Estimating 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 an 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 (RPM) pdf by deriving the pdf of the relative phase of the noisy coefficients. Along with the derived pdf, a parameter estimation method based on the maximum likelihood approach is proposed by exploiting the relationships between the pdf's parameters and the complex covariance matrix of the corresponding complex coefficient vector. Simulation studies using simulated data are performed to show the effectiveness of the estimation method. Moreover, we use the proposed estimation method in the application of texture retrieval in a noisy environment. The results show that the proposed method can estimate the parameters of the clean vector well in the case of simulated data and that the proposed estimation method improves the retrieval accuracy rate.