From f001099b7a362a56c1c174d83691b10b10cb4147 Mon Sep 17 00:00:00 2001 From: "Claudio Maggioni (maggicl)" Date: Mon, 30 Nov 2020 21:02:20 +0100 Subject: [PATCH] mp5: done --- mp5/Project_5_Maggioni_Claudio.pdf | Bin 209518 -> 420518 bytes mp5/Project_5_Maggioni_Claudio.tex | 36 ++- .../{code_template.m => deblurring.asv} | 13 +- mp5/Project_5_Maggioni_Claudio/deblurring.m | 69 ++++ mp5/img_my-1.png | Bin 57287 -> 59326 bytes mp5/img_my.tex | 212 +------------ mp5/img_orig-1.png | Bin 0 -> 53870 bytes mp5/img_orig.tex | 26 ++ mp5/img_rcg-1.png | Bin 59326 -> 58872 bytes mp5/img_rcg.tex | 10 +- mp5/res_log.tex | 296 +++++++++--------- 11 files changed, 296 insertions(+), 366 deletions(-) rename mp5/Project_5_Maggioni_Claudio/{code_template.m => deblurring.asv} (83%) create mode 100644 mp5/Project_5_Maggioni_Claudio/deblurring.m create mode 100644 mp5/img_orig-1.png create mode 100644 mp5/img_orig.tex diff --git a/mp5/Project_5_Maggioni_Claudio.pdf b/mp5/Project_5_Maggioni_Claudio.pdf index dc851bf1db13ab756cba4e3ff7ce2b64f9888a28..f78ea03e1cfcc7981ecfddcf7d8c81693c296387 100644 GIT binary patch delta 396826 zcma&N1ytQo)9($G;uI)a^b~h@cXxMpcZc8(#hp^z-Q9}26^gsN73b1NUb*+Z-*?YC z$w_u*XHRyr&YJ)HCTBYch4Wtk5_w@!8U|VxIFhmXp1JY^Wf+4g7a8Wpf{kL{zr-FQ6SKFNiXHc6qX=eU5< zGbyQx@NOEWKBgqx(G}cPrZDHDG*J;z&~lhyZK=qFIYXH^x4mS^ zu>jA-pMHy^Ax7Yq(1Ia|D&cwI*m>bj5}X=}HMW77*RrJFOO?bS(PY(p2rYIrL>||& z0%WNQlmH7Yx3BSa-!tV*=mM7xbj3?DE=m=XKdy+Xczm1Rl_R?q_|>a*%pg%y*xLv` zF4Zg4+Zl{0`6VY;3oQ4dSr$B69*k(LTd)Ka#YNf+{k6eT7-5zKrf6={8`mT#xH(N0 z9xz8~5vC|-Xfn;)dyqF{<0tmzVG6;+O050Vj{;!8FJhj)L4O$?LZ?kuE%59rWj7tM z3=)@}q{gO2OPsabAxK;bO!G|Kh96ugWyqmreMUy4J!Z(Xh!ZuPms#CANr$Jb zDTz^0W4p-|#LEw@ZB1$Srd?J zW?%&iN7B^&b6nuZ4$K&f3yKvFl1o{atn}=7%akCjgrnR%o;`J*c^+rjEN!KsrmoH% z%=~QN}3pO9hV@9g7lwJpJ^!qgn|L{OQmANlC4}7fp2qab$)3|MQh&4$4fh74gJq! zH?6R@40F9L3y9yYiqi6rTFIZPdk~oh5o?9|yuAp=LRoC1b`-CcxQ9HVK5}j^MPWoR zmN(;zA)M3y3hy`SjhVWnUkd!L+3uRk{4og?H;PoVI)!E5IKys&Rm+!6+`A00Z8qc^ z=_^e+i*N!CIFl;26@QC5`ckC}=y%{bbx#a(Fc^?6$uYmqW|F1lIY4j-p6npIEc34w zJf15K4I=Sv>Pxx{-7^Q*gA5%7G~ufYDTtpH&}!Kc^}hb<1@|J@9}DV89fd~a`_>@} z8Fj=DbrQr!=@nODa&C2(_CyW%W^!p^;G73T-~JXz3|Ga1UnU>A&BVlgte=8{I#fbJ6Oz6^zjI8s!mbCsCYeuAyKP9B(TAr6vIiJxD`c$=}VcYcUJP zkGRg+yR!(#t>#zHv-qx62E}tE9k(T(=VkDldXWWEh>9k2Fbrmgc})<=rU*Der%HYb zO2MDCJ?aTD?CLh`!ne32E}E|=6uLIJIZ#YhD%P0?@`W15gk@8izLvsOww2p5oKCpBU1`gdNmOX;Vb9lnsS)6LhGBimHtVLGYU2xE5{~vK5m@~pJPr? 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a/mp5/Project_5_Maggioni_Claudio.tex +++ b/mp5/Project_5_Maggioni_Claudio.tex @@ -89,7 +89,8 @@ The plot of the squared residual 2-norms over all iterations can be found in Fig \ref{fig:plot1}. \begin{figure}[h] - \input{test_semilogy} + \centering + \resizebox{0.6\textwidth}{!}{\input{test_semilogy}} \caption{Semilog plot of the plot of the squared residual 2-norms over all iterations}\label{fig:plot1} \end{figure} @@ -104,7 +105,8 @@ reflected in the eigenvalue plot, which shows a not so drastic increase of the first eigenvalues ordered in increasing order. \begin{figure}[h] - \input{A_eig} + \centering + \resizebox{0.6\textwidth}{!}{\input{A_eig}} \caption{Semilog plot of the eigenvalues of A}\label{fig:plot2} \end{figure} @@ -120,13 +122,39 @@ $max\_iter=200$ $tol= 10^{-6}$. Plot the convergence (residual vs iteration) of each solver and display the original and final deblurred image.} -Plots already rendered. +My implementation is in the file \texttt{deblurring.m}. Plots for the original image, the deblurred image from +\texttt{myCG}, the deblurred image from \texttt{pcg}, and a semi-logarithmic plot on the y-axis of the residuals +from the two conjugate gradient functions over the iteration count can be found respectively in figure \ref{fig:orig}, +\ref{fig:mycg}, \ref{fig:pcg}, and \ref{fig:rvec}. +\begin{figure}[h] + \begin{subfigure}{0.33\textwidth} + \centering + \resizebox{0.8\textwidth}{!