Objective
Two main objectives are treated by this project: To develop advanced theory of inverse problems under the conditions of fundamental lack of data for the purposes of Non-Destructive Testing. To develop the theory, algorithms, software and concept of application of advanced 3D cone-beam X-ray Tomography which will allow to decrease the required number of radiographic projections about 10-100 times, the angle of observation about 3 times, the necessary time of computation about 3-10 times and the radiation load about 10-100 times. Conventional X-ray Computer Tomography (CT) offers the possibility to study in detail the internal structures of an object in terms of the local linear attenuation coefficients (AC). According to theory the space distribution of AC can be reconstructed if data from hundreds of projections is provided, and the sources and detectors are located on all-around trajectories. The missing data are interpolated. The need for a huge number of projections and all-around circular observation of an object limits the potential use of CT.
This project addresses the reconstruction of incomplete projection data using MEM. The reconstruction is considered as a variational problem, which operates with appropriate functional measures that support in unbiased form some expected features of structures of the reconstructed object. The approach focuses on two main jects, whose objective is to compensate for the extreme lack of data in such kind of problems: to provide optimal zero-level approximation using non- trivial steps with the goal to reduce the region of interest to the Virtual Defect Space (VDS) before starting the minimisation procedure; to introduce some functional measures which describe the main expected features of structures, namely the presence of interphase boundaries, clusters, plane defects etc. That can be achieved by transition to Gibbs statistics of the potential 3D lattices using the theory of Markov random fields and developing suitable models of Gibbs potentials to be applied to the expected features. This ensures the linearity of trade-off functionals and unbiased formalisation of a priori information. Some basic problems of MEM will as well be investigated with reference to the multi-step concept. Among them most adequate simulation of the radiographic process; procedure of selecting the regularisation parameter; optimising the minimisation procedure.
The results will concern both basic knowledge and practical application. The first one supposes that both the principles of involving the a priori knowledge in MEM for the solution of inverse imposed problems and the new multi-step concept of reconstruction will be advanced. The second leads to the development of the concept of extreme limited projections and views real 3D X-ray Tomography of objects which are inaccessible for all-around circular observation.
Topic(s)
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12205 Berlin
Germany