what is the function of W, Nsig and Ssig in this program?

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

Especially i want to know about W,AntonB,nor dualtree, eps, Nsig, Ssig

Answer 1

[Walter Roberson]

max(Wsig-Nsig.^2,eps)

is the same as

temp = Wsig-Nsig.^2;
temp(temp < eps) = eps;

and then using temp as the value.

Why one would want to do that? Well, it avoids division by 0.

Answer 2

[Wayne King]

W is simply the dual-tree wavelet transform.

Nsig is the "universal threshold" for wavelet denoising based on the level-1 detail coefficients.