In multi-echo fMRI, data from multiple echoes are combined using weights. We use the framework of the generalized Rayleigh quotient (GRQ) to derive the optimal weights for temporal SNR (tSNR) and multi-echo tSNR (metSNR) measures of performance. We also examine the sensitivity of both these measures to the choice of weights. We find that metSNR measures are relatively insensitive to the weights in gray matter regions as compared to tSNR measures, which show greater sensitivity in these regions. We interpret the findings using the form of the GRQ.
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