Browsing by Author "Wan, Yi"

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    A Bayesian Multiscale Approach to Joint Image Restoration and Edge Detection
    (1999-07-20) Wan, Yi; Nowak, Robert David; Center for Multimedia Communications (http://cmc.rice.edu/)
    This paper presents a novel wavelet-based method for simultaneous image restoration and edge detection. The Bayesian framework developed here is general enough to treat a wide class of linear inverse problems involving (white or colored) Gaussian observation noises, but we focus on convolution operators. In our new approach, a signal prior is developed by modeling the signal/image wavelet coefficients as independent Gaussian mixture random variables. We specify a uniform (non-informative) distribution on the mixing parameters, which leads to an extremely simple iterative algorithm for joint MAP restoration and edge detection. This algorithm is similar to the popular EM algorithm in that it alternates between a state estimation step and a maximization step, yet it is much simpler in each step and has a very intuitive derivation. Moreover, we show that our algorithm converges monotonically to a local maximum of the posterior distribution. Experimental results show that this new method can perform better than wavelet-vaguelette type methods that are based on linear inverse filtering followed by wavelet coefficient denoising.
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    A Multiscale Bayesian Framework for Linear Inverse Problems and Its Application to Image Restoration
    (2001-01-20) Wan, Yi; Nowak, Robert David; Digital Signal Processing (http://dsp.rice.edu/)
    In this paper we develop a wavelet-based statistical method for solving linear inverse problems. The Bayesian framework developed here is general enough to treat a wide class of linear inverse problems involving (white or colored) Gaussian observation noise. In this approach, a signal prior is developed by modeling the signal/imgage wavelet coefficients as independent Gaussian mixture random variabls. We first specify a uniform (non-informative) distribution on the mixing parameters, which leads to a simple and efficient iterative algorithm for MAP estimation. This algorithm is similar to the EM algorithm in that it alternates between a state estimation step and a maximization step. Moreover, we show that our algorithm converges monotonically to a local maximum of the posterior distribution. We next generalize the result to non-uniform priors and develop an efficient integer programming algorithm that enables a similar alternating optimization procedure. Experimental reults show that this new method outperforms recent results, including multiscale Kalman filtering and wavelet-vaguelette type methods based on linear inverse filtering followed by wavelet coefficient denoising.
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    New Bayesian Model Averaging Framework for Wavelet-Based Signal Processing
    (2000-06-20) Wan, Yi; Nowak, Robert David; Center for Multimedia Communications (http://cmc.rice.edu/)
    This paper develops a new signal modeling framework using Bayesian model averaging formulation and the redundant or translation-invariant wavelet transform. The aim of this framework is to provide a paradigm general enough to effectively treat fundamental problems arising in wavelet-based signal processing, segmentation, and modeling. Unlike many other attempts to mitigate the translation-dependent nature of wavelet analysis and processing, this framework is based on a well-defined statistical model averaging paradigm and improves over standard translation-invariant schemes for wavelet denoising. In addition to deriving new and more powerful signal modeling and denoising schemes, we demonstrate that certain existing methods are special suboptimal solutions of our proposed model averaging criterion. Experimental results demonstrate the promise of this framework.
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    Quasi-Circular Rotation Invariance in Image Denoising
    (1999-10-20) Wan, Yi; Nowak, Robert David; Center for Multimedia Communications (http://cmc.rice.edu/)
    This paper studies a new method for wavelet-based image denoising which is translation invariant (TI) and rotation invariant (RI). These invariances are crucial in image denoising and, more generally, may play important roles in image modeling. In contrast to other approximately RI methods, like the steerable pyramid, our new method employs standard separable wavelet bases in conjunction with a pseudo-circular image rotation. This scheme does not involve interpolation and hence the observation model (likelihood function) is invariant under this rotation. The superiority of our new method with respect to existing TI (non-RI) techniques is supported by experiments.
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    Wavelet-based signal modeling and processing algorithms with applications
    (2003) Wan, Yi; Nowak, Robert D.
    Good signal representation and the corresponding signal processing algorithms lie at the heart of the signal processing research effort. Since the 1980's wavelet analysis has become more and more a mature tool in many applications such as image compression due to some key advantages over the traditional Fourier analysis. In this thesis we first develop a wavelet-based statistical framework and an efficient algorithm for solving the linear inverse problems with application to image restoration. The result is an efficient method that produces state-of-the-art results for such problems and has potential further applications in other areas. To overcome the issues such as the blocking artifacts in using orthogonal wavelets, we next investigate the design issue of more flexible basis representations based on frames. In particular, we develop a quasi image rotation method that is based on pixel reassignment and hence retains the original image statistics. When combined with translation operators, this method provides very efficient and desirable frames for image processing. Given a frame, due to the large number of redundant basis functions in it, how to efficiently implement a frame-based algorithm is the key issue. We show this through the example of optimal signal denoising in the presence of added zero-mean white noise. We show that the optimal solution exists yet the computation toward the solution is very heavy. We develop a framework that allows for fast approximations to the optimal solution and has clear physical interpretation. This method is in essence different from the other various approximate approaches such the basis pursuit and has applications in other areas such as image segmentation. We also develop a complexity regularized iterative algorithm for getting sparse solutions to the frame-based signal denoising problem.
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    A Wavelet-Based Statistical Model for Image Restoration
    (2001-10-20) Wan, Yi; Nowak, Robert David; Digital Signal Processing (http://dsp.rice.edu/)
    In this paper we develop a wavelet-based statistical method for solving the image restoration problem. In this approach, a signal prior is set up by modeling the image wavelet coefficients as independent Gaussian mixture random variables. We first specify a uniform (non-informative) distribution on the mixing parameters, which leads to a simple and efficient iterative algorithm for MAP estimation. This algorithm is similar to the EM algorithm in that it alternates between a state estimation step and a maximization step. Moreover, we show that our algroithm converges monotonically to a local maximum of the posterior distribution. We next generalize the result to non-uniform priors and develop an efficient integer programming algorithm that enables a similar alternating optimization procedure.