Multivariate Statistical Modeling of Retinal Optical Coherence Tomography

Abstract

In this paper a new statistical multivariate model for retinal Optical Coherence Tomography (OCT) B-scans is proposed. Due to the layered structure of OCT images, there is a horizontal dependency between adjacent pixels at specific distances, which led us to propose a more accurate multivariate statistical model to be employed in OCT processing applications such as denoising. Due to the asymmetric form of the probability density function (pdf) in each retinal layer, a generalized version of multivariate Gaussian Scale Mixture (GSM) model, which we refer to as GM-GSM model, is proposed for each retinal layer. In this model, the pixel intensities in each retinal layer are modeled with an asymmetric Bessel K Form (BKF) distribution as a specific form of the GM-GSM model. Then, by combining some layers together, a mixture of GM-GSM model with eight components is proposed. The proposed model is then easily converted to a multivariate Gaussian Mixture model (GMM) to be employed in the spatially constrained GMM denoising algorithm. The Q-Q plot is utilized to evaluate goodness of fit of each component of the final mixture model. The improvement in the noise reduction results based on the GM-GSM model, indicates that the proposed statistical model describes the OCT data more accurately than other competing methods that do not consider spatial dependencies between neighboring pixels.