S More edited untitled.tex  over 8 years ago

Commit id: b5e07395bc5afc6c5522935dfde5f950355f3edb

deletions | additions      

       

\textit{Oh, an empty article!} \section{Introduction}  You can get started by \textbf{double clicking} this text block and begin editing. You can also click Consider  the \textbf{Text} button below to add new block elements. Or you can \textbf{drag following integral:  \begin{equation}  F = \int dx dy f P(f, \sigma)  \end{equation}  where f is the number of photon counts in a pixel $(x, y)$ and $P(f, \sigma)$ is a Gaussian distribution centered at zero  and drop an image} right onto with dispersion $\sigma$.  Assuming ergodicity, we can reduce  this text. Happy writing! integral to  \begin{equation}  F = \int_{-\infty}^{\infty} df f P(f, \sigma) = 0  \end{equation}  Instead if we decided to do,  \begin{equation}  F = \int dx dy |f| P(f, \sigma)  \end{equation}  Then we would end up with  \begin{eqnarray}  F &=& 2 \int_{0}^{\infty} df f P(f, \sigma) \\  &=& 2 \int_{0}^{\infty} df f \frac{1}{\sqrt(2*\pi)\sigma}\exp\left(-\frac{f^2}{2\sigma^2} \right) \\  &=& 2 \int_{0}^{\infty} \frac{\sigma dt}{\sqrt{2*\pi}}\exp(-t) \\  &=& \sqrt{\frac{2}{\pi}} \sigma  \end{eqnarray}