Real-time tomographic reconstruction

With tomography it is possible to reconstruct the interior of an object without destroying. It is an important technique for many applications in, e.g., science, industry, and medicine. The runtime of conventional reconstruction algorithms is typically much longer than the time it takes to perform the tomographic experiment, and this prohibits the real-time reconstruction and visualization of the imaged object. The research in this dissertation introduces various techniques such as new parallelization schemes, data partitioning methods, and a quasi-3D reconstruction framework, that significantly reduce the time it takes to run conventional tomographic reconstruction algorithms without affecting image quality. The resulting methods and software implementations put reconstruction times in the same ballpark as the time it takes to do a tomographic scan, so that we can speak of real-time tomographic reconstruction.NWONumber theory, Algebra and Geometr

Scalability Analysis of CGLS Algorithm for Sparse Least Squares Problems on Massively Distributed Memory Computers

In this paper we study the parallelization of CGLS, a basic iterative method for large and sparse least squares problems whose main idea is to organize the computation of conjugate gradient method to normal equations. A performance model of computation and communication phases with isoefficiency concept are used to analyze the qualitative scalability behavior of this method implemented on massively parallel distributed memory computers with two dimensional mesh communication scheme. Two different mappings of data to processors, namely simple stripe and cyclic stripe partitionings are compared by putting these communication times into the isoefficiency concept which models scalability aspects. Theoretically, the cyclic stripe partitioning is shown to be asymptotically more scalable. 1 Introduction Many scientific and engineering applications such as linear programming [4], augmented Lagrangian method for CFD [7], and the natural factor method in structure engineering [1, 9] give rise t..

Advanced Electrical Resistivity Modelling and Inversion using Unstructured Discretization

In this dissertation an approach is presented for the three-dimensional electrical resistivity tomography (ERT) using unstructured discretizations. The geoelectrical forward problem is solved by the finite element method using tetrahedral meshes with linear and quadratic shape functions. Unstructured meshes are suitable for modelling domains of arbitrary geometry (e.g., complicated topography). Furthermore, the best trade-off between accuracy and numerical effort can be achieved due to the capability of problem-adapted mesh refinement. Unstructured discretizations also allow the consideration of spatial extended finite electrodes. Due to a corresponding extension of the forward operator using the complete electrode model, known from medical impedance tomography, a study about the influence of such electrodes to geoelectrical measurements is given. Based on the forward operator, the so-called triple-grid-technique is developed to solve the geoelectrical inverse problem. Due to unstructured discretization, the ERT can be applied by using a resolution dependent parametrization on arbitrarily shaped two-dimensional and three-dimensional domains. A~Gauss-Newton method is used with inexact line search to fit the data within error bounds. A global regularization scheme is applied using special smoothness constraints. Furthermore, an advanced regularization scheme for the ERT is presented based on unstructured meshes, which is able to include a-priori information into the inversion and significantly improves the resulting ERT images. Structural information such as material interfaces known from other geophysical techniques are incorporated as allowed sharp resistivity contrasts. Model weighting functions can define individually the allowed deviation of the final resistivity model from given start or reference values. As a consequent further development the region concept is presented where the parameter domain is subdivided into lithological or geological regions with individual inversion and regularization parameters. All used techniques and concepts are part of the open source C++ library GIMLi, which has been developed during this thesis as an advanced tool for the method-independent solution of the inverse problem