A statistical approach to SENSE regularization with arbitrary k‐space trajectories

SENSE reconstruction suffers from an ill‐conditioning problem, which increasingly lowers the signal‐to‐noise ratio (SNR) as the reduction factor increases. Ill‐conditioning also degrades the convergence behavior of iterative conjugate gradient reconstructions for arbitrary trajectories. Regularization techniques are often used to alleviate the ill‐conditioning problem. Based on maximum a posteriori statistical estimation with a Huber Markov random field prior, this study presents a new method for adaptive regularization using the image and noise statistics. The adaptive Huber regularization addresses the blurry edges in Tikhonov regularization and the blocky effects in total variation (TV) regularization. Phantom and in vivo experiments demonstrate improved image quality and convergence speed over both the unregularized conjugate gradient method and Tikhonov regularization method, at no increase in total computation time. Magn Reson Med 60:414–421, 2008. © 2008 Wiley‐Liss, Inc.     

A noniterative method to design large-tip-angle multidimensional spatially-selective radio frequency pulses for parallel transmission.

Recently, theoretical and experimental work has shown that parallel transmission of RF pulses can be used to shorten the duration of multidimensional spatially-selective pulses and compensate for B(1) field inhomogeneity. However, all the existing noniterative methods can design only excitation pulses for parallel transmission with a small flip angle (e.g., 30 degrees , or at most 90 degrees ) and cannot design large-tip-angle inversion/refocusing pulses, because these methods are based on the small-tip-angle (STA) approximation of the Bloch equation. In this work, a method to design large-tip-angle multidimensional spatially-selective pulses for parallel transmission is proposed, based on an extension of the single-channel linear-class large-tip-angle (LCLTA) theory. Design examples of 2D refocusing and inversion parallel transmit pulses and magnetization profiles from Bloch equation simulations demonstrate the strength of the proposed method. A 2D spin-echo parallel transmission experiment on a slab phantom using a 180 degrees refocusing pulse with an eight-channel transmit-only array further validates the effectiveness of the proposed method.     

Direct parallel image reconstructions for spiral trajectories using GRAPPA.

The use of spiral trajectories is an efficient way to cover a desired k-space partition in magnetic resonance imaging (MRI). Compared to conventional Cartesian k-space sampling, it allows faster acquisitions and results in a slight reduction of the high gradient demand in fast dynamic scans, such as in functional MRI (fMRI). However, spiral images are more susceptible to off-resonance effects that cause blurring artifacts and distortions of the point-spread function (PSF), and thereby degrade the image quality. Since off-resonance effects scale with the readout duration, the respective artifacts can be reduced by shortening the readout trajectory. Multishot experiments represent one approach to reduce these artifacts in spiral imaging, but result in longer scan times and potentially increased flow and motion artifacts. Parallel imaging methods are another promising approach to improve image quality through an increase in the acquisition speed. However, non-Cartesian parallel image reconstructions are known to be computationally time-consuming, which is prohibitive for clinical applications. In this study a new and fast approach for parallel image reconstructions for spiral imaging based on the generalized autocalibrating partially parallel acquisitions (GRAPPA) methodology is presented. With this approach the computational burden is reduced such that it becomes comparable to that needed in accelerated Cartesian procedures. The respective spiral images with two- to eightfold acceleration clearly benefit from the advantages of parallel imaging, such as enabling parallel MRI single-shot spiral imaging with the off-resonance behavior of multishot acquisitions.     

Sensitivity encoding reconstruction with nonlocal total variation regularization

In sensitivity encoding reconstruction, the issue of ill conditioning becomes serious and thus the signal‐to‐noise ratio becomes poor when a large acceleration factor is employed. Total variation (TV) regularization has been used to address this issue and shown to better preserve sharp edges than Tikhonov regularization but may cause blocky effect. In this article, we study nonlocal TV regularization for noise suppression in sensitivity encoding reconstruction. The nonlocal TV regularization method extends the conventional TV norm to a nonlocal version by introducing a weighted nonlocal gradient function calculated from the weighted difference between the target pixel and its generalized neighbors, where the weights incorporate the prior information of the image structure. The method not only inherits the edge‐preserving advantage of TV regularization but also overcomes the blocky effect. The experimental results from in vivo data show that nonlocal TV regularization is superior to the existing competing methods in preserving fine details and reducing noise and artifacts. Magn Reson Med, 2011. © 2010 Wiley‐Liss, Inc.     

Encoding and reconstruction in parallel MRI

The advent of parallel MRI over recent years has prompted a variety of concepts and techniques for performing parallel imaging. A main distinguishing feature among these is the specific way of posing and solving the problem of image reconstruction from undersampled multiple-coil data. The clearest distinction in this respect is that between k-space and image-domain methods. The present paper reviews the basic reconstruction approaches, aiming to emphasize common principles along with actual differences. To this end the treatment starts with an elaboration of the encoding mechanisms and sampling strategies that define the reconstruction task. Based on these considerations a formal framework is developed that permits the various methods to be viewed as different solutions of one common problem. Besides the distinction between k-space and image-domain approaches, special attention is given to the implications of general vs lattice sampling patterns. The paper closes with remarks concerning noise propagation and control in parallel imaging and an outlook upon key issues to be addressed in the future.     

Motion corrected free-breathing delayed-enhancement imaging of myocardial infarction using nonrigid registration

PURPOSE: To develop and test an automatic free-breathing, delayed enhancement imaging method with improved image signal-to-noise ratio (SNR). MATERIALS AND METHODS: The proposed approach uses free-breathing, inversion-recovery single-shot fast imaging with steady precession (FISP) delayed-enhancement with respiratory motion compensation based on nonrigid image registration. Motion-corrected averaging is used to enhance SNR. RESULTS: Fully automatic, nonrigid registration was compared to previously validated rigid body registration that required user interaction. The performance was measured using the variance of edge positions in intensity profiles through the myocardial infarction (MI) enhanced region and through the right ventricular (RV) wall. Measured variation of the MI edge was 1.16 +/- 0.71 mm (N = 6 patients; mean +/- SD) for rigid body and 1.08 +/- 0.76 mm for nonrigid registration (no significant difference). On the other hand, significant improvement (P < 0.005) was found in the measurements at the RV edge where the SD was 2.06 +/- 0.56 mm for rigid body and 0.59 +/- 0.22 mm for nonrigid registration. CONCLUSION: The proposed approach achieves delayed enhancement images with high resolution and SNR without requiring a breathhold. Motion correction of free-breathing delayed-enhancement imaging using nonrigid image registration may be implemented in a fully automatic fashion and performs uniformly well across the full field of view (FOV).