Leslie Ying

Accelerating SENSE using compressed sensing

Both parallel MRI and compressed sensing (CS) are emerging techniques to accelerate conventional MRI by reducing the number of acquired data. The combination of parallel MRI and CS for further acceleration is of great interest. In this paper, we propose a novel method to combine sensitivity encoding (SENSE), one of the standard methods for parallel MRI, and compressed sensing for rapid MR imaging (SparseMRI), a recently proposed method for applying CS in MR imaging with Cartesian trajectories. The proposed method, named CS‐SENSE, sequentially reconstructs a set of aliased reduced‐field‐of‐view images in each channel using SparseMRI and then reconstructs the final image from the aliased images using Cartesian SENSE. The results from simulations and phantom and in vivo experiments demonstrate that CS‐SENSE can achieve a reduction factor higher than those achieved by SparseMRI and SENSE individually and outperform the existing method that combines parallel MRI and CS. Magn Reson Med, 2009.

Joint image reconstruction and sensitivity estimation in SENSE (JSENSE).

Parallel magnetic resonance imaging (pMRI) using multichannel receiver coils has emerged as an effective tool to reduce imaging time in various applications. However, the issue of accurate estimation of coil sensitivities has not been fully addressed, which limits the level of speed enhancement achievable with the technology. The self‐calibrating (SC) technique for sensitivity extraction has been well accepted, especially for dynamic imaging, and complements the common calibration technique that uses a separate scan. However, the existing method to extract the sensitivity information from the SC data is not accurate enough when the number of data is small, and thus erroneous sensitivities affect the reconstruction quality when they are directly applied to the reconstruction equation. This paper considers this problem of error propagation in the sequential procedure of sensitivity estimation followed by image reconstruction in existing methods, such as sensitivity encoding (SENSE) and simultaneous acquisition of spatial harmonics (SMASH), and reformulates the image reconstruction problem as a joint estimation of the coil sensitivities and the desired image, which is solved by an iterative optimization algorithm. The proposed method was tested on various data sets. The results from a set of in vivo data are shown to demonstrate the effectiveness of the proposed method, especially when a rather large net acceleration factor is used. Magn Reson Med 57:1196–1202, 2007.

Regularized sensitivity encoding (SENSE) reconstruction using bregman iterations

In parallel imaging, the signal‐to‐noise ratio (SNR) of sensitivity encoding (SENSE) reconstruction is usually degraded by the ill‐conditioning problem, which becomes especially serious at large acceleration factors. Existing regularization methods have been shown to alleviate the problem. However, they usually suffer from image artifacts at high acceleration factors due to the large data inconsistency resulting from heavy regularization. In this paper, we propose Bregman iteration for SENSE regularization. Unlike the existing regularization methods where the regularization function is fixed, the method adaptively updates the regularization function using the Bregman distance at different iterations, such that the iteration gradually removes the aliasing artifacts and recovers fine structures before the noise finally comes back. With a discrepancy principle as the stopping criterion, our results demonstrate that the reconstructed image using Bregman iteration preserves both sharp edges lost in Tikhonov regularization and fines structures missed in total variation (TV) regularization, while reducing more noise and aliasing artifacts. Magn Reson Med 61:145–152, 2009.

On Tikhonov regularization for image reconstruction in parallel MRI

Parallel imaging using multiple receiver coils has emerged as an effective tool to reduce imaging time in various MRI applications. When a large number of receiver channels are used to achieve large acceleration factors, the image reconstruction problem can become very ill conditioned. This problem can be alleviated by optimizing the geometry of the coils or by mathematical regularization. Among the regularization methods, the Tikhonov scheme is most popular because of rough Gaussianity of the data noise, the easiness to incorporate prior information, as well as the existence of a closed-form solution. A central issue in implementing the Tikhonov scheme is the choice of the regularization parameter and the regularization image, which is addressed systematically in this paper. A new algorithm is also proposed for generating the regularization image and selecting the regularization parameter. Experimental results will be shown to demonstrate the performance of the algorithm.

K-t ISD: Dynamic cardiac MR imaging using compressed sensing with iterative support detection

Compressed sensing (CS) has been used in dynamic cardiac MRI to reduce the data acquisition time. The sparseness of the dynamic image series in the spatial‐ and temporal‐frequency (x‐f) domain has been exploited in existing works. In this article, we propose a new k‐t iterative support detection (k‐t ISD) method to improve the CS reconstruction for dynamic cardiac MRI by incorporating additional information on the support of the dynamic image in x‐f space based on the theory of CS with partially known support. The proposed method uses an iterative procedure for alternating between image reconstruction and support detection in x‐f space. At each iteration, a truncated ℓ1 minimization is applied to obtain the reconstructed image in x‐f space using the support information from the previous iteration. Subsequently, by thresholding the reconstruction, we update the support information to be used in the next iteration. Experimental results demonstrate that the proposed k‐t ISD method improves the reconstruction quality of dynamic cardiac MRI over the basic CS method in which support information is not exploited. Magn Reson Med, 2012.

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.

Toeplitz block matrices in compressed sensing and their applications in imaging

Recent work in compressed sensing theory shows that sensing matrices whose entries are drawn independently from certain probability distributions guarantee exact recovery of a sparse signal from a small number of measurements with high probability. In most medical imaging systems, the encoding matrices cannot take that form. Instead, they are Toeplitz block matrix. Motivated by this fact, we consider Toeplitz block matrices as the sensing matrices. We show that the probability of perfect reconstruction from a smaller number of filter outputs is also high if the filter coefficients are independently and identically-distributed random variable. Their applications in medical imaging is discussed. Simulation results are also shown to validate the theorem.

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.

Adaptive Dictionary Learning in Sparse Gradient Domain for Image Recovery

Image recovery from undersampled data has always been challenging due to its implicit ill-posed nature but becomes fascinating with the emerging compressed sensing (CS) theory. This paper proposes a novel gradient based dictionary learning method for image recovery, which effectively integrates the popular total variation (TV) and dictionary learning technique into the same framework. Specifically, we first train dictionaries from the horizontal and vertical gradients of the image and then reconstruct the desired image using the sparse representations of both derivatives. The proposed method enables local features in the gradient images to be captured effectively, and can be viewed as an adaptive extension of the TV regularization. The results of various experiments on MR images consistently demonstrate that the proposed algorithm efficiently recovers images and presents advantages over the current leading CS reconstruction approaches.

Functional MRI in the assessment of cortical activation during gait-related imaginary tasks.

Imaginary tasks can be used to investigate the neurophysiology of gait. In this study, we explored the cortical control of gait-related imagery in 21 healthy volunteers using functional magnetic resonance imaging. Imaginary tasks included gait initiation, stepping over an obstacle, and gait termination. Subjects watched a video clip that showed an actor in gait motion under an event-related design. We detected activation in the supplementary motor area during major gait-related imagery tasks, and especially during gait initiation. During gait termination and stepping over an obstacle, the amount of cortical resources allocated to the imaginary tasks included a large visuomotor network comprising the dorsal and ventral premotor areas. We conclude that our paradigm to study the cortical control of gait may help in elucidating the pathophysiology of higher-level gait disorders.