Optimization of Weights for Multi-echo fMRI Combination
Due to the higher sensitivity to bold oxygenation level dependent (BOLD) signals and the ability to distinguish neurally related signals, multi-echo fMRI (ME-fMRI) has been a hot topic of research recently. Weighted combination in ME-fMRI is critical for the quality of the combined signal, which can be used for the analysis of brain functions. However, a convincing weighting method has never been put forward in previously published research. In this work, we optimized the weighting methods based on the Rayleigh quotient when using temporal signal-noise-ratio (tSNR) and multi-echo temporal signal-noise-ratio (metSNR) as metrics. These two metrics strongly represent the contrast-noise-ratio (CNR) which has been widely used to estimate fMRI quality. In our case of steady-state fMRI, with the optimal weighting methods, both tSNR and metSNR of the combined signal were improved significantly as compared to other widely-used weighting methods. In the meantime, we obtained negative weights that were not used in the combination for previous research, which drove us to find the causes and re-define the normalization as 'L1 Normalization'. We also found the distribution characteristics of negative weights in terms of brain region and TE. The occurrence and features of negative weights were explained by the correlation between echoes' data and the change of the multipliers (e.g. the mean value). In addition, we found that the metSNR performs more robustly than tSNR when comparing non-optimal methods to optimal methods and explained their variations based on the ratio from a mathematical viewpoint.