Dalam dunia nyata, suatu proses pencitraan hampir dapat dipastikan akan menghasilkan citra keluaran yang mengalami degradasi. Penyebab degradasi ini antara lain berupa sensor yang tidak fokus, pergerakan dari obyek maupun sistem pencitraan, gangguan derau termal pada sensor dan perangkat elektronik sistem pencitraan, maupun sebab-sebab lainnya yang terkait dengan lingkungan pengambilan data seperti turbulensi atmosfir pada praktek remote sensing dan pengamatan astronomi.

Untuk memperoleh citra yang lebih tepat, diperlukan adanya suatu proses restorasi citra. Restorasi citra berkaitan dengan upaya memperoleh kembali suatu citra asal dari sebuah citra yang terdegradasi, dengan memanfaatkan suatu pengetahuan mengenai proses terjadinya degradasi tersebut.

Restorasi citra (image restoration) dapat dibedakan dengan perbaikan citra (image enhancement), di mana proses yang dilakukan dalam perbaikan citra lebih bersifat heuristik dan lebih dititikberatkan pada upaya melakukan aksentuasi fitur dalam citra.

Berikut ini merupakan contoh aplikasi pemrograman matlab mengenai restorasi citra. Coding dapat dijalankan menggunakan software matlab minimal versi r2014b.

A. Model Derau Aditif
1. Citra noise test

2. Derau impuls (salt & pepper)

3. Derau uniform

4. Derau gaussian

5. Derau rayleigh

B. Restorasi Derau secara Spasial
1. Derau impuls

2. Derau uniform

3. Derau gaussian

4. Derau rayleigh

C. Restorasi Derau Periodik
1. Filter band-stop ideal

2. Filter band-stop butterworth

3. Filter band-stop gauss

D. Inverse Filter

E. Pseudo-Inverse Filter

F. Filter Wiener

Tampilan source codenya adalah sebagai berikut:

function restorasi_citra
f = figure('Name','Restorasi Citra','MenuBar','none',...
    'ToolBar','none','NumberTitle','off','Position',[250 130 800 500]);

tgroup = uitabgroup('Parent', f);
tab1 = uitab('Parent', tgroup, 'Title', 'Model Derau Aditif');
tab2 = uitab('Parent', tgroup, 'Title', 'Restorasi Derau secara Spasial');
tab3 = uitab('Parent', tgroup, 'Title', 'Restorasi Derau Periodik');
tab4 = uitab('Parent', tgroup, 'Title', 'Inverse Filter');
tab5 = uitab('Parent', tgroup, 'Title', 'Pseudo-Inverse Filter');
tab6 = uitab('Parent', tgroup, 'Title', 'Filter Wiener');

tgroup1 = uitabgroup('Parent', tab1);
tgroup2 = uitabgroup('Parent', tab2);
tgroup3 = uitabgroup('Parent', tab3);

tab1a = uitab('Parent', tgroup1, 'Title', 'Citra Asli');
tab1b = uitab('Parent', tgroup1, 'Title', 'Derau Impuls');
tab1c = uitab('Parent', tgroup1, 'Title', 'Derau Uniform');
tab1d = uitab('Parent', tgroup1, 'Title', 'Derau Gaussian');
tab1e = uitab('Parent', tgroup1, 'Title', 'Derau Rayleigh');

tab2a = uitab('Parent', tgroup2, 'Title', 'Derau Impuls');
tab2b = uitab('Parent', tgroup2, 'Title', 'Derau Uniform');
tab2c = uitab('Parent', tgroup2, 'Title', 'Derau Gaussian');
tab2d = uitab('Parent', tgroup2, 'Title', 'Derau Rayleigh');

tab3a = uitab('Parent', tgroup3, 'Title', 'BandStop Ideal');
tab3b = uitab('Parent', tgroup3, 'Title', 'BandStop ButterWorth');
tab3c = uitab('Parent', tgroup3, 'Title', 'BandStop Gauss');

panel1 = uipanel('Parent',tab1a,'Title','Noise Test','FontWeight','bold',...
    'FontSize',10,'Position',[.1 .3 .35 .6]);

panel2 = uipanel('Parent',tab1a,'Title','Histogram','FontWeight','bold',...
    'FontSize',10,'Position',[.55 .3 .35 .6]);

ax1 = axes('Parent',panel1,'Position',[.065 .08 .85 .85],'XTick',[],...
    'YTick',[],'Visible','on');

ax2 = axes('Parent',panel2,'Position',[.14 .1 .8 .8],'XTick',[],...
    'YTick',[],'Visible','on');

