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A Multiscale Bayesian Framework for Linear Inverse Problems and Its Application to Image Restoration

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Title: A Multiscale Bayesian Framework for Linear Inverse Problems and Its Application to Image Restoration
Author: Wan, Yi; Nowak, Robert David
Type: Journal Paper
Keywords: bayesian; image restoration; wavelet; Gaussian; Kalman filtering
Citation: Y. Wan and R. D. Nowak, "A Multiscale Bayesian Framework for Linear Inverse Problems and Its Application to Image Restoration," IEEE Transactions on Image Processing, 2001.
Abstract: 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.
Date Published: 2001-01-20

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  • ECE Publications [1034 items]
    Publications by Rice University Electrical and Computer Engineering faculty and graduate students
  • DSP Publications [508 items]
    Publications by Rice Faculty and graduate students in digital signal processing.