Abstract #2850

Magnetic Resonance Spectroscopy Denoising with the Automatic Regularization Parameter Estimation in Low-Rank Hankel Matrix Reconstruction

Tianyu Qiu¹, Wenjing Liao², Di Guo³, Zhangren Tu³, Bingwen Hu⁴, and Xiaobo Qu¹

¹Department of Electronic Science, Xiamen University, Xiamen, China, ²School of Mathematics, Georgia Institute of Technology, Atlanta, GA, United States, ³School of Computer and Information Engineering, Xiamen University of Technology, Xiamen, China, ⁴Department of Physics, East China Normal University, Shanghai, China

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.

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