Multidimensional compressed sensing MRI using tensor decomposition-based sparsifying transform.

Compressed Sensing (CS) has been applied in dynamic Magnetic Resonance Imaging (MRI) to accelerate the data acquisition without noticeably degrading the spatial-temporal resolution. A suitable sparsity basis is one of the key components to successful CS applications. Conventionally, a multidimensional dataset in dynamic MRI is treated as a series of two-dimensional matrices, and then various matrix/vector transforms are used to explore the image sparsity. Traditional methods typically sparsify the spatial and temporal information independently. In this work, we propose a novel concept of tensor sparsity for the application of CS in dynamic MRI, and present the Higher-order Singular Value Decomposition (HOSVD) as a practical example. Applications presented in the three- and four-dimensional MRI data demonstrate that HOSVD simultaneously exploited the correlations within spatial and temporal dimensions. Validations based on cardiac datasets indicate that the proposed method achieved comparable reconstruction accuracy with the low-rank matrix recovery methods and, outperformed the conventional sparse recovery methods.

Sparsity-constrained SENSE reconstruction: an efficient implementation using a fast composite splitting algorithm.

Parallel imaging and compressed sensing have been arguably the most successful and widely used techniques for fast magnetic resonance imaging (MRI). Recent studies have shown that the combination of these two techniques is useful for solving the inverse problem of recovering the image from highly under-sampled k-space data. In sparsity-enforced sensitivity encoding (SENSE) reconstruction, the optimization problem involves data fidelity (L2-norm) constraint and a number of L1-norm regularization terms (i.e. total variation or TV, and L1 norm). This makes the optimization problem difficult to solve due to the non-smooth nature of the regularization terms. In this paper, to effectively solve the sparsity-regularized SENSE reconstruction, we utilize a new optimization method, called fast composite splitting algorithm (FCSA), which was developed for compressed sensing MRI. By using a combination of variable splitting and operator splitting techniques, the FCSA algorithm decouples the large optimization problem into TV and L1 sub-problems, which are then, solved efficiently using existing fast methods. The operator splitting separates the smooth terms from the non-smooth terms, so that both terms are treated in an efficient manner. The final solution to the SENSE reconstruction is obtained by weighted solutions to the sub-problems through an iterative optimization procedure. The FCSA-based parallel MRI technique is tested on MR brain image reconstructions at various acceleration rates and with different sampling trajectories. The results indicate that, for sparsity-regularized SENSE reconstruction, the FCSA-based method is capable of achieving significant improvements in reconstruction accuracy when compared with the state-of-the-art reconstruction method.

Compressed sensing MRI with singular value decomposition-based sparsity basis.

Compressed sensing MRI (CS-MRI) aims to significantly reduce the measurements required for image reconstruction in order to accelerate the overall imaging speed. The sparsity of the MR images in transformation bases is one of the fundamental criteria for CS-MRI performance. Sparser representations can require fewer samples necessary for a successful reconstruction or achieve better reconstruction quality with a given number of samples. Generally, there are two kinds of 'sparsifying' transforms: predefined transforms and data-adaptive transforms. The predefined transforms, such as the discrete cosine transform, discrete wavelet transform and identity transform have usually been used to provide sufficiently sparse representations for limited types of MR images, in view of their isolation to the object images. In this paper, we present singular value decomposition (SVD) as the data-adaptive 'sparsity' basis, which can sparsify a broader range of MR images and perform effective image reconstruction. The performance of this method was evaluated for MR images with varying content (for example, brain images, angiograms, etc), in terms of image quality, reconstruction time, sparsity and data fidelity. Comparison with other commonly used sparsifying transforms shows that the proposed method can significantly accelerate the reconstruction process and still achieve better image quality, providing a simple and effective alternative solution in the CS-MRI framework.

Compressed sensing MRI using Singular Value Decomposition based sparsity basis.

Magnetic Resonance Imaging (MRI) is an essential medical imaging tool limited by the data acquisition speed. Compressed Sensing is a newly proposed technique applied in MRI for fast imaging with the prior knowledge that the signals are sparse in a special mathematic basis (called the 'sparsity' basis). During the exploitation of the sparsity in MR images, there are two kinds of 'sparsifying' transforms: predefined transforms and data adaptive transforms. Conventionally, predefined transforms, such as the discrete cosine transform and discrete wavelet transform, have been adopted in compressed sensing MRI. Because of their independence from the object images, the conventional transforms can only provide ideal sparse representations for limited types of MR images. To overcome this limitation, this work proposed Singular Value Decomposition as a data-adaptive sparsity basis for compressed sensing MRI that can potentially sparsify a broader range of MRI images. The proposed method was evaluated by a comparison with other commonly used predefined sparsifying transformations. The comparison shows that the proposed method could give a sparser representation for a broader range of MR images and could improve the image quality, thus providing a simple and effective alternative solution for the application of compressed sensing in MRI.

Comparison and analysis of nonlinear algorithms for compressed sensing in MRI.

Compressed sensing (CS) theory has been recently applied in Magnetic Resonance Imaging (MRI) to accelerate the overall imaging process. In the CS implementation, various algorithms have been used to solve the nonlinear equation system for better image quality and reconstruction speed. However, there are no explicit criteria for an optimal CS algorithm selection in the practical MRI application. A systematic and comparative study of those commonly used algorithms is therefore essential for the implementation of CS in MRI. In this work, three typical algorithms, namely, the Gradient Projection For Sparse Reconstruction (GPSR) algorithm, Interior-point algorithm (l(1)_ls), and the Stagewise Orthogonal Matching Pursuit (StOMP) algorithm are compared and investigated in three different imaging scenarios, brain, angiogram and phantom imaging. The algorithms' performances are characterized in terms of image quality and reconstruction speed. The theoretical results show that the performance of the CS algorithms is case sensitive; overall, the StOMP algorithm offers the best solution in imaging quality, while the GPSR algorithm is the most efficient one among the three methods. In the next step, the algorithm performances and characteristics will be experimentally explored. It is hoped that this research will further support the applications of CS in MRI.