Uncertainty in denoising of MRSI using low-rank methods

Purpose: Low-rank denoising of MRSI data results in an apparent increase in spectral SNR. However, it is not clear if this translates to a lower uncertainty in metabolite concentrations after spectroscopic fitting. Estimation of the true uncertainty after denoising is desirable for downstream analysis in spectroscopy. In this work the uncertainty reduction from low-rank denoising methods based on spatio-temporal separability and linear predictability in MRSI are assessed. A new method for estimating metabolite concentration uncertainty after denoising is proposed. Automatic rank threshold selection methods are also assessed in simulated low SNR regimes. Methods: Assessment of denoising methods is conducted using Monte Carlo simulation of proton MRSI data, and by reproducibility of repeated in vivo acquisitions in five subjects. Results: In simulated and in vivo data, spatio-temporal based denoising is shown to reduce the concentration uncertainty, but linear prediction denoising increases uncertainty. Uncertainty estimates provided by fitting algorithms after denoising consistently under-estimate actual metabolite uncertainty. However, the proposed uncertainty estimation, based on an analytical expression for entry-wise variance after denoising, is more accurate. It is also shown automated rank threshold selection using Marchenko-Pastur distribution can bias the data in low SNR conditions. An alternative soft-thresholding function is proposed. Conclusion: Low-rank denoising methods based on spatio-temporal separability do reduce uncertainty in MRS(I) data. However, thorough assessment is needed as assessment by SNR measured from residual baseline noise is insufficient given the presence of non-uniform variance. It is also important to select the right rank thresholding method in low SNR cases.