Compressed sensing for magnetic resonance images with phase variations

The application of compressed sensing (CS) to MRI has the potential to significantly reduce scan time. However, the quality of reconstructed images will be degraded when the MR images have strong phase variations. In the present paper, we propose a new CS method that is easy to implement and robust to phase variations on MR images. When the signal trajectory in k-space is symmetrical with respect to its origin, the k-space signal corresponding to the real and imaginary parts of the complex image can be synthesized independently by restricting the k-space signal to an even function or an odd function. The proposed method involves random but symmetrical k-space acquisition and independent reconstruction of the real and imaginary parts of images using the real-valued constraint. Several numerical experiments demonstrate that the proposed CS method provides a better quality of images compared to the other methods.