Multivariate texture discrimination based on geodesics to class centroids on a generalized Gaussian Manifold

A texture discrimination scheme is proposed wherein probability distributions are deployed on a probabilistic manifold for modeling the wavelet statistics of images. We consider the Rao geodesic distance (GD) to the class centroid for texture discrimination in various classification experiments. We compare the performance of GD to class centroid with the Euclidean distance in a similar context, both in terms of accuracy and computational complexity. Also, we compare our proposed classification scheme with the k-nearest neighbor algorithm. Univariate and multivariate Gaussian and Laplace distributions, as well as generalized Gaussian distributions with variable shape parameter are each evaluated as a statistical model for the wavelet coefficients. The GD to the centroid outperforms the Euclidean distance and yields superior discrimination compared to the k-nearest neighbor approach

Incorporating magnetic equilibrium information in Gaussian process tomography for soft X-ray spectroscopy at WEST

Paper published as part of the Proceedings of the 22nd Topical Conference on High-Temperature Plasma Diagnostics, San Diego, California, April 2018International audienceGaussian process tomography (GPT) [J. Svensson, JET Internal Report EFDA-JET-PR(11)24, 2011 and D. Li, J. Svensson, H. Thomsen, F. Medina, A. Werner, and R. Wolf, Rev. Sci. Instrum. 84, 083506 (2013)] is a recently developed tomography method applied earlier to soft X-ray (SXR) spectroscopy on WEST---Tungsten (W) Environment in Steady-state Tokamak. The short execution time of the algorithm makes GPT an important candidate for providing real-time information on impurity transport and for fast MHD control. In earlier work, GPT has shown its flexibility by providing good reconstruction results without background information about the magnetic equilibrium. On the other hand, information about the magnetic flux surface geometry can in general be useful for additional regularization of the solution. In this paper, we develop a way to take into account the equilibrium information, by constructing a covariance matrix of the prior Gaussian process depending on the flux surface geometry. The GPT method is validated using synthetic SXR emissivity profiles relevant to WEST plasmas and compares favorably with the classical algorithm based on minimization of the Fisher information

Color texture discrimination using the principal geodesic distance on a multivariate generalized Gaussian manifold

We present a new texture discrimination method for textured color images in the wavelet domain. In each wavelet subband, the correlation between the color bands is modeled by a multivariate generalized Gaussian distribution with fixed shape parameter (Gaussian, Laplacian). On the corresponding Riemannian manifold, the shape of texture clusters is characterized by means of principal geodesic analysis, specifically by the principal geodesic along which the cluster exhibits its largest variance. Then, the similarity of a texture to a class is defined in terms of the Rao geodesic distance on the manifold from the texture's distribution to its projection on the principal geodesic of that class. This similarity measure is used in a classification scheme, referred to as principal geodesic classification (PGC). It is shown to perform significantly better than several other classifiers

A First Approach Toward Bayesian Estimation of Turbulent Plasma Properties from Reflectometry

The possibility of inferring the properties of electron density fluctuations in tokamak plasmas from a reflectometer signal by means of Bayesian methods is investigated. Within the physical optics approximation, the interaction of the probing beam with the plasma is described as reflection from a surface with stochastic properties that is simulated numerically. A Bayesian technique is outlined to solve the inverse problem to determine the surface characteristics from the power spectrum of the reflectometer signal. It is shown that satisfactory estimates of the length and timescales and the amplitude of density fluctuations can be obtained in conditions relevant to core tokamak plasmas