The only preprocessing step used is convolving the image with a $$(2n+1)\times(2n+1) $$ kernel where the center element is \(1/(n+1)\) and the k-th layer surrounding the center is made up of values \(1/{(8k\cdot(n+1))}\). For example, when n=1 the kernel would be
\[
\left( \begin{array}{ccc}
^1/_{16} & ^1/_{16} & ^1/_{16}\\\\
^1/_{16} & ^1/_{2}& ^1/_{16}\\\\
^1/_{16} & ^1/_{16} & ^1/_{16} \end{array} \right)
\]
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 \(n=1\).