deletions | additions       diff --git a/res_pre.md b/res_pre.md  index 19732e9..33a3257 100644  --- a/res_pre.md  +++ b/res_pre.md 
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\[  \left( \begin{array}{ccc}  1/16 & 1/16 & 1/16\\\\  1/16 & 1/2 ^1/_2  & 1/16\\\\ 1/16 & 1/16 & 1/16 \end{array} \right)  \]  Convolving the image with this kind of kernel reduces the noise while retaining more of the original signal than simple averaging. Contributions from the i-th layer around the center will have the same weight as the central pixel. In this work we use the kernel with \(n=1\).