Abstract: To improve the 3D imaging and reconstruction speed of Magnetic Particle Imaging (MPI), reduce the requirement of 3D refactoring to the completeness of sampled projection data, a novel Noise-Robust 3D Sparse Sampling Magnetic Particle Imaging (3D NRSS-MPI) method was proposed. The algorithm was arranged to reconstruct 3D MPI noisy data by solving a convex optimization problem formed with the l₂ norm and sparse regular constraint of MPI projection imaging. Eliminating the limit of MPI scanning trajectory, the proposed method was designed as a universal basic model for the developing MPI technique. Taking the advantage of MPI priori information to improve the 3D reconstruction robustness of noisy MPI projection data, 3D total variation sparse operator was established to realize matrix-free operation, improving the efficiency of operation. The results of point source and coronary phantom imaging experiments show that the proposed 3D NRSS-MPI method can effectively eliminate the reconstructed image star artifacts at 1/4 undersampling, obtain a higher image signal-to-noise ratio, and make the coronary reconstruction structure similarity exceed 0.701, which can accurately reconstruct the undersampled and noisy MPI data, effectively shortening the imaging and reconstruction time by 4 times.