function u_kp1 = debruitage(b, u_k, lambda, Dx, Dy, epsilon)

    N = length(b);

%     coeffs = 1 ./ sqrt( gradient(u_k).^2 + epsilon );
    coeffs = 1 ./ sqrt( (Dx * u_k).^2 + (Dy * u_k).^2 + epsilon );

    W = spdiags(coeffs, 0, N, N);

    A = speye(N) + lambda * (Dx' * W * Dx + Dy' * W * Dy);

    u_kp1 = A \ b;

end