In Magnetic Resonance Spectroscopy (MRS), denoising is an important task for MRS due to its poor sensitivity. In this work, noise removal serves as a low rank Hankel matrix reconstruction from noisy free induction decay (FID) signals, since noiseless FID signals are commonly modeled as exponential functions and their Hankel matrices are usually low rank. A faithful denoising mainly depends on the regularization parameter helping to distinguish meaningful signal from noise. We further derived a theoretical bound to automatically set this parameter. Numerical experiments on the realistic MRS data show that noise can be effectively removed with the proposed approach.