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      The Nonsubsampled Contourlet Transform: Theory, Design, and Applications

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          The contourlet transform: an efficient directional multiresolution image representation

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            Image denoising using scale mixtures of Gaussians in the wavelet domain.

            We describe a method for removing noise from digital images, based on a statistical model of the coefficients of an overcomplete multiscale oriented basis. Neighborhoods of coefficients at adjacent positions and scales are modeled as the product of two independent random variables: a Gaussian vector and a hidden positive scalar multiplier. The latter modulates the local variance of the coefficients in the neighborhood, and is thus able to account for the empirically observed correlation between the coefficient amplitudes. Under this model, the Bayesian least squares estimate of each coefficient reduces to a weighted average of the local linear estimates over all possible values of the hidden multiplier variable. We demonstrate through simulations with images contaminated by additive white Gaussian noise that the performance of this method substantially surpasses that of previously published methods, both visually and in terms of mean squared error.
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              New tight frames of curvelets and optimal representations of objects with piecewiseC2singularities

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                Author and article information

                Journal
                IEEE Transactions on Image Processing
                IEEE Trans. on Image Process.
                Institute of Electrical and Electronics Engineers (IEEE)
                1057-7149
                October 2006
                October 2006
                : 15
                : 10
                : 3089-3101
                Article
                10.1109/TIP.2006.877507
                17022272
                ea101a8c-270d-4ee8-93f9-a4b975af6c8e
                © 2006
                History

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