}{\input{img_orig}} + \caption{Original image grayscale matrix}\label{fig:orig} + \end{subfigure} + \begin{subfigure}{0.33\textwidth} + \centering + \resizebox{0.8\textwidth}{!}{\input{img_my}} + \caption{Deblurred image using \texttt{myCG}}\label{fig:mycg} + \end{subfigure} + \begin{subfigure}{0.33\textwidth} + \centering + \resizebox{0.8\textwidth}{!}{\input{img_rcg}} + \caption{Deblurred image using \texttt{rcg}}\label{fig:pcg} + \end{subfigure} + \caption{Blurred and deblurred images} +\end{figure} +\begin{figure}[h] + \centering + \resizebox{0.6\textwidth}{!}{\input{res_log}} + \caption{Residuals of \texttt{myCG} (in blue) and \texttt{rcg} (in orange) over iteration count (y axis is a log scale)}\label{fig:rvec} +\end{figure} \subsection{ When would \texttt{pcg} be worth the added computational cost? What about if you are debluring lots of images with the same blur operator?} -\textit{pcg} better for many, myCG better for one thanks to cost of ichol. +The \textit{pcg} algorithm provided by MATLAB would be worth for many deblurring operations useing the same blur operator, since the cost of computing the incomplete cholesky decomposition (i.e. \texttt{ichol}) can be payed only once and thus amortized. \texttt{myCG} is better for few iterations thanks to not needing any seed that is expensive to compute. \end{document} diff --git a/mp5/Project_5_Maggioni_Claudio/code_template.m b/mp5/Project_5_Maggioni_Claudio/deblurring.asv similarity index 83% rename from mp5/Project_5_Maggioni_Claudio/code_template.m rename to mp5/Project_5_Maggioni_Claudio/deblurring.asv index 0e173ed..893e3d1 100644 --- a/mp5/Project_5_Maggioni_Claudio/code_template.m +++ b/mp5/Project_5_Maggioni_Claudio/deblurring.asv @@ -14,6 +14,7 @@ im_l=min(min(B)); im_u=max(max(B)); imshow(B,[im_l,im_u]) title('Blured Image') +matlab2tikz('showInfo', false, '../img_orig.tex'); % Vectorize the image (row by row) b=B'; @@ -64,15 +65,3 @@ im_u=max(max(X2)); imshow(X2,[im_l,im_u]) title('Sharp Image (rcg)') matlab2tikz('showInfo', false, '../img_rcg.tex'); - - - -%% Validate Test values -load('test_data/A_test.mat'); -load('test_data/x_test_exact.mat'); -load('test_data/b_test.mat'); - -%res=||x^*-A^{-1}b|| -res=x_test_exact-inv(A_test)*b_test; -norm(res); -%(Now do it with your CG and Matlab's PCG routine!!!) diff --git a/mp5/Project_5_Maggioni_Claudio/deblurring.m b/mp5/Project_5_Maggioni_Claudio/deblurring.m new file mode 100644 index 0000000..5b5ad1d --- /dev/null +++ b/mp5/Project_5_Maggioni_Claudio/deblurring.m @@ -0,0 +1,69 @@ +close all; +clear; clc; +addpath /Users/maggicl/Git/matlab2tikz/src/; + +%% Load Default Img Data +load('blur_data/B.mat'); +B=double(B); +load('blur_data/A.mat'); +A=double(A); + +% Show Image +figure; +im_l=min(min(B)); +im_u=max(max(B)); +imshow(B,[im_l,im_u]) +title('Blurred Image') +matlab2tikz('showInfo', false, '../img_orig.tex'); + +% Vectorize the image (row by row) +b=B'; +b=b(:); + +AT = A' * A; +bt = A' * b; + +IL = ichol(AT, struct('type', 'nofill', 'diagcomp', 0.01)); + +[x, rvec] = myCG(AT, bt, zeros(size(b)), 200, 1e-6); +[x2, ~, ~, ~, rvec2] = pcg(AT, bt, 1e-6, 200, IL, IL'); + +X2 = zeros(250, 250); +for i = 0:249 + for j = 1:250 + X2(i + 1, j) = x2(i * 250 + j); + end +end + +figure; +im_l=min(min(X2)); +im_u=max(max(X2)); +imshow(X2,[im_l,im_u]) +title('Sharp Image (rcg)') +matlab2tikz('showInfo', false, '../img_rcg.tex'); + + +X = zeros(250, 250); +for i = 0:249 + for j = 1:250 + X(i + 1, j) = x(i * 250 + j); + end +end + +figure; +im_l=min(min(X)); +im_u=max(max(X)); +imshow(X,[im_l,im_u]) +title('Sharp Image (myCG)') +matlab2tikz('showInfo', false, '../img_my.tex'); + + + + +figure; +semilogy(rvec / norm(bt)); +hold on; +semilogy(rvec2 / norm(bt)); +hold off; +title('Residual norms over iteration (y is log)') 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