1. A Novel Anomaly Detection Scheme for Hyperspectral Images Based on a Non-Gaussian Mixture Model Tiziana Veracini , Marco Diani, Giovanni Corsini Dipartimento di Ingegneria dell’Informazione, Università di Pisa via G. Caruso 16, 56122 Pisa, Italy 2010 IEEE GOLD REMOTE SENSING CONFERENCE 29, 30 april 2010 Accademia Navale, Livorno, Italy

8. Learning approach [1] [1] C. Archambeau, and M. Verleysen, “Robust Bayesian Clustering”, Neural Networks, vol.20, pp. 129-138, 2007. Gauss-Wishart prior distribution governs both the mean vector and the precision matrix of each component. The analysis is carried out by using PRIOR DISTRIBUTIONS CONJUGATE TO THE LIKELIHOOD FUNCTION . Dirichlet prior distribution governs the mixing proportions. The number of degrees of freedom of each component is obtained by maximizing the expected log-likelihood function, evaluated taking into account the observed data and the parameters considered as random variables, and imposing ν j >2. No prior distribution is imposed on the number of degrees of freedom of each mixture component.

9. Anomaly detection strategy: StMM GLRT AD 1. Clustering step 2. PDF estimation 3. GLRT The image pixels are grouped into clusters. The clustering strategy is conducted by assuming a StMM PDF for each hyperspectral pixel. The background continuous PDF is approximated as a linear combination of Student’s t distributions based on the statistics estimated for each cluster. The anomaly detector decision criterion is given by: where η is the detection threshold. Once the PDF has been estimated, the Generalized Likelihood Ratio Test (GLRT) can be applied.

15. Conclusions AD philosophy The proposed strategy combines a StMM PDF for modeling each hyperspectral pixel along with the GLRT decision rule. The StMM learning is based on a Bayesian approach that automatically estimates the mixture parameters during the learning procedure. Only the pure target pixels were assumed as targets to detect, whereas evident undesired anomalies were neglected. AD: StMM vs GMM The experimental analysis has shown the BStMM ability to reliably estimate the background PDF, and its effectiveness in detecting rare anomalous objects within the image employed. The conducted analysis has highlighted how the discrete search over the number of components in a mixture distribution conducted by adopting the classical EM learning can be avoided by adopting a Bayesian philosophy within AD schemes. AD philosophy The proposed strategy combines a StMM PDF for modeling each hyperspectral pixel along with the GLRT decision rule. The StMM learning is based on a Bayesian approach that automatically estimates the mixture parameters during the learning procedure. AD: StMM vs GMM The experimental analysis has shown the BStMM ability to reliably estimating the background PDF, and its effectiveness in detecting rare anomalous objects within the image employed. The conducted analysis has highlighted how the discrete search over the number of components in a mixture distribution conducted by adopting the classical EM learning can be avoided by adopting a Bayesian philosophy within AD schemes.

16. Thanks for your attention