In this paper, a multivariate statistical model that is suitable for describing Optical Coherence Tomography (OCT) images is introduced. The proposed model is comprised of a multivariate Gaussianization function in sparse domain. Such an approach has two advantages, i.e. 1) finding a function that can effectively transform the input – which is often not Gaussian – into normally distributed samples enables the reliable application of methods that assume Gaussianity, 2) although multivariate Gaussianization in spatial domain is a complicated task and rarely results in closed-form analytical model, by transferring data to sparse domain, our approach facilitates multivariate statistical modeling of OCT images. To this end, a proper multivariate probability density function (pdf) which considers all three properties of OCT images in sparse domains (i.e. compression, clustering, and persistence properties) is designed and the proposed sparse domain Gaussianization framework is established. Using this multivariate model, we show that the OCT images often follow a 2-component multivariate Laplace mixture model in the sparse domain. To evaluate the performance of the proposed model, it is employed for OCT image denoising in a Bayesian framework. Visual and numerical comparison with previous prominent methods reveals that our method improves the overall contrast of the image, preserves edges, suppresses background noise to a desirable amount, but is less capable of maintaining tissue texture. As a result, this method is suitable for applications where edge preservation is crucial, and a clean noiseless image is desired.

中文翻译：

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视网膜OCT图像的多元统计建模的稀疏域高斯化

在本文中， 多变量介绍了适合描述光学相干断层扫描（OCT）图像的统计模型。提议的模型包括多变量稀疏域中的高斯函数。这种方法具有两个优点，即1）找到可以有效地将输入（通常不是高斯）转换为正态分布样本的函数，可以可靠地应用假设为高斯的方法，2）尽管多变量 空间域的高斯化是一项复杂的任务，很少会导致闭式分析模型，通过将数据传输到稀疏域，我们的方法有助于 多变量OCT图像的统计建模。为此，适当的多变量设计了考虑了OCT图像在稀疏域中的所有三个属性（即压缩，聚类和持久性）的概率密度函数（pdf），并建立了所提出的稀疏域高斯化框架。使用这个多变量 模型，我们显示OCT图像通常遵循2分量 多变量稀疏域中的拉普拉斯混合模型。为了评估所提出模型的性能，将其用于贝叶斯框架中的OCT图像降噪。与以前的突出方法的视觉和数值比较表明，我们的方法可以改善图像的整体对比度，保留边缘，将背景噪声抑制到所需的数量，但保持组织纹理的能力较弱。因此，此方法适用于边缘保留至关重要且需要干净无噪图像的应用。