MAHI 2012 workshop: Methodological Aspects of Hyperspectral Imaging

A glance at information-geometric signal processing
Frank Nielsen, Sony Computer Science Laboratories, Inc (JP)

Statistical signal processing models raw signals by stochastic processes, analyzes their statistical properties, and design algorithmic applications on top of those models. Besides the two prominent normalized histograms (multinomials) and Gaussians, many other family of probability distributions are encountered in natural sound or image statistics [1,2]. Those family of distributions are canonically studied under the framework of differential geometry derived from statistical invariance first principles. We review recent advances and challenges of the Fisher-Rao Riemannian geometry of parametric models, the Hilbertian geometry of non-parametric models, and the algorithmically-friendly dually flat geometry [3,4]. Those various geometric embeddings of statistical models provides intrinsic (coordinate-independent) data analysis, and offer the rich language of geometry (e.g., geodesics, balls, projections, Pythagoras’ theorem and orthogonality) to design novel or re-interpret old algorithms. We illustrate the information-geometric algorithmic toolbox [5] with some imaging applications (eg., filtering, regularization, retrieval, classification).

References

1. Natural Image Statistics: A Probabilistic Approach to Early Computational Vision, Springer (2009). A. Hyvrinen, J. Hurri, and P. O. Hoyer book online

2. Matrix Information Geometry, Springer, (2012). F. Nielsen and R. Bhatia (eds) book home page

3. Computational Geometry for Statistics, International Workshop on Anomalous Statistics, Generalized Entropies, and Information Geometry, (2012). F. Nielsen slides online

4. k-MLE: A fast algorithm for learning statistical mixture models, ICASSP, (2012). F. Nielsen pdf online

5. jMEF: A Java library to create, process and manage mixtures of exponential families. Java with Matlab binding, or in Python