Random phase modulation of spatial aliasing in temporal domain for dynamic MRI

Introduction: Parallel imaging has been widely used in dynamic MRI for improved spatial or temporal resolution. In this study, we propose a new k-t space sampling trajectory for dynamic parallel imaging techniques. This method applies a random phase modulation to the spatial aliasing of images in temporal domain. As a result, the spatial aliasing induced by k-space undersampling at every time frame has a noise pattern in temporal dimension. By applying a temporal constraint that can be known from the priori knowledge of dynamic MRI data, the noise-like aliasing can be easily removed. This work uses the fMRI and cardiac imaging applications as examples to demonstrate the feasibility of the proposed method. Theory: Consider undersampling a set of 2D k-space data with a reduction factor of R. One will have R choices of undersampling trajectories, which correspond to the use of different k-space shifts, m=0,1,2,...,R-1, in phase encoding direction. The aliased image Am(r), corresponding to the sampling trajectory with a k-space shift equal to m, can be given by the below equation: