Browsing by Author "Hua, Gang"
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Item Noncoherent image denoising(2005) Hua, Gang; Orchard, Michael T.The techniques of Translation Invariant (TI) denoising and statistical modeling are widely used in image denoising. This thesis studies how these techniques exploit location information in images and identifies a class of noncoherent image denoising algorithms. We analyze the performance of TI denoising from the perspective of cyclic-basis reconstruction. It shows that TI denoising achieves an average performance without direct estimation of location information. Motivated by this perspective, we propose a Redundant Quaternion Wavelet Transform (RQWT) which both avoids aliasing and separates local signal energy and location information into quaternion magnitude and phases respectively. RQWT is a natural framework for studying the statistical models in noncoherent image denoisers, because they all ignore quaternion phases. Straightforward signal estimation in the RQWT framework closely matches the state-of-the-art noncoherent image denoisers and provides a natural bound on their performance, thereby showing the importance of exploring location information in quaternion phases.Item Spatial and Temporal Image Prediction with Magnitude and Phase Representations(2011) Hua, Gang; Orchard, Michael T.In this dissertation, I develop the theory and techniques for spatial and temporal image prediction with the magnitude and phase representation of the Complex Wavelet Transform (CWT) or the over-complete DCT to solve the problems of image inpainting and motion compensated inter-picture prediction. First, I develop the theory and algorithms of image reconstruction from the analytic magnitude or phase of the CWT. I prove the conditions under which a signal is uniquely specified by its analytic magnitude or phase, propose iterative algorithms for the reconstruction of a signal from its analytic CWT magnitude or phase, and analyze the convergence of the proposed algorithms. Image reconstruction from the magnitude and pseudo-phase of the over-complete DCT is also discussed and demonstrated. Second, I propose simple geometrical models of the CWT magnitude and phase to describe edges and structured textures and develop a spatial image prediction (inpainting) algorithm based on those models and the iterative image reconstruction mentioned above. Piecewise smooth signals, structured textures and their mixtures can be predicted successfully with the proposed algorithm. Simulation results show that the proposed algorithm achieves appealing visual quality with low computational complexity. Finally, I propose a novel temporal (inter-picture) image predictor for hybrid video coding. The proposed predictor enables successful predictive coding during fades, blended scenes, temporally decorrelated noise, and many other temporal evolutions that are beyond the capability of the traditional motion compensated prediction methods. The proposed predictor estimates the transform magnitude and phase of the desired motion compensated prediction by exploiting the temporal and spatial correlations of the transform coefficients. For the case of implementation in standard hybrid video coders, the over-complete DCT is chosen over the CWT. Better coding performance is achieved with the state-of-the-art H.264/AVC video encoder equipped with the proposed predictor. The proposed predictor is also successfully applied to image registration.