In Eq. 5, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{F}}^{-1}$$\end{document}F-1 is the inverse Fourier transform operator. Since the measurement noise \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$e(t)$$\end{document}e(t) is assumed to be white, the covariance of the noise term must be 0. For task-related fMRI, the stimulus function provides the prior information about neural activity and a generative model whose inversion corresponds to deconvolution. Here, resting state fMRI is considered as a spontaneous event-related signal, and these events can be reflected by relatively large amplitude BOLD signal peaks [58, 86]. Therefore, the time series from each vertex was evaluated against a given amplitude threshold around the local maximum (threshold was set to 1, since the input time series were normalized) to obtain a set of estimated onsets (the timing of delta functions) for these pseudo-events. To get the delay \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau $$\end{document}τ (the delay between the peak of fMRI and the peak of neural signal), we searched all integers between [0 8] based on a previous study
