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% Toni: Noise Model
% Toni: Algorithm for EWF or DCT and neighborhood filter
% Toni: Biais, Variance as a joint section with aggregation
% Toni: Algorithm for aggregation
% Toni: Section of experimentation



\begin{document}

\title{Secrets of denoising "cuisine"}
\author{A. Buades \and M. Colom \and M. Lebrun \and J.M Morel}
\date{}
\maketitle
\tableofcontents
\clearpage

\graphicspath{{./images/}}




 






\begin{table}
\small
\centering 
\begin{tabular}{||c||c||c||c||c||c||c||}
	\hline
	 & \multicolumn{6}{c||}{$\sigma = 2$}\\
	 \hline
	 \hline
	 &  {NL-Bayes} & {BM3D} &   {BLS-GSM} &   {K-SVD}  & {NL-means} & {DCT denoising} \\
	\hline
	Alley & {\bf 45.42}  & 44.95   & - &   41.51  & 42.75  & 44.58  \\
 	\hline
 	Computer & {\bf 45.96}   & 45.22 &   44.69   & 44.52 & 44.03 & 44.54    \\
 	\hline
 	Dice & {\bf 49.00}   & 48.86 &  48.59 &   47.79 & 48.51  & 48.39    \\
 	\hline
 	Flowers & {\bf 47.77} & 47.31   & 47.12  & 47.09 & 46.36 &  47.05  \\
 	\hline
 	Girl & {\bf 47.56}   & 47.40  & 47.14 &   47.28  &46.96  & 46.76    \\
 	\hline
 	Traffic & {\bf 45.33}   & 44.56 & 44.15   & 43.80& 43.55 &  44.26   \\
 	\hline
 	Trees & {\bf 43.51}  & 43.07  & - &   42.05 & 42.22 &  42.95  \\
 	\hline
 	Valldemossa & {\bf 45.17}  & 44.68 &   44.41  & 40.08 &  43.33 &  44.50  \\
 	\hline
 	\hline
 	Mean & {\bf 46.22}   & 45.76 &  -   & 44.27  & 44.71 &  45.37 \\
 	\hline
\end{tabular}













\begin{tabular}{||c||c||c||c||c||c||c||}
	\hline
	 & \multicolumn{6}{c||}{$\sigma = 5$}\\
	 \hline
	 \hline
	 &  {NL-Bayes} & {BM3D} &   {BLS-GSM} &   {K-SVD}  & {NL-means} & {DCT denoising} \\
	\hline
	Alley & {\bf 39.24}  & 38.95 &  - &  38.45 & 37.18 &  38.37   \\
 	\hline
 	Computer & {\bf 40.69} &  39.98 &  39.30 &  39.58 & 38.86  & 39.03   \\
 	\hline
 	Dice & {\bf 46.09} & 45.80 &  45.21 & 45.27 & 45.12  & 45.22   \\
 	\hline
 	Flowers & {\bf 43.44}  & 42.99 & 42.76 & 43.09 & 42.05  & 42.78   \\
 	\hline
 	Girl & {\bf 44.26} &  44.03 &  43.70 & 43.59 & 43.44 &  43.36  \\
 	\hline
 	Traffic & {\bf 39.70} &   38.67 &   38.10 &  38.75 & 37.50  & 38.21  \\
 	\hline
 	Trees & {\bf 36.70}   & 36.10 & - & 35.61 & 34.69 & 35.76   \\
 	\hline
 	Valldemossa & {\bf 38.73}   & 38.33 &   38.02  & 37.87 & 35.94  & 37.94   \\
 	\hline
 	\hline
 	Mean & {\bf 41.11} &  40.61  & - &  40.28 & 39.35 &  40.08 \\
 	\hline
\end{tabular}












\begin{tabular}{||c||c||c||c||c||c||c||}
	\hline
	 & \multicolumn{6}{c||}{$\sigma = 10$}\\
	 \hline
	 \hline
	 &  {NL-Bayes} & {BM3D} &   {BLS-GSM} &   {K-SVD}  & {NL-means} & {DCT denoising} \\
	\hline
	Alley & {\bf 35.05} & 34.82  & - &  34.29 & 33.53 &  34.04 \\
 	\hline
 	Computer & {\bf 36.58}  & 36.28  & 35.47 & 35.79  & 35.44 &  35.22 \\
 	\hline
 	Dice & {\bf 43.30} &  43.02 & 42.21 & 41.71 & 42.06 & 42.25 \\
 	\hline
 	Flowers & {\bf 39.52}  & 39.49 &  39.10 & 39.31 & 38.49 &  39.01   \\
 	\hline
 	Girl & {\bf 41.69} & 41.45  & 41.14 & 40.29 & 40.42 & 40.52   \\
 	\hline
 	Traffic & {\bf 34.93} & 34.54 & 33.92 &  34.69 & 33.89 &  33.97   \\
 	\hline
 	Trees & {\bf 36.70}  & 36.10  & - & 35.61 & 29.42 & 30.73   \\
 	\hline
 	Valldemossa & {\bf 38.73} &  38.33 &  38.02 & 37.87& 32.02 &  33.28   \\
 	\hline
 	\hline
 	Mean & {\bf 37.06} &  36.83 &  - &  36.31& 35.66 & 36.12 \\
 	\hline
\end{tabular}
\caption{PSNR table for $\sigma=2$, $5$ and $10$.} \label{tb:psnr1}
\end{table}

