Specific aims of the project are:
1. A synthesis of globally convergent numerical methods with the Finite Element Adaptive technique (adaptivity) for optical tomography and in imaging using electromagnetic waves. In the first version of this synthesis, solution obtained by the globally convergent method will serve as a good first guess for the adaptivity for a further
enhancement, similarly with [3,4]. However, in the second version we will apply the adaptivity idea directly to the globally convergent algorithm, develop a posteriori error analysis in a globally convergent method and formulate an adaptive algorithm similar with [1].
2. A detailed study of the case of many source locations, since the idea of [2] works only with a single source. In this case we plan to use sources sequentially for a possible sequential improvement of the image. The reason of
working with several source is that this case might provide better quality images because it is more informative.
3. A detailed study of applications developed numerical methods to medical optical imaging, where we will work with realistic range of parameters to determine the absorption coefficient in tumor-like abnormalities. Recently we have already obtained results with experimental data [13]. In the nearest future we will get more experimental data from Optoelectronics Center at University of North Carolina at Charlotte, USA, to be able test our new methods.
4. Application of adaptivity technique in signal reconstruction in scanning electron tomography. This method is one of the most prospective nondestructive diagnostic methods in microtomography of backscattered electrons, see [19].
5. Organization of annual workshops on the topic of Inverse problems with all researchers participating in the project.