Spatio-temporal filtering of blood flow in 4D Phase-Contrast MRI

4D PC-MRI provides the spatio-temporal imaging of the blood-flow velocity in a region of interest such as the aortic system during a cardiac cycle. However, the resolution and the signal-to-noise ratio (SNR) are limited by acquisition constraints. In order to improve the SNR, we propose to regularize the blood-flow velocity field by introducing a physical constraint, incompressibility, and a temporal quadratic penalization. The advantage of the developed solution is its simple implementation.