I = imread('noisetest.bmp');
axes(ax1)
imshow(I)
axes(ax2)
imhist(I)

panel3 = uipanel('Parent',tab1b,'Title','Noise Test','FontWeight','bold',...
    'FontSize',10,'Position',[.1 .3 .35 .6]);

panel4 = uipanel('Parent',tab1b,'Title','Histogram','FontWeight','bold',...
    'FontSize',10,'Position',[.55 .3 .35 .6]);

ax3 = axes('Parent',panel3,'Position',[.065 .08 .85 .85],'XTick',[],...
    'YTick',[],'Visible','on');

ax4 = axes('Parent',panel4,'Position',[.14 .1 .8 .8],'XTick',[],...
    'YTick',[],'Visible','on');

g1 = imnoise(I,'salt & pepper',0.2);
axes(ax3)
imshow(g1)
axes(ax4)
imhist(g1)

panel5 = uipanel('Parent',tab1c,'Title','Noise Test','FontWeight','bold',...
    'FontSize',10,'Position',[.1 .3 .35 .6]);

panel6 = uipanel('Parent',tab1c,'Title','Histogram','FontWeight','bold',...
    'FontSize',10,'Position',[.55 .3 .35 .6]);

ax5 = axes('Parent',panel5,'Position',[.065 .08 .85 .85],'XTick',[],...
    'YTick',[],'Visible','on');

ax6 = axes('Parent',panel6,'Position',[.14 .1 .8 .8],'XTick',[],...
    'YTick',[],'Visible','on');

g2 = uint8(double(I)+60*rand(256,256));
axes(ax5)
imshow(g2)
axes(ax6)
imhist(g2)

panel7 = uipanel('Parent',tab1d,'Title','Noise Test','FontWeight','bold',...
    'FontSize',10,'Position',[.1 .3 .35 .6]);

panel8 = uipanel('Parent',tab1d,'Title','Histogram','FontWeight','bold',...
    'FontSize',10,'Position',[.55 .3 .35 .6]);

ax7 = axes('Parent',panel7,'Position',[.065 .08 .85 .85],'XTick',[],...
    'YTick',[],'Visible','on');

ax8 = axes('Parent',panel8,'Position',[.14 .1 .8 .8],'XTick',[],...
    'YTick',[],'Visible','on');

g3 = uint8(double(I)+10*randn(256,256));
axes(ax7)
imshow(g3)
axes(ax8)
imhist(g3)

panel9 = uipanel('Parent',tab1e,'Title','Noise Test','FontWeight','bold',...
    'FontSize',10,'Position',[.1 .3 .35 .6]);

panel10 = uipanel('Parent',tab1e,'Title','Histogram','FontWeight','bold',...
    'FontSize',10,'Position',[.55 .3 .35 .6]);

ax9 = axes('Parent',panel9,'Position',[.065 .08 .85 .85],'XTick',[],...
    'YTick',[],'Visible','on');

ax10 = axes('Parent',panel10,'Position',[.14 .1 .8 .8],'XTick',[],...
    'YTick',[],'Visible','on');

g4 = uint8(double(I)+raylrnd(20,256,256));
axes(ax9)
imshow(g4)
axes(ax10)
imhist(g4)

panel11 = uipanel('Parent',tab2a,'Title','Noise Test','FontWeight','bold',...
    'FontSize',10,'Position',[.05 .025 .3 .95]);

panel12 = uipanel('Parent',tab2a,'Title','Hasil Restorasi','FontWeight','bold',...
    'FontSize',10,'Position',[.4 .025 .55 .95]);

