clear;
% This code illustrates possible blurring and deblurring in 2D.
% It is motivated by heat diffusion in 2D.
% Blurring is modeled by diffusion of heat in positive time steps.
% Deblurring is done by diffusion of "heat" in negative time steps.
ncsu = [lettern(5) letterc(7) letters(9) letteru(11)];
u = ncsu;
newu = u;
[nx ny] = size(ncsu)
dt = .00006;
dx = 1/(nx-1); 
dy = 3.2/(ny-1);
subplot(1,2,1)      % Forward in "time" or "blurring"
mesh(u)
axis([0 ny 0 nx 0 15]);
%hold on  
for k = 1:20
    for j = 2:ny-1
        for i = 2:nx-1
            newu(i,j) = u(i,j) + (dt/(dx*dx))*(u(i-1,j) -2*u(i,j) + u(i+1,j))...
                               + (dt/(dy*dy))*(u(i,j-1) -2*u(i,j) + u(i,j+1));
        end                  
    end
    mesh(newu);
    axis([0 ny 0 nx 0 15]);
    k
    pause;
    u = newu;
end
blurncsu = 20*u;
blurncsu = blurncsu(nx:-1:1,:);
blurncsu1 = uint8(blurncsu);
imwrite(blurncsu1, 'blurncsu.jpg');

subplot(1,2,2)      % Backward in "time" or "deblurring"
mesh(u')
axis([0 ny 0 nx 0 15]);
%hold on
for k = 1:20
    for j = 2:ny-1
        for i = 2:nx-1
            newu(i,j) = u(i,j) - (dt/(dx*dx))*(u(i-1,j) -2*u(i,j) + u(i+1,j))...
                               - (dt/(dy*dy))*(u(i,j-1) -2*u(i,j) + u(i,j+1));
        end                  
    end
    mesh(newu);
    axis([0 ny 0 nx 0 15]);
    k
    pause;
    u = newu;
end
deblurncsu = 20*u;
deblurncsu = deblurncsu(nx:-1:1,:);
deblurncsu1 = uint8(deblurncsu);
imwrite(deblurncsu1, 'deblurncsu.jpg');