	








	
\begin{table} 
\small
\centering 
\begin{tabular}{||c||c||c||c||c||c||c||}
	\hline
	 & \multicolumn{6}{c||}{$\sigma = 20$}\\
	 \hline
	 \hline
	 &  {NL-Bayes} & {BM3D} &   {BLS-GSM} &   {K-SVD}  & {NL-means} & {DCT denoising} \\
	\hline
	\hline
	Alley & {\bf 31.36} & 31.23  & -  &30.55 & 29.94 &  30.21   \\
 	\hline
 	Computer & {\bf 33.08} &  32.71 & 31.89 & 31.96 & 31.59 & 31.45   \\
 	\hline
 	Dice & {\bf 40.19} & 39.93 & 39.00 & 37.23 & 38.17 &  38.67   \\
 	\hline
 	Flowers & {\bf 35.87} &  35.85 &  35.34 &  35.24& 34.56 &  34.89   \\
 	\hline
 	Girl & {\bf 38.92} & 38.71 & 38.49 & 36.36 & 36.81 & 37.27   \\
 	\hline
 	Traffic & {\bf 31.14} & 30.83& 30.14 &  30.70 & 30.12 &  29.98   \\
 	\hline
 	Trees & {\bf 27.22} &  26.92  & - & 26.88 & 26.28 & 26.27   \\
 	\hline
 	Valldemossa & {\bf 29.81} &   29.57 & 26.97 & 29.08& 28.37 & 28.91   \\

 	\hline
 	\hline
 	Mean & {\bf 33.45} & 33.22 & - &  32.25 & 31.98 &  32.20  \\
 	\hline
\end{tabular}










\begin{tabular}{||c||c||c||c||c||c||c||}
	\hline
	 & \multicolumn{6}{c||}{$\sigma = 30$}\\
	 \hline
	 \hline
	 &  {NL-Bayes} & {BM3D} &   {BLS-GSM} &   {K-SVD}  & {NL-means} & {DCT denoising}  \\
	\hline
	\hline
	Alley & {\bf 29.42} &  29.33  & - &  28.60 & 27.58 &  28.25  \\
 	\hline
 	Computer & {\bf 31.00}  & 30.67 & 29.90 & 29.84 & 28.98 &  29.20   \\
 	\hline
 	Dice & {\bf 38.20} & 37.88 &  37.05 & 36.52 & 37.18 &  35.89   \\
 	\hline
 	Flowers & 33.67 & {\bf 33.73} &  33.19 &  33.54 & 32.66 & 32.46  \\
 	\hline
 	Girl & {\bf 37.12} &  36.97 &  36.91 &  35.38 & 35.54 &  34.67   \\
 	\hline
 	Traffic & {\bf 29.08} & 28.87 & 28.20 &  28.60 & 27.40 & 27.87  \\
 	\hline
 	Trees & {\bf 24.95} &  24.64 &  - &  24.52 & 23.29 & 23.83  \\
	\hline
 	Valldemossa & {\bf 27.51} &  27.30 & 26.97 &  26.80 & 25.55 &  26.48 \\
 	\hline
 	\hline
 	Mean & {\bf 31.37} & 31.17 &  - &  30.48  &29.77 & 29.83 \\
 	\hline
\end{tabular}














\begin{tabular}{||c||c||c||c||c||c||c||}
	\hline
	 & \multicolumn{6}{c||}{$\sigma = 40$}\\
	 \hline
	 \hline
	 &  {NL-Bayes} & {BM3D} &   {BLS-GSM} &   {K-SVD}  & {NL-means} & {DCT denoising}  \\
	\hline
	\hline	Alley & {\bf 28.16} &  28.08  & - &  27.29  & 26.30 & 27.01   \\
 	\hline
 	Computer & {\bf 29.55} & 29.15 &  28.52 &  28.25 & 27.31 &  27.44  \\
 	\hline
 	Dice & {\bf 36.91} & 36.28 &  35.50 &  34.49 & 35.31 & 33.38  \\
 	\hline
 	Flowers & 31.94 & {\bf 32.10} & 31.68 & 31.90 & 30.99 & 30.79  \\
 	\hline
 	Girl & {\bf 36.09} &  35.62 & 35.61 & 33.73 & 34.03 & 32.22  \\
 	\hline
 	Traffic & {\bf 27.67} &  27.50 &  26.93 &  27.19& 26.01 &  26.40   \\
 	\hline
 	Trees & {\bf 23.35} &  23.17  & - &  23.06 & 21.91 & 22.25  \\
 	\hline
 	Valldemossa & {\bf 27.51} & 25.78 & 25.50 & 25.28 & 24.10 & 24.90      \\
 	\hline
 	\hline
 	Mean & {\bf 30.15} & 29.71 & - & 28.90& 28.25 & 28.04  \\
 	\hline
\end{tabular}

\caption{PSNR table for $\sigma=20$, $30$ and $40$.} \label{tb:psnr2}
\end{table}





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