ax11 = axes('Parent',panel11,'Position',[.12 .53 .75 .4],'XTick',[],...
    'YTick',[],'Visible','on');

ax12 = axes('Parent',panel11,'Position',[.12 .03 .75 .4],'XTick',[],...
    'YTick',[],'Visible','on');

ax13 = axes('Parent',panel12,'Position',[.06 .53 .4 .4],'XTick',[],...
    'YTick',[],'Visible','on');

ax14 = axes('Parent',panel12,'Position',[.06 .03 .4 .4],'XTick',[],...
    'YTick',[],'Visible','on');

ax15 = axes('Parent',panel12,'Position',[.54 .53 .4 .4],'XTick',[],...
    'YTick',[],'Visible','on');

ax16 = axes('Parent',panel12,'Position',[.54 .03 .4 .4],'XTick',[],...
    'YTick',[],'Visible','on');

axes(ax11)
imshow(I);
title('citra asli');

axes(ax12)
imshow(g1);
title('citra + derau Salt & pepper');

axes(ax13)
j1 = imfilter(g1,ones(3)/9);
imshow(j1);
title('filter rata-rata 3x3');

axes(ax14)
j2 = imfilter(g1,ones(5)/25);
imshow(j2);
title('filter rata-rata 5x5');

axes(ax15)
j3 = medfilt2(g1,[3 3]);
imshow(j3);
title('filter median 3x3');

axes(ax16)
j4 = medfilt2(g1,[5 5]);
imshow(j4);
title('filter median 5x5');

panel13 = uipanel('Parent',tab2b,'Title','Noise Test','FontWeight','bold',...
    'FontSize',10,'Position',[.05 .025 .3 .95]);

panel14 = uipanel('Parent',tab2b,'Title','Hasil Restorasi','FontWeight','bold',...
    'FontSize',10,'Position',[.4 .025 .55 .95]);

ax17 = axes('Parent',panel13,'Position',[.12 .53 .75 .4],'XTick',[],...
    'YTick',[],'Visible','on');

ax18 = axes('Parent',panel13,'Position',[.12 .03 .75 .4],'XTick',[],...
    'YTick',[],'Visible','on');

ax19 = axes('Parent',panel14,'Position',[.06 .53 .4 .4],'XTick',[],...
    'YTick',[],'Visible','on');

ax20 = axes('Parent',panel14,'Position',[.06 .03 .4 .4],'XTick',[],...
    'YTick',[],'Visible','on');

ax21 = axes('Parent',panel14,'Position',[.54 .53 .4 .4],'XTick',[],...
    'YTick',[],'Visible','on');

ax22 = axes('Parent',panel14,'Position',[.54 .03 .4 .4],'XTick',[],...
    'YTick',[],'Visible','on');

axes(ax17)
imshow(I);
title('citra asli');

axes(ax18)
imshow(g2);
title('citra + derau Uniform');

axes(ax19)
j1 = imfilter(g2,ones(3)/9);
imshow(j1);
title('filter rata-rata 3x3');

axes(ax20)
j2 = imfilter(g2,ones(5)/25);
imshow(j2);
title('filter rata-rata 5x5');

axes(ax21)
j3 = medfilt2(g2,[3 3]);
imshow(j3);
title('filter median 3x3');

axes(ax22)
j4 = medfilt2(g2,[5 5]);
imshow(j4);
title('filter median 5x5');

panel15 = uipanel('Parent',tab2c,'Title','Noise Test','FontWeight','bold',...
    'FontSize',10,'Position',[.05 .025 .3 .95]);

panel16 = uipanel('Parent',tab2c,'Title','Hasil Restorasi','FontWeight','bold',...
    'FontSize',10,'Position',[.4 .025 .55 .95]);

ax23 = axes('Parent',panel15,'Position',[.12 .53 .75 .4],'XTick',[],...
    'YTick',[],'Visible','on');

ax24 = axes('Parent',panel15,'Position',[.12 .03 .75 .4],'XTick',[],...
    'YTick',[],'Visible','on');

