A second order statistical analysis of the 2D Discrete Wavelet Transform

We present a general second order statistical analysis of the 2D Discrete Wavelet Transform (DWT) resulted after the computation of the correlation functions in all possible cases: inter-scale and inter-band dependency, inter-scale and intra-band dependency and intra-scale and intra-band dependency. The expected value and the variance of the wavelet coefficients are also computed. The resulting equations are useful for the design of different signal processing systems based on the wavelet theory.