In the case of radial imaging with nonlinear spatial encoding fields, a prominent star-shaped artifact has been observed if a spin distribution is encoded with an undersampled trajectory. This work presents a new iterative reconstruction method based on the total generalized variation (TGV), which reduces this artifact. For this approach, a sampling operator (as well as its adjoint) is needed that maps data from PatLoc k-space to the final image space. It is shown that this can be realized as a Type-3 non-uniform FFT, which is implemented by a combination of a Type-1 and Type-2 non-uniform FFT. Using this operator, it is also possible to implement an iterative conjugate gradient (CG) SENSE based method for PatLoc reconstruction, which leads to a significant reduction of computation time in comparison to conventional PatLoc image reconstruction methods. Results from numerical simulations and in-vivo PatLoc measurements with as few as 16 radial projections are presented, which demonstrate significant improvements in image quality with the TGV based approach.
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