ax25 = axes('Parent',panel16,'Position',[.06 .53 .4 .4],'XTick',[],...
    'YTick',[],'Visible','on');

ax26 = axes('Parent',panel16,'Position',[.06 .03 .4 .4],'XTick',[],...
    'YTick',[],'Visible','on');

ax27 = axes('Parent',panel16,'Position',[.54 .53 .4 .4],'XTick',[],...
    'YTick',[],'Visible','on');

ax28 = axes('Parent',panel16,'Position',[.54 .03 .4 .4],'XTick',[],...
    'YTick',[],'Visible','on');

axes(ax23)
imshow(I);
title('citra asli');

axes(ax24)
imshow(g3);
title('citra + derau Gaussian');

axes(ax25)
j1 = imfilter(g3,ones(3)/9);
imshow(j1);
title('filter rata-rata 3x3');

axes(ax26)
j2 = imfilter(g3,ones(5)/25);
imshow(j2);
title('filter rata-rata 5x5');

axes(ax27)
j3 = medfilt2(g3,[3 3]);
imshow(j3);
title('filter median 3x3');

axes(ax28)
j4 = medfilt2(g3,[5 5]);
imshow(j4);
title('filter median 5x5');

panel17 = uipanel('Parent',tab2d,'Title','Noise Test','FontWeight','bold',...
    'FontSize',10,'Position',[.05 .025 .3 .95]);

panel18 = uipanel('Parent',tab2d,'Title','Hasil Restorasi','FontWeight','bold',...
    'FontSize',10,'Position',[.4 .025 .55 .95]);

ax29 = axes('Parent',panel17,'Position',[.12 .53 .75 .4],'XTick',[],...
    'YTick',[],'Visible','on');

ax30 = axes('Parent',panel17,'Position',[.12 .03 .75 .4],'XTick',[],...
    'YTick',[],'Visible','on');

ax31 = axes('Parent',panel18,'Position',[.06 .53 .4 .4],'XTick',[],...
    'YTick',[],'Visible','on');

ax32 = axes('Parent',panel18,'Position',[.06 .03 .4 .4],'XTick',[],...
    'YTick',[],'Visible','on');

ax33 = axes('Parent',panel18,'Position',[.54 .53 .4 .4],'XTick',[],...
    'YTick',[],'Visible','on');

ax34 = axes('Parent',panel18,'Position',[.54 .03 .4 .4],'XTick',[],...
    'YTick',[],'Visible','on');

axes(ax29)
imshow(I);
title('citra asli');

axes(ax30)
imshow(g4);
title('citra + derau Rayleigh');

axes(ax31)
j1 = imfilter(g4,ones(3)/9);
imshow(j1);
title('filter rata-rata 3x3');

axes(ax32)
j2 = imfilter(g4,ones(5)/25);
imshow(j2);
title('filter rata-rata 5x5');

axes(ax33)
j3 = medfilt2(g4,[3 3]);
imshow(j3);
title('filter median 3x3');

axes(ax34)
j4 = medfilt2(g4,[5 5]);
imshow(j4);
title('filter median 5x5');

%%%%
ax35 = axes('Parent',tab3a,'Position',[.165 .55 .22 .38],'XTick',[],...
    'YTick',[],'Visible','on');

ax36 = axes('Parent',tab3a,'Position',[.55 .55 .32 .38],'XTick',[],...
    'YTick',[],'Visible','on');

ax37 = axes('Parent',tab3a,'Position',[.16 .06 .32 .38],'XTick',[],...
    'YTick',[],'Visible','on');

ax38 = axes('Parent',tab3a,'Position',[.55 .06 .22 .38],'XTick',[],...
    'YTick',[],'Visible','on');

g=imread('cameramannoise.tif');
axes(ax35)
imshow(g);
title('citra + derau periodik');

