Chunk #47 — Methods — Blind deconvolution

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Resting state fMRI connectivity is sensitive to laminar connectional architecture in the human brain.

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yes

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as follows:4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ D\left( \omega \right) = \frac{{H^{*} \left( \omega \right)}}{{\left| {H\left( \omega \right)} \right|^{2} + \left| {E\left( \omega \right)} \right|^{2} }}, $$\end{document}Dω=H∗ωHω2+Eω2,where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$*$$\end{document}∗ denotes complex conjugate. The estimate \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{x} \left( t \right)$$\end{document}x⌣t of the latent neural signals \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x\left(t\right)$$\end{document}xt is then given by5\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{x} \left( t \right) = {\mathcal{F}}^{ - 1} \left\{ {D\left( \omega \right)\left. {Y\left( \omega \right)} \right\} = {\mathcal{F}}^{ - 1} } \right.\left\{ {\frac{{H^{*} \left( \omega \right)Y\left( \omega \right)}}{{\left| {H\left( \omega \right)} \right|^{2} + \left| {E\left( \omega \right)} \right|^{2} }}} \right\}. $$\end{document}x⌣t=F-1DωYω=F-1H∗ωYωHω2+Eω2.