CUDA powered MRI reconstruction with variational constraints

The acceleration of magnetic resonance imaging (MRI) has been a central research topic for many years. In addition to the correct measurement of time-dependent processes and the reduction of motion artifacts, the acceleration of MRT is of particular importance for the clinical applicability of new specific examination methods. Recently, work has focused in particular on subsampled "Parallel Imaging" methods. Only subsegments of the data necessary for a conventional reconstruction are acquired, but these are measured with several receiving coils in parallel. In combination with new mathematical methods it is possible to reconstruct artifact-free images or scans with high temporally resolution from these accelerated, mutli-coil measurements. With a special technique, the iteratively regularized Gauss-Newton (IRGN) method, it is also possible to determine the influence of the spatially variable receiver coil sensitivity in the reconstruction. The runtime-optimal implementation of this sophisticated reconstruction procedure in combination with different regularization techniques (Tikhonov L2-norm, "total variation" and "total generalized variation") is the subject of this work. To achieve fast reconstruction we leverage the power of high-end GPUs with CUDA and compared the results to a reference implementation in Matlab. In this thesis the mathematical background is described and then implementation techniques for a fast image reconstruction are discussed. A special challenge of the inherent nonlinear inverse problem is the Primal-Dual Extra-Gradient Algorithm for IRGN, which causes a high computational load. In order to accelerate the matrix-based calculations, the existing C++ Agile Library of the Institute of Medical Engineering was extended to include a CUDA framework for GPU image reconstruction. The GPU implementation made it possible to reduce the image reconstruction time to one tenth of the reference implementation. This work was concluded with a comparative analysis of the reconstruction quality by graphics card compared to a reference implementation in Matlab. The visual impression of the tissue signals showed no immediately recognizable differences. In the subtraction analysis differences occured primarily at the tissue edges. The results of the numerical evaluation showed deviations which are below the typical noise level.