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+//Ex5_11
+//Inverse Filtering
+// Version : Scilab 5.4.1
+// Operating System : Window-xp, Window-7
+//Toolbox: Image Processing Design 8.3.1-1
+//Toolbox: SIVP 0.5.3.1-2
+//Reference book name : Digital Image Processing
+//book author: Rafael C. Gonzalez and Richard E. Woods
+
+clc;
+close;
+clear;
+xdel(winsid())//to close all currently open figure(s).
+
+function[H,H1]=lowpassfilter(type1,M,N,D0,n,k)//lowpassfilter is used to filter an image .
+    u=0:(M-1);
+    v=0:(N-1);
+    idx=find(u>M/2);
+    u(idx)=u(idx)-M;
+    idy=find(v>N/2);
+    v(idy)=v(idy)-N;
+    [U,V]=meshgrid(v,u);
+    D=sqrt(U.^2+V.^2); //Distance Calculation
+    D=fftshift(D);
+    for i=1:M
+        for j=1:N
+            H(i,j)=exp(-k.*((i-(M/2))^2+(j-(N/2))^2).^(5/6)); //Atmospheric Degradation Function
+        end
+    end
+    
+    select type1
+        
+    case'inverse'then
+        if argn(2)==4 then
+            n=1;k=0.0025;
+        end
+        H=H;
+        H1=H;
+        
+    case'butterworth'then
+        if argn(2)==4 then
+            n=1;
+        end
+//        H1 = (ones(M,N)./(1+(D./D0).^(2*n)));
+        H1=double(D<=D0);
+        H=H.*H1;        
+       
+       else
+        disp('Unknownfiltertype.')
+    end
+endfunction
+
+///////////////////////////////////   Main Programm   ////////////////////////////////
+gray=imread('Ex5_11.png');
+gray=im2double(rgb2gray(gray));
+figure,ShowImage(gray,'Gray Image');
+title('Original Image','color','blue','fontsize',4);
+[M,N]=size(gray);
+
+h=fft2(gray);//fft2() is used to find 2-Dimensional Fast Fourier Transform of an matrix
+in=fftshift(h);//fftshift() is used to rearrange the fft output, moving the zero frequency to the center of the spectrum.
+i=log(1+abs(in));
+
+inm=mat2gray(i)
+
+////////////////////////// Filtering With Cut-off Frequency 480   ///////////////////////
+[filt,H1]=lowpassfilter('inverse',M,N,480,1,0.0025); // Function which generate Filter Mask Corresponding to Low Frequency
+//filt_shift=fftshift(filt);
+//figure,ShowImage(abs(filt),'Filter Mask');
+//title('Filter Mask to Specific Cut-Off Frequency');
+n=in./(filt+%eps);//Multiply the Original Spectrum with the Filter Mask.
+Image_filter=abs(ifft(fftshift(n)));
+Image_filter=mat2gray(Image_filter)
+figure,ShowImage(Image_filter,'Filtered Image');
+title('Filtered Image with Full Inverse Filter','color','blue','fontsize',4);
+
+////////////////////////// Filtering With Cut-off Frequency 40   ///////////////////////
+[filt,H1]=lowpassfilter('butterworth',M,N,40,10,0.0025); // Function which generate Filter Mask Corresponding to Low Frequency
+//filt_shift=fftshift(filt);
+//figure,ShowImage(abs(filt),'Filter Mask');
+//title('Filter Mask to Specific Cut-Off Frequency');
+n=(in.*H1)./(filt+%eps);//Multiply the Original Spectrum with the Filter Mask.
+Image_filter=abs(ifft(fftshift(n)));
+Image_filter=mat2gray(Image_filter)
+figure,ShowImage(Image_filter,'Filtered Image');
+title('Filtered Image with Cut-Off Frequency 40','color','blue','fontsize',4);
+
+////////////////////////// Filtering With Cut-off Frequency 70   ///////////////////////
+[filt,H1]=lowpassfilter('butterworth',M,N,70,10,0.0025); // Function which generate Filter Mask Corresponding to Low Frequency
+//filt_shift=fftshift(filt);
+//figure,ShowImage(abs(filt),'Filter Mask');
+//title('Filter Mask to Specific Cut-Off Frequency');
+n=(in.*H1)./(filt+%eps);//Multiply the Original Spectrum with the Filter Mask.
+Image_filter=abs(ifft(fftshift(n)));
+Image_filter=mat2gray(Image_filter)
+figure,ShowImage(Image_filter,'Filtered Image');
+title('Filtered Image with Cut-Off Frequency 70','color','blue','fontsize',4);
+
+////////////////////////// Filtering With Cut-off Frequency 100   ///////////////////////
+[filt,H1]=lowpassfilter('butterworth',M,N,100,10,0.0025); // Function which generate Filter Mask Corresponding to Low Frequency
+//filt_shift=fftshift(filt);
+//figure,ShowImage(abs(filt),'Filter Mask');
+//title('Filter Mask to Specific Cut-Off Frequency');
+n=(in.*H1)./(filt+%eps);//Multiply the Original Spectrum with the Filter Mask.
+Image_filter=abs(ifft(fftshift(n)));
+Image_filter=mat2gray(Image_filter)
+figure,ShowImage(Image_filter,'Filtered Image');
+title('Filtered Image with Cut-Off Frequency 100','color','blue','fontsize',4);
+