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Multivariate Statistical Models for Image Denoising in the Wavelet Domain

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Abstract

We model wavelet coefficients of natural images in a neighborhood using the multivariate Elliptically Contoured Distribution Family (ECDF) and discuss its application to the image denoising problem. A desirable property of the ECDF is that a multivariate Elliptically Contoured Distribution (ECD) can be deduced directly from its lower dimension marginal distribution. Using the property, we extend a bivariate model that has been used to successfully model the 2-D joint probability distribution of a two dimension random vector—a wavelet coefficient and its parent—to multivariate cases. Though our method only provides a simple and rough characterization of the full probability distribution of wavelet coefficients in a neighborhood, we find that the resulting denoising algorithm based on the extended multivariate models is computably tractable and produces state-of-the-art restoration results. In addition, we discuss the equivalence relation between our denoising algorithm and several other state-of-the-art denoising algorithms. Our work provides a unified mathematic interpretation of a type of statistical denoising algorithms. We also analyze the limitations and advantages of algorithms of this type.

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Authors and Affiliations

  1. Institute of Intelligent Information Processing, Xidian University, Xi’an, China

    Shan Tan & Licheng Jiao

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  1. Shan Tan
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  2. Licheng Jiao
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Tan, S., Jiao, L. Multivariate Statistical Models for Image Denoising in the Wavelet Domain. Int J Comput Vis 75, 209–230 (2007). https://doi.org/10.1007/s11263-006-0019-7

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  • DOI: https://doi.org/10.1007/s11263-006-0019-7

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