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This paper aims to propose two main contributions in the field of multivariate data analysis through the possibility theory. The first proposition is the definition of a generalized family of multivariate elliptical possibility distributions. These distributions have been derived from a consistent probability–possibility transformation over the family of so-called elliptical probability distributions. The second contribution proposed by this paper is the definition of two divergence measures between possibilistic distributions. We prove that a symmetric version of the Kullback–Leibler divergence guarantees all divergence properties when related to the space of possibility distributions. We further derive analytical expressions of the latter divergence and of the Hellinger divergence for certain possibility distributions pertaining to the elliptical family proposed, especially the normal multivariate possibility divergence in two dimensions. Finally, this paper provides an illustration of the developed possibilistic tools in an application of bi-band change detection between optical satellite images. [ABSTRACT FROM AUTHOR]

This letter presents an adaptive filtering approach of synthetic aperture radar (SAR) image times series based on the analysis of the temporal evolution. First, change detection matrices (CDMs) containing information on changed and unchanged pixels are constructed for each spatial position over the time series by implementing coefficient of variation (CV) cross tests. Afterward, the CDM provides for each pixel in each image an adaptive spatiotemporal neighborhood, which is used to derive the filtered value. The proposed approach is illustrated on a time series of 25 ascending TerraSAR-X images acquired from November 6, 2009 to September 25, 2011 over the Chamonix-Mont-Blanc test-site, which includes different kinds of change, such as parking occupation, glacier surface evolution, etc. [ABSTRACT FROM PUBLISHER]

The paper addresses the analysis and interpretation of second order random processes by using the wavelet packet transform. It is shown that statistical properties of the wavelet packet coefficients are specific to the filtering sequences characterizing wavelet packet paths. These statistical properties also depend on the wavelet order and the form of the cumulants of the input random process. The analysis performed points out the wavelet packet paths for which stationarization, decorrelation and higher order dependency reduction are effective among the coefficients associated with these paths. This analysis also highlights the presence of singular wavelet packet paths: the paths such that stationarization does not occur and those for which dependency reduction is not expected through successive decompositions. The focus of the paper is on understanding the role played by the parameters that govern stationarization and dependency reduction in the wavelet packet domain. This is addressed with respect to semi-analytical cumulant expansions for modeling different types of nonstatonarity and correlation structures. The characterization obtained eases the interpretation of random signals and time series with respect to the statistical properties of their coefficients on the different wavelet packet paths. [ABSTRACT FROM PUBLISHER]

This paper provides central limit theorems for the wavelet packet decomposition of stationary band-limited random processes. The asymptotic analysis is performed for the sequences of the wavelet packet coefficients returned at the nodes of any given path of the M-band wavelet packet decomposition tree. It is shown that if the input process is strictly stationary, these sequences converge in distribution to white Gaussian processes when the resolution level increases, provided that the decomposition filters satisfy a suitable property of regularity. For any given path, the variance of the limit white Gaussian process directly relates to the value of the input process power spectral density at a specific frequency. [ABSTRACT FROM AUTHOR]