Additive White Gaussian Noise (AWGN) and Undecimated DWT
One property of Orthogonal Transformations is that White Noise stays White (Uncorrelated) under Orthogonal Transformations (One could say it's a property of White Noise).  

Usually this property assist with deriving properties of operators (Things are simpler).  

Yet this property doesn't not hold for Transformations in general which might "Color" the noise in the new base.