Abstract: Theoretically, the compressed sensing (CS) requires incoherent sampling to satisfy the restricted isometry property (RIP) condition. However, the purely random sampling scheme is very unpractical in two-dimensional (2D) magnetic resonance imaging (MRI) due to hardware and physiological restraints and also does not follow the sprectum energy distribution of the signal. The existing literature on CS-MRI have been primarily focused on randomly sampling along the conventional trajectories such as cartesian, radial and spiral, however, such sampling still shows coherent property which cannot be neglected, in comparison with random k-space sampling. In this paper, a chaotic-like trajectory is proposed based on the chaos attractor which is a good candidate for MRI k-space sampling with noise-like under-sampling artifacts since chaotic systems can not only produce random sequences, but also are deterministic systems inherently which are easy to implement. Finally, a chaotic-like trajectory with under-sampling acceleration ratio R = 5 is designed, and the corresponding simulations are given. Simulation results demonstrate that the proposed trajectory can cause less down-sampling artifacts than the traditional variable density spiral trajectory in CS reconstruction.

Keywords: Chaos Trajectory, Compressed Sensing, k-Space Trajectory, MRI, Rapid Imaging, Random Sampling.