In this paper we study the error behavior of the well known fast Fourier transform for nonequispaced data (NFFT) with respect to the L2-norm. We compare the arising errors for different window functions and show that the accuracy of the algorithm can be significantly improved by modifying the shape of the window function. Based on the considered error estimates for different window functions we are able to state an easy and efficient method to tune the involved parameters automatically. The numerical examples show that the optimal parameters depend on the given Fourier coefficients, which are assumed not to be of a random structure or roughly of the same magnitude but rather subject to a certain decrease.

This thesis deals with parallelization of complex tasks in reconstruction of dynamic magnetic resonance. It describes the basic principle of magnetic resonance and its relation to Fourier transform. It deals with the difference between static and dynamic magnetic resonance image reconstruction. It analyzes SVD algorithm and its use in magnetic resonance image reconstruction. It presents the principles and the importance of parallel computing in magnetic resonance imaging and describes CUDA technology. The thesis also contains a description and execution of the implementation of the reconstruction model in MATLAB and Java programming language which were optimized by JCuda library for Java implementation and gpuArray function in case of MATLAB implementation.

This thesis deals with parallelization of complex tasks in reconstruction of dynamic magnetic resonance. It describes the basic principle of magnetic resonance and its relation to Fourier transform. It deals with the difference between static and dynamic magnetic resonance image reconstruction. It analyzes SVD algorithm and its use in magnetic resonance image reconstruction. It presents the principles and the importance of parallel computing in magnetic resonance imaging and describes CUDA technology. The thesis also contains a description and execution of the implementation of the reconstruction model in MATLAB and Java programming language which were optimized by JCuda library for Java implementation and gpuArray function in case of MATLAB implementation.

In this paper we study the error behavior of the well known fast Fourier transform for nonequispaced data (NFFT) with respect to the L2-norm. We compare the arising errors for different window functions and show that the accuracy of the algorithm can be significantly improved by modifying the shape of the window function. Based on the considered error estimates for different window functions we are able to state an easy and efficient method to tune the involved parameters automatically. The numerical examples show that the optimal parameters depend on the given Fourier coefficients, which are assumed not to be of a random structure or roughly of the same magnitude but rather subject to a certain decrease.