Image Deblurring using Conjugate Gradient Method

Question

I am working on debluring and image using the conjugate gradient method and I can seem to make any progress.  I get a big issue that I have is that I end up attempting to divide scalar my matrices based on the formulas that I have.  If anyone could have a look and lend a hand that'd be great.  Or if anyone is aware of a sample of this online that I could take a look at?

  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  % INPUT u0 = noisy image 
  % OUTPUT: I(i,j) = denoised image 
  
  % read the noisy data I0 in .jpg format
  
  Io=imread('figure.jpg'); %opens image and assigns variable Io
  Io=double(Io); %returns double precision value for u0
  I=Io; %sets u to equal u0 so that u will give a new figure after H1 regularization
  [M,N]=size(I); %sets size to equal I
  imagesc(Io); axis image; axis off; colormap(gray);
  
  %         PARAMETERS  %
  %-----------------------------------------------
  
  % coefficient of the H1 norm (needs to be adapted for each image) 
  lambda=0.028; 
  
  %  space discretization 
  h=1.;
  
  %  number of iterations (depends on the image) 
  IterMax=100;
  
  %  needed to regularize at the origin 
  eps=0.000001;
  
  %-----------------------------------------------------------
  %---------------------------------------------------------------------------
  
  b = lambda*Io;
  
  %%    Step 1: 
  %-----------------------------------------------------------
   %%initial guess
   
  for i = 1:length(M)
   for i=2:M-1,
        for j=2:N-1, 
  
        r(i,j) =  - (I(i,j+1)-2*I(i,j)+I(i,j-1)-(I(i+1,j)-2*I(i,j)+I(i-1,j))); 
        ep = ones(253,252)*eps;
        
        end
   end
   end
      %%   Step 2:
      
         mu = norm(r)*norm(r); %step two
         r = ep + r;
         p = r;
    
  %%      Step 3:
  %-----------------------------------------------------------
  %for Iter=1:IterMax, %1 to 100 for loop
  
  	%Iter     
  
  
  for Iter=1:IterMax, %1 to 100 for loop
  
  	Iter
      
      for i=2:M-1
        for j=2:N-1 
            
       q(i,j) = lambda*I(i,j) -(I(i,j+1)-2*I(i,j)+I(i,j-1))-(I(i+1,j)-2*I(i,j)+I(i-1,j));
       q(i,j) = q(i,j) + eps;
       p(i,j) = p(i,j) + eps;
        end
      end
      
     for i=2:M-1
        for j=2:N-1
            
       alpha =mu./(p(i,j)'*q(i,j)); %(3) alpha = mu/(p*q)        
       I(i,j) = I(i,j) + alpha * p(i,j); %
       r(i,j) = r(i,j) - alpha * q(i,j);
       mu_pre = mu;
       mu = norm(r)*norm(r);
       p(i,j) = r(i,j) + mu/mu_pre*p(i,j);
       I(i,j) = I(i,j)-alpha*p(i,j);    
           
        end
     end
  
  %end
  %end
  
  figure 
  imagesc(I); axis image; axis off; colormap(gray);
  
  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Image Deblurring using Conjugate Gradient Method

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Image Deblurring using Conjugate Gradient Method

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