Keynote Speaker

Dr. David Donoho, Stanford University

Exotic new data need exotic new wavelets

Exotic new data types are constantly being developed and deployed in many fields of science and technology, and this causes exciting new challenges for statisticians and applied mathematicians. Data coming from navigation, motion capture, extragalactic astronomy, medical imagery, and other fields can be interpreted as manifold-valued data, i.e. as data where the individual data points, instead of being numbers on the real line, are points in a smooth manifold.

Examples include orientations (the manifold is a sphere) subspaces (the manifold is then the Grassmann manifold) and diffusion tensors (the manifold of positive definite matrices).

In the examples I will discuss, we have values in a manifold as a function of time and/or space. Thus for example, human motion is captured as a series of values in the manifold formed by the product of several Grassmann manifolds, one for each joint.

I will give numerous examples of manifold-valued data, stressing the intuitive nature of such data. I will describe some standard problems in signal processing, including compression, noise removal, enhancement, and explain why these are also important in the manifold-valued setting.

I will then discuss recent results providing multiscale `wavelet' methods for dealing with such data. I will show how to use differential geometry to generalize existing notions of wavelets and will give novel examples of compressed, denoised, and contrast-enhanced human motion. The talk should be accessible to a broad audience with some mathematical background.

This is joint work with Inam Rahman and Iddo Drori of Stanford and Peter Schroeder (Caltech).

About the Speaker

Dr. David Donoho is Professor of Statistics and the Anne T. and Robert M. Bass Professor of Humanities and Sciences at Stanford University. As a highly distinguished statistical scientist, Professor Donoho has conducted groundbreaking research in the analysis and recovery of data. In particular, he has made significant contributions to signal processing, multiresolutional analysis and high dimensional data analysis.

Among his many honors, Professor Donoho has received a MacArthur Fellowship, the John von Neumann prize from the Society of Industrial and Applied Mathematics, and the Presidents' Award of the Committee of Presidents of Statistical Sciences. He is an elected member of both the American Academy of Arts and Sciences and the National Academy of Sciences USA.

For more detailed information concerning Professor Donoho's research and publications, please visit his website: http://www-stat.stanford.edu/~donoho/ .