Evaluating random–Nyquist sampling ratios in combined compressed sensing magnetic resonance imaging

Abstract

Compressed sensing (CS) has been widely applied in magnetic resonance imaging (MRI) to accelerate the image acquisition without significantly reducing its image quality. In Cartesian MRI, acquisition time can be reduced by skipping phase-encoding steps for faster data acquisition. However, the balance between random under-sampling and Nyquist sampling at the k-space center strongly determines image quality. In this study, we systematically evaluate the impact of different random-to-Nyquist sampling ratios for both single-coil (CS-MRI) and multi-coil (CS-pMRI) reconstructions. Simulation results reveal that dense Nyquist sampling around the k-space center is essential for maintaining image fidelity, whereas reconstruction quality deteriorates sharply when random sampling exceeds approximately 60% of the total under-sampled data. Moreover, CS-pMRI consistently outperforms CS-MRI under equivalent under-sampling factors, benefiting from additional coil sensitivity information that improves resilience against aliasing and noise. These findings provide practical guidelines for hybrid under-sampling design, emphasizing that sufficient Nyquist sampling coverage of central k-space is crucial for achieving high-quality reconstructions while enabling high acceleration in CS-MRI.