Faculty Bibliography

A model-based reconstruction technique for accelerated T2 mapping with improved accuracy is proposed using undersampled Cartesian spin-echo magnetic resonance imaging (MRI) data. The technique employs an advanced signal model for T2 relaxation that accounts for contributions from indirect echoes in a train of multiple spin echoes. An iterative solution of the nonlinear inverse reconstruction problem directly estimates spin-density and T2 maps from undersampled raw data. The algorithm is validated for simulated data as well as phantom and human brain MRI at 3T. The performance of the advanced model is compared to conventional pixel-based fitting of echo-time images from fully sampled data. The proposed method yields more accurate T2 values than the mono-exponential model and allows for retrospective undersampling factors of at least 6.Although limitations are observed for very long T2 relaxation times, respective reconstruction problems may be overcome by a gradient dampening approach. The analytical gradient of the utilized cost function is included as appendix. The source code is made available to the community.

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, 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 nonuniform fast Fourier transform, which is implemented by a combination of a type-1 and type-2 nonuniform fast Fourier transform. Using this operator, it is also possible to implement an iterative conjugate gradient 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 total generalized variation-based approach.

We study the total generalised variation regularisation of symmetric tensor fields from medical applications, namely diffusion tensor regularisation. We study the effect of the pointwise positivity constraint on the tensor field, as well as the difference between direct denoising of the tensor field first solved from the Stejskal-Tanner equation, as was done in our earlier work, and of incorporating this equation into the fidelity function. Our results indicate that the latter novel approach provides improved computational results.

A cheap way to speed up image-reconstruction software is to use modern graphics hardware that can execute algorithms in a massively parallel manner. Here, the authors discuss Agile, an open source library designed for image reconstruction in biomedical sciences. Its modular, object-oriented, and templated design eases the integration of the library into user code.

We study the extension of total variation (TV), total deformation (TD), and (second-order) total generalized variation (TGV 2) to symmetric tensor fields. We show that for a suitable choice of finite-dimensional norm, these variational seminorms are rotation-invariant in a sense natural and well suited for application to diffusion tensor imaging (DTI). Combined with a positive definiteness constraint, we employ these novel seminorms as regularizers in Rudin-Osher-Fatemi (ROF) type denoising of medical in vivo brain images. For the numerical realization, we employ the ChambollePock algorithm, for which we develop a novel duality-based stopping criterion which guarantees error bounds with respect to the functional values. Our findings indicate that TD and TGV 2, both of which employ the symmetrized differential, provide improved results compared to other evaluated approaches.