Accelerated phase contrast imaging using compressed sensing with complex difference sparsity

Methods Figure 1 shows the proposed CS reconstruction with CD sparsity for phase contrast MR. The objective function J = ‖FΩmi-yi‖2+l‖Ψmi‖1‖+lCD‖m1-m2‖1, where mi=1,2 are the two bipolar encoding acquisitions and |m1-m2| is the corresponding CD image, is used in the reconstruction. The reconstruction performs iteratively between two bipolar images. Every iteration, the recon of m1 makes the intermediate image of m1 and pass it to the recon of m2, which uses it for calculating CD image and makes the intermediate image of m2 and pass it back to the recon of m1. To evaluate the proposed method, phase contrast images were acquired using an axial slice of ascending aorta at the level of the bifurcation of the pulmonary artery. A retrospectively ECG-gated flowencoded 2D PC MRI pulse sequence was used with typical parameters of: FOV= 320×320 mm, resolution = 2.5ms x 2.5 ms, slice thickness = 6mm, TR/TE=15/ 6.5ms, flip angle= 30°, temporal resolution = 30ms, VENC = 300 cm/s. The under-sampling was performed retrospectively from a fully sampled data using a Gaussian random under-sampling for rates of 3 and 5. In an IRB approved study, 14 healthy adult subjects (5 males, 17-70 years) were recruited. Reconstructed images were compared with fully-sampled acquisition and CS without CD sparsity (i.e. lCD= 0).