Optimal Sampling

Brandoch Calef, University of California, Berkeley

Rarely in science is one interested in quantities that can be measured directly. More often, the interesting parts of a system are only accessible by means of a model relating them to (experimentally measurable) external features. Furthermore, since the number of measurements that can be taken is necessarily finite, the problem of deciding which ones to take must inevitably be addressed. This is the optimal sampling problem.

X-ray tomography provides a good example of this. Suppose an image of a certain area inside the body is to be reconstructed from a fixed number of views. From which angles should the views be collected so as to permit the best reconstruction of the region of interest?

We will formulate the optimal sampling problem in a very general setting, consider what is meant by the "best" sampling scheme, and look at some examples.

Abstract Author(s): Brandoch Calef