Project Description
Optimal measurements
2006-01-01 -> 2008-12-31
Project Description
Although imaging and inverse scattering problems have been thoroughly studied during the last century there is only a partial understanding of these complex problems. Most of the efforts have been placed on the development of efficient inversion algorithms and mathematical uniqueness results. In comparison, there are very few results and a limited knowledge about the information content in the inversion data and the design of optimal measurements.
The specific objective in this project is to establish and merge tools and methods from statistical signal processing such as the Fisher information to quantify the quality of data in inverse scattering problems. Using these tools, the objective is furthermore to analyze fundamental properties of the inverse scattering problems with respect to various parameters of the system setup and of the physical model itself. Finally, given an objective function based on the Fisher information measure, we will also exploit and develop new convex interior point optimization techniques for efficient optimization of the system parameters such as suitable measurement positions, frequency bands etc.
The project encompasses the following topics
· Development of tools to quantify the information content in inversion data for inverse scattering problems. This involves the use and extension of the Fisher information measure to uncountable sets and proper modeling of the noise.
· Use of the Fisher information measure to quantify what should be measured and how a measurement setup can be improved. This involves choice of frequency spectra and pules shape and measurement geometry such as mono--, bi--, and multi--static setups.
· Development of modern convex optimization techniques to design optimal measurement setups. This involves the use and extension of semidefinite as well as semiinfinite programming theory and techniques.
· Experimental verification of the results on inverse scattering applications such as microwave tomography, digital holography, non--destructive testing, and near-field imaging.