k‐t group sparse: A method for accelerating dynamic MRI

Abstract

Compressed sensing (CS) is a data-reduction technique that has been applied to speed up the acquisition in MRI. However, the use of this technique in dynamic MR applications has been limited in terms of the maximum achievable reduction factor. In general, noise-like artefacts and bad temporal fidelity are visible in standard CS MRI reconstructions when high reduction factors are used. To increase the maximum achievable reduction factor, additional or prior information can be incorporated in the CS reconstruction. Here, a novel CS reconstruction method is proposed that exploits the structure within the sparse representation of a signal by enforcing the support components to be in the form of groups. These groups act like a constraint in the reconstruction. The information about the support region can be easily obtained from training data in dynamic MRI acquisitions. The proposed approach was tested in two-dimensional cardiac cine MRI with both downsampled and undersampled data. Results show that higher acceleration factors (up to 9-fold), with improved spatial and temporal quality, can be obtained with the proposed approach in comparison to the standard CS reconstructions. Key words: compressed sensing; undersampling; group sparsity; l 1 minimization; dynamic MRI Dynamic MRI applications usually require high spatial and temporal resolution. The acquisition speed of MR images, however, is limited by physical (e.g., gradient strength and slew rate) and physiological (e.g., nerve stimulation) constraints (1). To address this issue, several reconstruction techniques have been proposed that can reconstruct MR images of significant quality from reduced data acquisitions. Following Tsao et al.'s classification (2), these techniques can be classified into those which exploit correlations in the k-space (3-8), in time domain (9-13) or in both k-space and time domains (2,14,15).Recently, a new data reduction technique titled ''compressed sensing'' (CS) (16,17) has been proposed for application in MRI. According to the CS theory, perfect reconstruction of a signal is possible from sampling rates below the Shannon-Nyquist limit, provided the signal is sparse (in itself or in some transform domain) and the measurement samples are obtained with an incoherent basis. For dynamic MRI, Lustig et al. proposed a CS technique called ''k-t sparse'' (18) in which the undersampled data acquisition was done in the phase encodetime dimension (k-t space) by randomly skipping the phase encodes for each time frame. The sparsity was introduced by transforming the dynamic MR data using a wavelet transform and a Fourier transform along spatial and temporal directions, respectively. Alternatively, Gamper et al. (19) showed that a Fourier transform along the temporal dimension was sufficient to achieve sparsity in x-f space, where x is spatial position and f is temporal frequency. For low reduction factors (up to 3-fold), Gamper demonstrated that CS reconstructions exhibit less error than k-t Broad-use Linear Acquisition Speedup Technique (BLAST...

Motion Compensation Strategies in Magnetic Resonance Imaging

“…113,114 Here, sparsity can often be found in the evolution of the signal intensity of a given voxel through the frames when this voxel is analyzed in the time-frequency domain. In whole-heart coronary MRA, CS can also be applied to overcome the strict constraints that are set by motion, thus allowing the acquisition of a whole-heart volume in one breath hold, 115 or it can be used to compensate for respiratory motion in free-breathing acquisitions.…”

Group Sparse Reconstruction of Multi-Dimensional Spectroscopic Imaging in Human Brain in vivo

“…The Split Bregman algorithm has been previously used for TV-based reconstruction of NUS MRSI data [16] and for multi-channel reconstruction of NUS MRI data where the multiple measurement vector (MMV) problem was solved by extending the algorithm to accommodate row-wise grouping of jointly sparse samples [20]. GS reconstruction has previously been applied to the under-sampled k y − t planes of 2D cine and perfusion cardiac MRI and provided superior results to CS [21,22].…”

Reference-Driven Compressed Sensing MR Image Reconstruction with Partially Known Support and Group Sparsity Constraints

“…Since Lustig et al [7] proposed CS-based MR image reconstruction, applying state-of-the-art methods in CS to MRI reconstruction is one of the CS-MRI research trends. Prieto and Usman et al [8,12] improved the standard CS-MRI by exploiting the group sparsity of dynamic MRI. Babacan et al [1] presented a framework based on image modeling within union-of-subspaces, and applying it to interventional MRI (iMRI).…”