numerical and graphicalexperiments, that the proposed scheme reduces blurring artefacts and preservesthe target shape and fine details. We also report the highest qualityreconstruction under highly undersampling rates in comparison to several stateof the art techniques.

Compressed Sensing Plus Motion (CS+M): A New Perspective for Improving Undersampled MR Image Reconstruction