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

Purpose: To obtain high-quality reconstructions from highly undersampled dynamic MRI data with the goal of reducing the acquisition time and towards improving physicians' outcome in clinical practice in a range of clinical applications. Theory and Methods: In dynamic MRI scans, the interaction between the target structure and the physical motion affects the acquired measurements. We exploit the strong repercussion of motion in MRI by proposing a variational framework - called Compressed Sensing Plus Motion (CS+M) - that links in a single model, simultaneously and explicitly, the computation of the algorithmic MRI reconstruction and the physical motion. Most precisely, we recast the image reconstruction and motion estimation problems as a single optimisation problem that is solved, iteratively, by breaking it up into two more computationally tractable problems. The potentials and generalisation capabilities of our approach are demonstrated in different clinical applications including cardiac cine, cardiac perfusion and brain perfusion imaging. Results: The proposed scheme reduces blurring artefacts and preserves the target shape and fine details whilst observing the lowest reconstruction error under highly undersampling up to 12x. This results in lower residual aliasing artefacts than the compared reconstructions algorithms. Overall, the results coming from our scheme exhibit more stable behaviour and generate a reconstruction closer to the gold-standard. Conclusion: We show that incorporating physical motion to the CS computation yields a significant improvement of the MR image reconstruction, that in fact, is closer to the gold-standard. This translates to higher reconstruction quality whilst requiring less measurements.