Browsing by Author "Zhang, Huipin"

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    Image processing via undecimated wavelet systems
    (2000) Zhang, Huipin; Wells, Raymond O., Jr.
    We have studied undecimated wavelet transforms and their applications in image denoising. Because of the redundancy of the undecimated wavelet transform, the inversion scheme which implements the Moore-Penrose inverse of the forward transform makes undecimated wavelet systems have excellent performance in signal denoising. We propose an image denoising algorithm that prunes the complete undecimated discrete wavelet packet binary tree to select the best basis. Since we believe discarding the small coefficients permits to choose the best basis from the set of coefficients that will really contribute to the reconstructed image, we propose to select the best basis based on the thresholded wavelet coefficients rather than the original ones. We also propose an exponential decay model for autocorrelations of undecimated wavelet coefficients of real-world images. This is a model that captures the dependency of wavelet coefficients within a scale. With this model we present a parametric solution for FIR Wiener filtering in the undecimated wavelet domain. The persistence property of wavelet coefficients indicates strong dependency across scales. To capture the persistence of UDWT we propose an extension of the wavelet-domain hidden Markov tree model (HMT). By introducing the concept of composite coefficient, we simplify the general coefficient graph to be a tree-structure graph which is very suitable for training to obtain the HMT model parameters. This Bayesian framework allows us to formulate the image denoising problem as computing the posterior estimate.
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    System identification for robust control
    (1998) Zhang, Huipin; Antoulas, Athanasios C.
    In the design of a robust control system, one needs a nominal model together with a quantitative bound on the uncertainty that results from under-modeling and disturbances. In this thesis we do not intentionally seek a nominal model and a quantitative bound, instead, the uncertainty is directly parameterized so that the resulting uncertain model family can be characterized by means of a real parameter vector with at most unit length. This is an innovative approach to the control-oriented system identification, since it is not in accordance with the general philosophy of robust identification. However, it is applicable to the robust synthesis problem by taking advantage of a convex parameterization of robust controllers that simultaneously stabilize the uncertain models in the family. The robust performance problem becomes tractable since it can be converted into a quasi-convex optimization problem with Linear Matrix Inequality (LMI) constraints. The relation between the optimal robust performance and the uncertainty is studied by analyzing the explicit bounds of the maximal robust margin. Model (in)validation is a complement to system identification. In our approach it is an integral ingredient of the process of obtaining robust control-oriented system models. A single model is not invalidated if it is inside the ellipsoid, and thus the intersection of the ellipsoids is not invalidated. In order to make the unfalsified model set (the intersection) fit in our framework, we can compute an optimal ellipsoid bounding the intersection of the ellipsoids. (Abstract shortened by UMI.)