Sparse MRI: The application of compressed sensing for rapid MR imaging

@article{Lustig2007SparseMT,
  title={Sparse MRI: The application of compressed sensing for rapid MR imaging},
  author={Michael Lustig and David L. Donoho and John M. Pauly},
  journal={Magnetic Resonance in Medicine},
  year={2007},
  volume={58}
}
The sparsity which is implicit in MR images is exploited to significantly undersample k‐space. Some MR images such as angiograms are already sparse in the pixel representation; other, more complicated images have a sparse representation in some transform domain–for example, in terms of spatial finite‐differences or their wavelet coefficients. According to the recently developed mathematical theory of compressed‐sensing, images with a sparse representation can be recovered from randomly… 
Exploitation of Sparsity in MRI
TLDR
The most commonly used pseudorandom sampling patterns, ‘sparsifying transforms’, and iterative mathematical techniques for processing undersampled Cartesian data are described with examples for a speed-up factor near 5.0 and how this kind of processing might someday become product, as did its predecessor, parallel imaging is discussed.
Quality assessment of fast wavelet-encoded MRI utilizing compressed sensing
TLDR
The simulation results show that the performance of CS reconstruction in wavelet-encoded MRI is more accurate and stable than in Fourier-encoding MRI with the same undersampling rate and noise level, at a significantly reduced scan time.
Iterative thresholding compressed sensing MRI based on contourlet transform
TLDR
Simulation results demonstrate that contourlet-based CS-MRI can better reconstruct the curves and edges than traditional wavelet- based methods, especially at low k-space sampling rate.
Compressed sensing MRI with singular value decomposition-based sparsity basis
TLDR
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.
Hybrid regularization for compressed sensing MRI: Exploiting shearlet transform and group-sparsity total variation
TLDR
Undersampled MRI reconstruction is formulated as a least-squares optimization problem regularized by shearlet transform and overlapping-group sparsity-promoting total variation (OSTV) to improve image quality and guarantee solution stability and efficiency.
Compressed sensing MRI using Singular Value Decomposition based sparsity basis
TLDR
Singular Value Decomposition is proposed as a data-adaptive sparsity basis for compressed sensing MRI that can potentially sparsify a broader range of MRI images and improve the image quality, thus providing a simple and effective solution for the application of compressed sensing in MRI.
Wavelet encoded MR image reconstruction with compressed sensing
TLDR
Simulation results show that the proposed encoding scheme has different characteristics than conventional Fourier and wavelet encoding methods, and this scheme could be applied to fast MR image acquisition at relatively high resolution.
Fast magnetic resonance imaging simulation with sparsely encoded wavelet domain data in a compressive sensing framework
TLDR
This MR image reconstruction uses a CS algorithm based on the minimization of total-variation regularized signal to provide stable results and the simulated results show that this approach can reduce almost 70% of MR image acquisition time and achieve good reconstructed image quality.
...
...

References

SHOWING 1-10 OF 46 REFERENCES
k-t SPARSE: High frame rate dynamic MRI exploiting spatio-temporal sparsity
TLDR
A method for high frame-rate dynamic imaging based on similar ideas, now exploiting both spatial and temporal sparsity of dynamic MRI image sequences (dynamic scene) by exploiting sparsity by constraining the reconstruction to have a sparse representation and be consistent with the measured data by solving the constrained optimization problem.
Undersampled radial MRI with multiple coils. Iterative image reconstruction using a total variation constraint
TLDR
An iterative reconstruction method for undersampled radial MRI which is based on a nonlinear optimization, allows for the incorporation of prior knowledge with use of penalty functions, and deals with data from multiple coils is developed.
Highly constrained backprojection for time‐resolved MRI
TLDR
A simple non‐iterative unfiltered backprojection algorithm that incorporates the idea of a composite image consisting of portions or all of the acquired data to constrain the back projection process is presented, which significantly reduces streak artifacts and increases the overall SNR.
Faster Imaging with Randomly Perturbed, Undersampled Spirals and |L|_1 Reconstruction
TLDR
A fast imaging method based on undersampled k-space spiral sampling and non-linear reconstruction, inspired by theoretical results in sparse signal recovery, allowing 50% undersampling by adapting spiral MR imaging and introducing randomness by perturbing the authors' spiral trajectories.
Undersampled projection reconstruction applied to MR angiography
TLDR
Undersampled projection reconstruction (PR) is investigated as an alternative method for MRA (MR angiography), where bright, contrast‐filled vessels dominate, artifacts are often acceptable and the greater resolution per unit time provided by undersampled PR can be realized.
SENSE: Sensitivity encoding for fast MRI
TLDR
The problem of image reconstruction from sensitivity encoded data is formulated in a general fashion and solved for arbitrary coil configurations and k‐space sampling patterns and special attention is given to the currently most practical case, namely, sampling a common Cartesian grid with reduced density.
Non-Cartesian MRI scan time reduction through sparse sampling
TLDR
Non-Cartesian MRI Scan-Time Reduction through Sparse Sampling Magnetic resonance imaging (MRI) signals are measured in the Fourier domain, also called k-space, where no dimension is completely sampled and the image can not be treated column-wise, and two image reconstruction algorithms are presented.
Efficient k‐space sampling by density‐weighted phase‐encoding
TLDR
Density‐weighted phase‐encoding combines the improved shape of the spatial response function and the high SNR of acquisition‐weighting with an extended field of view to improve the localization of MRI experiments.
Extensions of compressed sensing
k‐t BLAST and k‐t SENSE: Dynamic MRI with high frame rate exploiting spatiotemporal correlations
TLDR
Based on this approach, two methods were developed to significantly improve the performance of dynamic imaging, named k‐t BLAST (Broad‐use Linear Acquisition Speed‐up Technique) and k-t SENSE (SENSitivity Encoding) for use with a single or multiple receiver coils, respectively.
...
...