Faculty Bibliography

Magnetic resonance images which are corrupted by noise and by smooth modulations are corrected using a variational formulation incorporating a total variation like penalty for the image and a high order penalty for the modulation. The optimality system is derived and numerically discretized. The cost functional used is non-convex, but it possesses a bilinear structure which allows the ambiguity among solutions to be resolved technically by regularization and practically by normalizing the maximum value of the modulation. Since the cost 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 cost is minimized with respect to one variable after the other using an inner generalized Newton iteration. Favorable computational results are shown for artificial phantoms as well as for realistic magnetic resonance images. Reported computational times demonstrate the feasibility of the approach in practice. (C) 2011 Published by Elsevier Inc.

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.

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