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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

          M.N. Do, M. C. Vetterli (2005)
          Article 0 comments Cited 303 times – based on 0 reviews     Review now
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            Image denoising using scale mixtures of Gaussians in the wavelet domain.

            J Portilla, V Strela, M.J. Wainwright … (2003)
            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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              Adaptive wavelet thresholding for image denoising and compression.

              S.G. Chang, Bin Yu, M. Vetterli (2000)
              The first part of this paper proposes an adaptive, data-driven threshold for image denoising via wavelet soft-thresholding. The threshold is derived in a Bayesian framework, and the prior used on the wavelet coefficients is the generalized Gaussian distribution (GGD) widely used in image processing applications. The proposed threshold is simple and closed-form, and it is adaptive to each subband because it depends on data-driven estimates of the parameters. Experimental results show that the proposed method, called BayesShrink, is typically within 5% of the MSE of the best soft-thresholding benchmark with the image assumed known. It also outperforms SureShrink (Donoho and Johnstone 1994, 1995; Donoho 1995) most of the time. The second part of the paper attempts to further validate claims that lossy compression can be used for denoising. The BayesShrink threshold can aid in the parameter selection of a coder designed with the intention of denoising, and thus achieving simultaneous denoising and compression. Specifically, the zero-zone in the quantization step of compression is analogous to the threshold value in the thresholding function. The remaining coder design parameters are chosen based on a criterion derived from Rissanen's minimum description length (MDL) principle. Experiments show that this compression method does indeed remove noise significantly, especially for large noise power. However, it introduces quantization noise and should be used only if bitrate were an additional concern to denoising.
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                Author and article information

                Journal
                Title: IEEE Transactions on Image Processing
                Abbreviated Title: IEEE Trans. on Image Process.
                Publisher: Institute of Electrical and Electronics Engineers (IEEE)
                ISSN (Print): 1057-7149
                Publication date Created: October 2006
                Publication date (Print): October 2006
                Volume: 15
                Issue: 10
                Pages: 3089-3101
                Article
                DOI: 10.1109/TIP.2006.877507
                PubMed ID: 17022272
                SO-VID: ea101a8c-270d-4ee8-93f9-a4b975af6c8e
                Copyright © © 2006
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