Model-based frequency-and-phase correction of ¹H MRS data with 2D linear-combination modeling

Retrospective frequency-and-phase correction (FPC) methods attempt to remove frequency-and-phase variations between transients to improve the quality of the averaged MR spectrum. However, traditional FPC methods like spectral registration struggle at low SNR. Here, we propose a method that directly integrates FPC into a two-dimensional linear-combination model (2D-LCM) of individual transients ('model-based FPC'). We investigated how model-based FPC performs compared to the traditional approach, i.e., spectral registration followed by 1D-LCM in estimating frequency-and-phase drifts and, consequentially, metabolite level estimates.

We created synthetic in-vivo-like 64-transient short-TE sLASER datasets with 100 noise realizations at 5 SNR levels and added randomly sampled frequency and phase variations. We then used this synthetic dataset to compare the performance of 2D-LCM with the traditional approach (spectral registration, averaging, then 1D-LCM). Outcome measures were the frequency/phase/amplitude errors, the standard deviation of those ground-truth errors, and amplitude Cramér Rao Lower Bounds (CRLBs). We further tested the proposed method on publicly available in-vivo short-TE PRESS data.

2D-LCM estimates (and accounts for) frequency-and-phase variations directly from uncorrected data with equivalent or better fidelity than the conventional approach. Furthermore, 2D-LCM metabolite amplitude estimates were at least as accurate, precise, and certain as the conventionally derived estimates. 2D-LCM estimation of frequency and phase correction and amplitudes performed substantially better at low-to-very-low SNR.

Model-based FPC with 2D linear-combination modeling is feasible and has great potential to improve metabolite level estimation for conventional and dynamic MRS data, especially for low-SNR conditions, e.g., long TEs or strong diffusion weighting.