MATLAB: Can anyone tell what windowfilt and “w” is doing in this program

dtdwtw

 function y = dtdwt(x)
 windowsize  = 7;
 windowfilt = ones(1,windowsize)/windowsize;
 % Number of Stages
 J = 6;
 I=sqrt(-1);
 L = length(x); 
 N = L+2^J;     
 x = symextend(x,2^(J-1));
 load nor_dualtree 
 [Faf, Fsf] = AntonB;
 [af, sf] = dualfilt1;
 W = dual2D(x, J, Faf, af);
 W = normcoef(W,J,nor);
 % Noise variance estimation using robust median estimator..
 tmp = W{1}{1}{1}{1};
 Nsig = median(abs(tmp(:)))/0.6745;
 for scale = 1:J-1
    for dir = 1:2
        for dir1 = 1:3
            Y_coef_real = W{scale}{1}{dir}{dir1};
            Y_coef_imag = W{scale}{2}{dir}{dir1};
            Y_parent_real = W{scale+1}{1}{dir}{dir1};
            Y_parent_imag = W{scale+1}{2}{dir}{dir1};
            Y_parent_real  = expand(Y_parent_real);
            Y_parent_imag   = expand(Y_parent_imag);
            Wsig = conv2(windowfilt,windowfilt,(Y_coef_real).^2,'same');
            Ssig = sqrt(max(Wsig-Nsig.^2,eps));
           % Threshold value estimation
            T = sqrt(3)*Nsig^2./Ssig;
            % Bivariate Shrinkage
            Y_coef = Y_coef_real+I*Y_coef_imag;
            Y_parent = Y_parent_real + I*Y_parent_imag;
            Y_coef = bishrink(Y_coef,Y_parent,T);
            W{scale}{1}{dir}{dir1} = real(Y_coef);
            W{scale}{2}{dir}{dir1} = imag(Y_coef);
        end
    end
end
 % Inverse Transform
 W = unnormcoef(W,J,nor);
 y = idual2D(W, J, Fsf, sf);
% Extract the image ind = 2^(J-1)+1:2^(J-1)+L; y = y(ind,ind);

Best Answer

windowfilt is a lowpass filter that is being used a separable 2D filter here:
 Wsig = conv2(windowfilt,windowfilt,(Y_coef_real).^2,'same');
The above line basically says filters the columns of (Y_coef_real).^2 with windowfilt, and then filter the rows of (Y_coef_real).^2 with windowfilt.
I don't see the variable, w, I see W (upper case). Be careful, MATLAB is case-sensitive. W is the dual-tree wavelet transform of the input image down to level J=6
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