An estimation method for the relative phase parameters of complex wavelet coefficients in noise

This paper proposes a method to estimate the parameters of the relative phase probability density function (RP pdf) of the complex coefficients when the image is corrupted by additive white Gaussian noise. With the complex Gaussian scale mixture (CGSM) assumption of the clean coefficients, we first introduce the relative phase mixture pdf (RPM pdf) by deriving the pdf of the relative phase of the noisy coefficients. Along with the derived pdf, the estimation method based on the maximum likelihood approach is proposed by exploiting the relationships between the RP pdf´s parameters and the complex covariance matrix of the corresponding complex coefficient vector. The experiments using the simulated data and the data extracted from the real images are performed to show the effectiveness of the estimation method. The results show that the proposed method can well estimate the RP pdf´s parameters of the clean vector in the case of simulated data and fit well with the histogram of phase samples extracted from the real images.