The normal inverse Gaussian distribution: a versatile model for heavy-tailed stochastic processes

Computer-aided obstructive sleep apnea detection using normal inverse Gaussian parameters and adaptive boosting

“…[18][19][20][21]. capture the underlying statistics of the TQWT sub-bands, establishing their suitability and appropriateness thereby.…”

Image denoising in contourlet domain based on a normal inverse Gaussian prior

“…According to Fig. 3, the statistical models of contourlet coefficients exhibit a sharp peak at zero amplitude and heavy tails to both sides of the peak, and normal inverse Gaussian model [21,22] can describe curves with any shape because of its four flexible parameters, so we choose normal inverse Gaussian model to describe the distribution of contourlet coefficients of image. For most images, two parameters in the four parameters of normal inverse Gaussian model are constant [23].…”

Non-negative sparse coding shrinkage for image denoising using normal inverse Gaussian density model

“…A stochastic variable u is said to be normal inverse Gaussian if its probability density takes the following form [18,19].…”

“…Finally it should be possible to estimate the model parameters from noisy observations. To meet the requirements, the normal inverse Gaussian (NIG) density, which was proposed recently [18,19] is used in this study. NIG is a four-parameter model that is suitable for non-negative sparse components.…”

“…The flexibility of the NIG density function makes it possible to meet all the requirements listed above. Moreover, fast cumulant based estimators can be used to compute the four parameters in the density function [19]. In the symmetric case, it can model data ranging from zero normalized kurtosis, i.e., the Gaussian distribution, to any positive valued kurtosis.…”