Residual Water Suppression Using the Squared Eigenfunctions of the Schrödinger Operator

Abstract

Water suppression, in proton magnetic resonance spectroscopy (MRS) using post-processing techniques, is very challenging due to the large amplitude of the water line, which shadows the metabolic peaks with small amplitudes and complicates their quantification. In addition, the peak-shaped structure of these spectra and the relatively small number of data points representing them makes the suppression process more cumbersome. In this paper, a post-processing water suppression technique based on the Schrödinger operator is proposed. The method is based on the decomposition of the input MRS spectrum, using the squared eigenfunctions of a semi-classical Schrödinger operator. The proposed approach proceeds in three steps: first, the water peak is estimated using an optimal choice of the value of $h$ to reconstruct the MRS spectrum with a minimum number of eigenfunctions. Second, these estimated eigenfunctions are further refined to ensure that they only represent the water line with no contribution from the metabolite peaks. Finally, the estimated water peak is subtracted from the input MRS spectrum. The proposed method is tested on simulated in vitro and real in vivo MRS data and compared with the Hankel-Lanczos singular value decomposition with partial reorthogonalization (HLSVD-PRO) method. The results obtained show that the semi-classical signal analysis (SCSA) performs comparably to the HLSVD-PRO in accurately suppressing the water peak.