function u_kp1 = inpainting(u0, u_k, u_d, lambda, Dx, Dy, epsilon)

    N = length(u0);
    u_kp1 = zeros(size(u_k));

    for i=1:size(u0, 3)

        coeffs = 1 ./ sqrt( (Dx * u_k(:,:,i)).^2 + (Dy * u_k(:,:,i)).^2 + epsilon );    
        
        W = spdiags(coeffs, 0, N, N);
        W_od = spdiags(1 - u_d, 0, N, N);

        A = W_od + lambda * (Dx' * W * Dx + Dy' * W * Dy);
        b = W_od * u0(:,:,i);

        u_kp1(:,:,i) = A \ b;

    end

end