Optimal k-space sampling scheme for compressive sampling MRI

A method for optimizing k-space sampling trajectory in compressive sampling MRI (CS-MRI) is presented. In k-space, most of the energies are concentrated around the center. When k-space is undersampled, it is required to take most of its higher energy samples for proper CS reconstruction. Therefore more samples are required around the center than the periphery. Using this prior knowledge on k-space energy distribution, a probability density function (PDF) was proposed to generate sampling trajectories. Sampling trajectories were generated for various PDF parameters. These sampling trajectories were applied on the spatial frequency data of fully acquired brain MR images. The optimum sampling trajectory was chosen based on the reconstruction performance. With this optimum trajectory, only 38% of k-space data were required for proper image reconstruction. It was also found that at least 20% of the higher energy samples around the center of k-space were fully required and the rest of the higher energy samples were to be acquired as closely as possible. The optimized sampling trajectory was applied on the simulated k-space data of virtual brain phantom and k-space data of quality assurance phantom. It was verified that the quality of CS reconstructed image matches with the fully reconstructed image.