Faculty Bibliography

PURPOSE–DTI acquisitions take a long time. Undersampling reduces scan time but leads to artifacts with normal reconstruction. Parallel imaging with nonlinear variational constraints has been shown to reduce artifacts in reconstruction of undersampled data [1, 2]. However, the effects of nonlinear regularization methods on quantitative evaluation of DTI data are not well studied. Here the quantitative accuracy of a 3D spiral acquisition using 3D second order Total Generalized Variation (TGV2) as a penalty term is evaluated in a simulated atlas-based DTI phantom. Reconstructed values of the FA and principle eigenvector direction were compared for different noise levels

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 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.

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.

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.