Faculty Bibliography

The primary goal is to reduce imaging times for isotropic, high-resolution 3D DTI by using a 3D undersampled diffusion-weighted steady state free precession (DW-SSFP) acquisition with a constrained non-linear parallel imaging reconstruction. DW-SSFP is an efficient multi-shot diffusion preparation amenable to fast 3D DTI acquisitions with proper phase navigation [1-3]. Undersampling in k-space reduces scan time at the expense of image artifacts, a well-known trade-off. Non-linear parallel reconstruction using a Total Generalized Variation (TGV2) constraint has been shown to mitigate undersampling artifacts by leveraging on coil sensitivities and a judicious choice of penalty term. Here, fully sampled in-vivo DW-SSFP DTI data is retrospectively undersampled to explore the feasibility of scan-time reduction using TGV2 reconstruction

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 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.

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.

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.

Quantitative evaluations of the T2 relaxation time are of high importance for diagnostic MRI. Standard T2 mapping procedures rely on the timedemanding acquisition of fully-sampled MSE datasets. Recently proposed nonlinear inversion strategies allow for T2 mapping from undersampled data by exploiting a mono-exponential signal model [1, 2]. However, in the presence of B1+ inhomogeneities and non-ideal slice profiles, the echo train of true MR data usually strongly deviates from the idealized model [3, 4]. The reconstructed T2 maps therefore contain systematic errors, even for fully-sampled data sets. Using the method [1] on undersampled MSE data, the strong model violation of the first echo can provoke artifacts in the reconstruction as well as a systematic deviation in the results for different acceleration factors. Consequently, the first echo has been discarded in [1] which seems common in practice [5]. Recently a new analytical formula has been proposed [6], which models the MSE signal much more accurately than a monoexponential curve (Fig. 1). The approach has been extended for slice selective sequences and its quantitative superiority demonstrated in [7]. This work evaluates the combination of the model in [7] with the nonlinear inversion approach in [1] to allow for accurate T2 reconstructions from highly undersampled Cartesian data.

A new approach based on nonlinear inversion for autocalibrated parallel imaging with arbitrary sampling patterns is presented. By extending the iteratively regularized Gauss-Newton method with variational penalties, the improved reconstruction quality obtained from joint estimation of image and coil sensitivities is combined with the superior noise suppression of total variation and total generalized variation regularization. In addition, the proposed approach can lead to enhanced removal of sampling artifacts arising from pseudorandom and radial sampling patterns. This is demonstrated for phantom and in vivo measurements.

The Cartesian parallel magnetic imaging problem is formulated variationally using a high-order penalty for coil sensitivities and a total variation like penalty for the reconstructed image. Then the optimality system is derived and numerically discretized. The objective function used is non-convex, but it possesses a bilinear structure that allows the ambiguity among solutions to be resolved technically by regularization and practically by normalizing a pre-estimated norm of the reconstructed image. Since the objective function is convex in each single argument, convex analysis is used to formulate the optimality condition for the image in terms of a primal-dual system. To solve the optimality system, a nonlinear Gauss-Seidel outer iteration is used in which the objective function is minimized with respect to one variable after the other using an inner generalized Newton iteration. Computational results for in vivo MR imaging data show that a significant improvement in reconstruction quality can be obtained by using the proposed regularization methods in relation to alternative approaches.