G=fftshift(fft2(double(g)));
axes(ax36)
imagesc(abs(sqrt(G+eps)));
axis image,colormap(ax36,jet),colorbar,title('fft (citra + derau periodik)');
r=meshgrid(-128:127,-128:127);
r=sqrt(r.^2+r'.^2);
W=15;D=65;
Hideal=abs(r-D)>W/2;
Hbuttw=1./(1+((r*W)./(r.^2-D.^2+eps)).^(2*1));
Hgauss=1-exp(-0.5*abs(r.^2-D.^2)./(r*W+eps));
J1=G.*Hideal;j1=uint8(real(ifft2(fftshift(J1))));
J2=G.*Hbuttw;j2=uint8(real(ifft2(fftshift(J2))));
J3=G.*Hgauss;j3=uint8(real(ifft2(fftshift(J3))));
axes(ax37)
imagesc(abs(sqrt(J1)));
axis image,colormap(ax37,jet),colorbar,title('hasil restorasi (domain frekuensi)');
axes(ax38)
imshow(j1);
title('hasil restorasi (domain spasial)');

ax39 = axes('Parent',tab3b,'Position',[.165 .55 .22 .38],'XTick',[],...
    'YTick',[],'Visible','on');

ax40 = axes('Parent',tab3b,'Position',[.55 .55 .32 .38],'XTick',[],...
    'YTick',[],'Visible','on');

ax41 = axes('Parent',tab3b,'Position',[.16 .06 .32 .38],'XTick',[],...
    'YTick',[],'Visible','on');

ax42 = axes('Parent',tab3b,'Position',[.55 .06 .22 .38],'XTick',[],...
    'YTick',[],'Visible','on');

axes(ax39)
imshow(g);
title('citra + derau periodik');

axes(ax40)
imagesc(abs(sqrt(G+eps)));
axis image,colormap(ax40,jet),colorbar,title('fft (citra + derau periodik)');

axes(ax41)
imagesc(abs(sqrt(J2)));
axis image,colormap(ax41,jet),colorbar,title('hasil restorasi (domain frekuensi)');

axes(ax42)
imshow(j2);
title('hasil restorasi (domain spasial)');

ax43 = axes('Parent',tab3c,'Position',[.165 .55 .22 .38],'XTick',[],...
    'YTick',[],'Visible','on');

ax44 = axes('Parent',tab3c,'Position',[.55 .55 .32 .38],'XTick',[],...
    'YTick',[],'Visible','on');

ax45 = axes('Parent',tab3c,'Position',[.16 .06 .32 .38],'XTick',[],...
    'YTick',[],'Visible','on');

ax46 = axes('Parent',tab3c,'Position',[.55 .06 .22 .38],'XTick',[],...
    'YTick',[],'Visible','on');

axes(ax43)
imshow(g);
title('citra + derau periodik');

axes(ax44)
imagesc(abs(sqrt(G+eps)));
axis image,colormap(ax44,jet),colorbar,title('fft (citra + derau periodik)');

axes(ax45)
imagesc(abs(sqrt(J3)));
axis image,colormap(ax45,jet),colorbar,title('hasil restorasi (domain frekuensi)');

axes(ax46)
imshow(j3);
title('hasil restorasi (domain spasial)');

panel15 = uipanel('Parent',tab4,'Title','Citra Asli','FontWeight','bold',...
    'FontSize',10,'Position',[.02 .25 .3 .5]);

panel16 = uipanel('Parent',tab4,'Title','Citra Terdistorsi','FontWeight','bold',...
    'FontSize',10,'Position',[.35 .25 .3 .5]);

panel17 = uipanel('Parent',tab4,'Title','Hasil Restorasi','FontWeight','bold',...
    'FontSize',10,'Position',[.68 .25 .3 .5]);

ax47 = axes('Parent',panel15,'Position',[.07 .08 .85 .85],'XTick',[],...
    'YTick',[],'Visible','on');

ax48 = axes('Parent',panel16,'Position',[.07 .08 .85 .85],'XTick',[],...
    'YTick',[],'Visible','on');

ax49 = axes('Parent',panel17,'Position',[.07 .08 .85 .85],'XTick',[],...
    'YTick',[],'Visible','on');

f = double(imread('bicycle.tif'));
axes(ax47)
imagesc(uint8(f));
axis off,colormap gray;

h = fspecial('motion',10,150);
g = imfilter(f,h,'circular','conv');
axes(ax48)
imagesc(uint8(g));
axis off,colormap gray;

