Multi-variable estimation of exponential parameters

Functions that are comprised of sums of a few exponential functions appear in all sorts of applications, and estimation of the corresponding exponential parameters is a field that goes back to 1795.

Modern applications include both Radar and MRI scanning.In the former, a pulse is sent out which is reflected on objects in the ambient environment and measured at a grid of sensors.

By estimating the exponential parameters in the reflected signal, one can reconstruct a 5 dimensional map containing information about what objects are nearby, as well as information about their respective direction of motion. One particular application of this that is presently being explored is safety systems in mining.

The latter application comprise both NMR-scanning of solid state materials and diffusion MRI for mapping of e.g. brain tissue.

In this case, the highdimensional estimation of these parameters can be used to produce accurate images of the brain structure, along with information about how the brain tissue is aligned.

This in turn can be used to study brain tumors, traumatic injury and neurodegeneration.The project aims at producing completely novel methods to do the corresponding parameter estimation, and relies on recent insights in pure mathematics (Hankel and Toeplitz operator theory) as well as applied mathematics (optimization for low-rank matrix recovery and compressed sensing).

In particular we aim to produce tailor made new algorithms for the above mentioned applications.