The Complex Gaussian Scale Mixtures Of Complex Wavelet Coefficients And Applications
In this thesis, the complex Gaussian scale mixture (CGSM), which is an extension of the Gaussian scale mixture (GSM) for real-valued random variables to the complex case, is presented to model the complex wavelet coefficients. Along with some related propositions and miscellaneous results, the probability density functions (pdf) of the magnitude and phase of the complex random variable are presented. Specifically, the closed forms of the magnitude pdf for the case of complex generalized Gaussian distribution (CGGD) and the phase pdf for the general case are presented. Subsequently, the pdf of the relative phase is derived.Moreover, parameter estimation methods in the presence of noise for several magnitude pdf's which are special cases of the magnitude pdf related to the CGSM, and for the relative phase pdf (RP pdf) are proposed. In addition, the parameter estimation of the RP pdf is investigated, and a non-iterative estimator for the relative phase pdf's parameters is also proposed.To show the usefulness of the proposed model, the CGSM is then applied to image denoising using Bayes least square estimator. The experimental results show that using the CGSM of complex wavelet coefficients visually improves the quality of denoised images from the real case. Moreover, the derived magnitude pdf of the CGGD is then utilized in texture image retrieval that uses complex coefficient magnitude to improve the accuracy rate from using the real or imaginary parts. Finally, the problem of noisy texture retrieval, where the query image is contaminated by noise, is studied. This texture retrieval scheme is based on the proposed parameter estimation methods in the presence of noise. The retrieval results show that using both magnitude and phase information of complex coefficients improves the accuracy rate from solely using the magnitude or phase information, and also from using the real or the imaginary parts. These simulation results are also consistent in several complex transform domains.