Research On Image Processing In Thequaternion Wavelet Domain With Applications

Quaternion wavelet transform(QWT) is a novel image analysis tool, which originates from the combination of the wavelet transform and quaternion algebra. The magnitude coefficients are nearly shift-invariant. When the 2D analytic signal is defined in the QWT domain, the advantage is that three local phases produce more texture information compared with that defined in the complex wavelet domain. However, there are several problems for the exisiting researches on QWT. First, the understanding about the physical meanings for QWT coefficients is limited- two phases are related to the local shift, and another is relevant to texture. Second, the number of literatures on the QWT coefficients modeling are not enough. Espetially, the phases application needs to be enhanced. To break through the abovementioned limits, the thesis focuses on delineating the QWT magnitude-phases model, moreover, builds the relationship between the phases model and image sharpness with applications to image denoising and image fusion.The thesis firstly researches on the basic concept for QWT-based analytic signal, and analyzes properties need to be satisfied by the 2D analytic signal extended from the 1D form. Based on the quaternionic analytic signal, the dual-tree QWT is constructed, and coefficients characteristics are concerned. To break through the understanding limit on the QWT coefficients and enrich the application scope, according to the coefficients distribution, Gaussian mixture model is exploited to model phases coefficients, and image sharpness metrics are proposed which provide the robust image quality evaluation under the noisy condition. Next, the research on the local smooth regions detection from a single image is done to estimate the image noise level.The thesis makes use of magnitude coefficients model to design the denoising threshold. First, introduce the wavelet threholding methods into the QWT domain. Wavelet basis is the best basis for image compression, noise reduction and statistical estimation. Wavelet thresholding is better than traditional signal recovery and estimation. But wavelet coefficients is not shift-invariant, which brings in the ring effect by wavelet thresholding, so the visual perception of the denoisd image is worse. When the threshold is fixed, QWT based denoising performance is better. Then analyze the imaging features for the noisy image, phase information is hardly affected by the noise. Based on the Rayleigh modeling for the magnitude coefficients, phase preserving based denoising method is proposed. Noise level estimation in wavelet domain is instable, to solve this problem, the noise level estimation method in the QWT domain is proposed and enhances the Bayesian thresholding performance.Existing multifocus image fusion methods show great focus detection errors, and the boundary blur along the focus regions. On account of the proposed local sharpness metric, the thesis proposes pixel-level and region-level image fusion methods. For the smooth regions, whether in focus or not, there are almost the same visual perception. Excluding multifocus image smooth regions, focus detection among non-smooth regions can reduce detection errors, which is the key point in the pixel-level fusion method. Structural similarity is used to evaluate the similarity degree between multifocus images. Higher similarity, smoother regions. The labeling algorithm is used to reduce the focus region detection errors. However, this method is not greatly ideal along the focus regions boundary. Next, normalized cut based region-level fusion is presented to solve the problem. The spatial frequency weighted fusion result plays as the reference image to locate the focus boundaries and visual perception of the fusion result is excellent. The narrow field of ultrasound images is not helpful for doctors to observe the lesions. Extended-of-view imaging ultilizes motion estimation and fusion techniques by means of QWT shift theorem to splice ultrasound video, which brings in the wider field of vision for patients physiology structure.The thesis aims to deeply researches on QWT, especially concerning about image coefficients modeling in the QWT domain and building the relationship between phases coefficients model and image sharpness with applications to image denoising and fusion. QWT, as a novel image analysis tool, is capable of depicting the geometric structure in the image. Therefore, it is significant to summary the theory and methods for the abovementioned background and exploit the QWT characteristics and advantages based on the coefficients modeling.