On the probability density function of the derotated phase of complex wavelet coefficients

The derotated phase of a complex wavelet coefficient is defined as the phase of that coefficient minus twice of the phase of its parent coefficient. It was recently introduced and found to be useful in terms of providing more correlation among coefficients near singularities in scale and space. In this paper, we investigate the derotated phase of a complex wavelet coefficient by deriving its probability density function (pdf). We show that the derotated phase can be well approximated by a Gaussian random variable for moderate signal to noise ratio. The simulation results are shown to confirm the consistency between the derived pdf and the derotated phase of the actual coefficients.