Statistical image modeling with the magnitude probability density function of complex wavelet coefficients

We derive the probability density function (pdf) of the magnitude of complex wavelet coefficients with the assumption that each of the real and imaginary parts is characterized by the generalized Gaussian distribution (GGD) model. The parameter estimation method using maximum likelihood for the derived pdf is presented. The derived pdf fits acceptably well with the actual coefficient magnitude of images. To show the usefulness of the derived pdf, we use it to model the magnitude of complex coefficients of texture images for an application in texture image retrieval. The experimental results show that using the derived magnitude pdf yields higher retrieval rate than using the GGD model to fit with the real part or imaginary part of coefficients, and than using the mean and standard deviation of the magnitude of coefficients.