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SNR_comparison_12_vs_32_channel.lyx
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SNR_comparison_12_vs_32_channel.lyx
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#LyX 1.6.5 created this file. For more info see http://www.lyx.org/
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\begin_document
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\begin_body
\begin_layout Title
SNR comparison 12 vs 32 channel coils
\end_layout
\begin_layout Standard
See complimentary file DSI_comparison_marta.ods and pdf for results
\end_layout
\begin_layout Standard
Registration:
\end_layout
\begin_layout Standard
\begin_inset Formula \begin{eqnarray*}
b0 & \rightarrow & MPRAGE\leftarrow ICBM\\
b0 & \leftarrow & MPRAGE\leftarrow ROI\end{eqnarray*}
\end_inset
\end_layout
\begin_layout Standard
Estimated noise sd computed using
\begin_inset Formula $\bar{M}=\sqrt{\pi/2}\sigma$
\end_inset
and
\begin_inset Formula $\sigma_{M}^{2}=\sigma^{2}(2-\pi/2)$
\end_inset
(estimated as Rician)
\end_layout
\begin_layout Standard
And this is then deviated by the signals to calculate the baseline.
\end_layout
\begin_layout Standard
The real signal A can be found by the measured signal
\begin_inset Formula $\left\langle M^{2}\right\rangle =\sqrt{A^{2}+\sigma^{2}}$
\end_inset
then
\begin_inset Formula $SNR_{0}=\frac{A}{\sigma}$
\end_inset
\end_layout
\begin_layout Standard
Here we use
\begin_inset Formula $SNR_{0}=\frac{<ROI>}{\sigma}$
\end_inset
.
\end_layout
\begin_layout Standard
Marta also said that another proper way to compute is
\begin_inset Formula $\left\langle M^{2}\right\rangle =\frac{1}{2}\sigma^{2}$
\end_inset
.
\end_layout
\end_body
\end_document