Faculty Bibliography

OBJECTIVE: Variable density random sampling patterns have recently become increasingly popular for accelerated imaging strategies, as they lead to incoherent aliasing artifacts. However, the design of these sampling patterns is still an open problem. Current strategies use model assumptions like polynomials of different order to generate a probability density function that is then used to generate the sampling pattern. This approach relies on the optimization of design parameters which is very time consuming and therefore impractical for daily clinical use. MATERIALS AND METHODS: This work presents a new approach that generates sampling patterns by making use of power spectra of existing reference data sets and hence requires neither parameter tuning nor an a priori mathematical model of the density of sampling points. RESULTS: The approach is validated with downsampling experiments, as well as with accelerated in vivo measurements. The proposed approach is compared with established sampling patterns, and the generalization potential is tested by using a range of reference images. Quantitative evaluation is performed for the downsampling experiments using RMS differences to the original, fully sampled data set. CONCLUSION: Our results demonstrate that the image quality of the method presented in this paper is comparable to that of an established model-based strategy when optimization of the model parameter is carried out and yields superior results to non-optimized model parameters. However, no random sampling pattern showed superior performance when compared to conventional Cartesian subsampling for the considered reconstruction strategy.

Total variation was recently introduced in many different magnetic resonance imaging applications. The assumption of total variation is that images consist of areas, which are piecewise constant. However, in many practical magnetic resonance imaging situations, this assumption is not valid due to the inhomogeneities of the exciting B1 field and the receive coils. This work introduces the new concept of total generalized variation for magnetic resonance imaging, a new mathematical framework, which is a generalization of the total variation theory and which eliminates these restrictions. Two important applications are considered in this article, image denoising and image reconstruction from undersampled radial data sets with multiple coils. Apart from simulations, experimental results from in vivo measurements are presented where total generalized variation yielded improved image quality over conventional total variation in all cases.

OBJECTIVE: Subsampling of radially encoded MRI acquisitions in combination with sparsity promoting methods opened a door to significantly increased imaging speed, which is crucial for many important clinical applications. In particular, it has been shown recently that total variation (TV) regularization efficiently reduces undersampling artifacts. The drawback of the method is the long reconstruction time which makes it impossible to use in daily clinical practice, especially if the TV optimization problem has to be solved repeatedly to select a proper regularization parameter. MATERIALS AND METHODS: The goal of this work was to show that for the case of MR Angiography, TV filtering can be performed as a post-processing step, in contrast to the common approach of integrating TV penalties in the image reconstruction process. With this approach, it is possible to use TV algorithms with data fidelity terms in image space, which can be implemented very efficiently on graphic processing units (GPUs). The combination of a special radial sampling trajectory and a full 3D formulation of the TV minimization problem is crucial for the effectiveness of the artifact elimination process. RESULTS AND CONCLUSION: The computation times of GPU-TV show that interactive elimination of undersampling artifacts is possible even for large volume data sets, in particular allowing the interactive determination of the regularization parameter. Results from phantom measurements and in vivo angiography data sets show that 3D TV, together with the proposed sampling trajectory, leads to pronounced improvements in image quality. However, while artifact removal was very efficient for angiography data sets in this work, it cannot be expected that the proposed method of TV post-processing will work for arbitrary types of scans.

Constrained image reconstruction of undersampled data facilitates pronounced speedups in MR data acquisition. This work introduces the new concept of Total Generalized Variation for image reconstruction of subsampled spiral k-space data. Results from brain and angiography examinations are shown which demonstrate effective elimination of aliasing artifacts and high SNR without the introduction of staircasing artifacts that are common for Total Variation based methods

ntroduction: The Total Variation (TV) regularization model is popular in MR research for various applications including denoising [1] or constrained image reconstruction [2]. In the TV-model, a regularization parameter controls the trade-off between noise elimination, and preservation of image details. However, MR images are comprised of multiple details. This indicates that different amounts of regularization are desirable for regions with fine image details in order to obtain better restoration results. In this work spatially dependent regularization parameter selection for TV based image restoration is introduced. Utilizing this technique, the regularization parameter is adapted automatically based on the details in the images, which improves the reconstruction of details while still providing adequate smoothing for the homogeneous parts. Theory: In order to enhance image regions containing details while still sufficiently smoothing homogeneous parts, we improve the TV-model by using a spatially dependent regularization parameter instead of a scalar value only, ie we consider

Introduction: Iterative image reconstruction methods have become increasingly popular for parallel imaging or constrained reconstruction methods, but the main drawback is the long reconstruction time. In the case of non-Cartesian imaging, resampling of k-space data between Cartesian and non-Cartesian grids has to be performed in each iteration step. Therefore the gridding procedure tends to be the time limiting step in these reconstruction strategies. With the upcoming parallel computing toolkits (such as CUDA [1]) for graphics processing units (GPUs) image reconstruction can be accelerated in a tremendous way [2, 3]. In this work, we present a fast GPU based gridding method and a corresponding inverse-gridding procedure by reformulating the gridding procedure as a linear problem with a sparse system matrix (see Fig. 1), similar to the approach in [4]. Methods: In MR literature the term “gridding” is often used as a synonym for a convolution interpolation. This process can be easily formulated as a problem of solving a set of linear equations

Nonlinear parallel imaging reconstruction using an iterative regularized Gauss Newton method (IRGN) has shown its potential in several applications [1]. This technique determines both the coil sensitivities and the image from undersampled multi-coil data. It enables high acceleration factors without pronounced local enhancement of noise. The numerical implementation of this sophisticated method requires data normalization steps which are usually performed individually for each slice and echo. In this study it was investigated if this type of reconstruction is applicable for quantitative imaging despite the complex reconstruction including image individual normalization. For that purpose high resolution multi-echo imaging with different acceleration factors was used for the quantification of the transverse relaxation time (T2).