Sparse Domain Gaussianization for Multi-Variate Statistical Modeling of Retinal OCT Images

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.