Multivariate Statistical Models for Image Denoising in the Wavelet Domain
Multivariate Statistical Models for Image Denoising in the Wavelet Domain
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DOI：
10.1007/s11263-006-0019-7
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发表时间：
2007-11
影响因子：
19.5
通讯作者：
Tan Shan;L. Jiao
中科院分区：
文献类型：
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作者：
Tan Shan;L. Jiao
利用多元椭圆等值线分布族(ECDF)对邻域内自然图像的小波系数进行建模，并讨论其在图像去噪问题中的应用。ECDF的一个理想性质是可以从其低维边缘分布直接推导出多元椭圆等值线分布(ECD)。利用这一性质，我们将一个已经成功地模拟二维随机向量--小波系数及其母体--的二维联合概率分布的二元模型扩展到多元情形。虽然我们的方法只提供了一个邻域内小波系数全概率分布的简单而粗略的描述，但我们发现基于扩展的多变量模型的去噪算法在计算上是容易处理的，并且可以得到最先进的恢复结果。此外，我们还讨论了我们的去噪算法与其他几种最先进的去噪算法之间的等价关系。我们的工作为一类统计去噪算法提供了统一的数学解释。我们还分析了这类算法的局限性和优势。
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.