Research On Image Processing Based On The Dual Tree Complex Wavelet Transform

In the 1980s, wavelets have been found applications in image processing due to the time-frequency localization and multiscale decomposition property. In recent years, with the development of the wavelet theory, discrete wavelet transform (DWT) has been widely used in image denoising. Although DWT is a powerful signal-processing tool, it has two disadvantages that undermine its usage in many applications. First, DWT is shift sensitive because input-signal shifts generate unpredictable changes in DWT coefficients. Second, the DWT suffers from poor directionality because discrete wavelet transform coefficients reveal only three spatial orientations.In order to overcome the shortcoming of the commonly-used denoisng methods, the image denoising method based on dual tree complex wavelet transform (DT-CWT) is proposed. Dual tree complex wavelet transform and its application in image processing are investigated in detail in this dissertation. The main work can be summarized as follows:(1) Many literatures of wavelet denoising methods have been studied, on which dual tree complex wavelet denoising method is proposed.(2) The basic principles and characteristics of dual tree complex wavelet transform are discussed. The dual tree complex wavelet transform has the properties of approximate shift invariance, good directional selectivity and perfect reconstruction. It has six subbands corresponding to six spatial orientations: +15°, +45°, +75°, - 75°,- 45°, - 15°. The image denoising method is proposed based on dual tree complex wavelet transform, which can do better both in features preserving and noise removing.(3) The image denoising method is proposed based on dual tree complex wavelet transform and Bayesian estimation. Compared with the traditional discrete wavelet transform, the dual tree complex wavelet transform has the properties of approximate shift invariance and more directionality. These properties are good for tracing, locating and preserving image features. Combined with statistical based Bayesian estimation and adaptive distribution parameter estimation, an effective denoising algorithm is gained. The experiment results show the method not only removes most noises but also preserves features better.(4) We have proposed a simple non-Gaussian bivariate probability distribution functions to model the statistics of wavelet coefficients of natural images. The model captures the dependence between a wavelet coefficient and its parents. The shrinkage function, which depends on both the coefficient and its parent, yields improved results for wavelet-based image denoising. The theoretical analysis and experimental results presented in this paper show that, compared with the commonly-used wavelet threshold denoising methods, our denoising method can improve the denoising results.