G = fft2(g,256,256);
H = fft2(h,256,256);
J = G./H;
epsilon = 1e-6; J(abs(H)<epsilon)=0;
j = real(ifft2(J));
j = circshift(j,[floor(size(h,1)/2) floor(size(h,2)/2)]);
axes(ax49)
imagesc(uint8(j));
axis off,colormap gray;

ax50 = axes('Parent',tab5,'Position',[.18 .55 .25 .38],'XTick',[],...
    'YTick',[],'Visible','on');

ax51 = axes('Parent',tab5,'Position',[.55 .55 .25 .38],'XTick',[],...
    'YTick',[],'Visible','on');

ax52 = axes('Parent',tab5,'Position',[.18 .06 .25 .38],'XTick',[],...
    'YTick',[],'Visible','on');

ax53 = axes('Parent',tab5,'Position',[.55 .06 .25 .38],'XTick',[],...
    'YTick',[],'Visible','on');

f = double(imread('bicycle.tif'));
axes(ax50)
imagesc(uint8(f));
axis off,colormap gray,title('citra asli');

h = fspecial('motion',10,150);
g = imfilter(f,h,'circular','conv');
g = g + 0.1*randn(size(g));
axes(ax51)
imagesc(uint8(g));
axis off,colormap gray,title('citra terdistorsi + derau');

G = fft2(g,256,256);
H = fft2(h,256,256);
J = G./H;
epsilon = 1e-6; J(abs(H)<epsilon)=0;
j = real(ifft2(J));
j = circshift(j,[floor(size(h,1)/2) floor(size(h,2)/2)]);
axes(ax52)
imagesc(uint8(j));
axis off,colormap gray,title('citra restorasi inverse filter');

gamma = 1e-3;
K = (G./H).*(abs(H).^2./(abs(H).^2+gamma));
k = real(ifft2(K));
k = circshift(k,[floor(size(h,1)/2) floor(size(h,2)/2)]);
axes(ax53)
imagesc(uint8(k));
axis off,colormap gray,title('citra restorasi pseudo-inverse');

ax54 = axes('Parent',tab6,'Position',[.18 .55 .25 .38],'XTick',[],...
    'YTick',[],'Visible','on');

ax55 = axes('Parent',tab6,'Position',[.55 .55 .25 .38],'XTick',[],...
    'YTick',[],'Visible','on');

ax56 = axes('Parent',tab6,'Position',[.18 .06 .25 .38],'XTick',[],...
    'YTick',[],'Visible','on');

ax57 = axes('Parent',tab6,'Position',[.55 .06 .25 .38],'XTick',[],...
    'YTick',[],'Visible','on');

I = im2double(imread('cameraman.tif'));
axes(ax54)
imagesc(I), axis off;
title('Original Image')

LEN = 21;
THETA = 11;
PSF = fspecial('motion', LEN, THETA);
blurred = imfilter(I, PSF, 'conv', 'circular');
noise_mean = 0;
noise_var = 0.0001;
blurred_noisy = imnoise(blurred, 'gaussian',noise_mean, noise_var);
axes(ax55)
imagesc(blurred_noisy), axis off;
title('Simulate Blur and Noise')

estimated_nsr = 0;
wnr2 = deconvwnr(blurred_noisy, PSF, estimated_nsr);
axes(ax56)
imagesc(wnr2), axis off;
title('Restoration Using NSR = 0')

estimated_nsr = noise_var / var(I(:));
wnr3 = deconvwnr(blurred_noisy, PSF, estimated_nsr);
axes(ax57)
imagesc(wnr3), axis off;
title('Restoration Using Estimated NSR');

File source code lengkap beserta citra pendukung pada materi di atas dapat diperoleh melalui halaman berikut ini: Source Code

Referensi:
A.B. Suksmono, Materi kuliah Pengolahan Citra dan Pengenalan Pola: Pemulihan Citra.
A.K. Jain, Fundamentals of Digital Image Processing, Prentice-Hall International.

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