# 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…

## 5,762 Citations

Exploitation of Sparsity in MRI

- Computer Science
- 2013

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.

Dynamic MRI reconstruction exploiting blind compressed sensing combined transform learning regularization

- Computer ScienceNeurocomputing
- 2020

Quality assessment of fast wavelet-encoded MRI utilizing compressed sensing

- Computer ScienceMedical Imaging
- 2012

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

- Computer Science
- 2010

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.

Sparse representations and compressive sensing in multi-dimensional signal processing

- Computer ScienceCSI Transactions on ICT
- 2019

State-of-the-art sparse reconstruction algorithms developed for parallel computing with multi-core CPU and GP-GPU is required for realtime or near-realtime implementations of multi-dimensional signal processing involving MRI, BAN and remote sensing images.

Hybrid regularization for compressed sensing MRI: Exploiting shearlet transform and group-sparsity total variation

- Computer Science2017 20th International Conference on Information Fusion (Fusion)
- 2017

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.

Magnetic resonance image reconstruction from undersampled measurements using a patch-based nonlocal operator

- Computer ScienceMedical Image Anal.
- 2014

Wavelet encoded MR image reconstruction with compressed sensing

- Computer ScienceMedical Imaging
- 2011

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

- Computer ScienceJ. Electronic Imaging
- 2013

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.

Data-driven adaptation of a union of sparsifying transforms for blind compressed sensing MRI reconstruction

- Computer ScienceSPIE Optical Engineering + Applications
- 2015

This work focuses on blind compressed sensing, and proposes a framework to simultaneously reconstruct the underlying image as well as the unknown model from highly undersampled measurements, and extends this model to a union of transforms model that is better suited to capture the diversity of features in MR images.

## References

SHOWING 1-10 OF 46 REFERENCES

k-t SPARSE: High frame rate dynamic MRI exploiting spatio-temporal sparsity

- Computer Science
- 2006

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

- PhysicsMagnetic resonance in medicine
- 2007

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

- MathematicsMagnetic resonance in medicine
- 2006

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

- Computer Science
- 2004

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

- PhysicsMagnetic resonance in medicine
- 2000

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

- PhysicsMagnetic resonance in medicine
- 1999

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

- Mathematics
- 2001

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.

Projection reconstruction MR imaging using FOCUSS

- MathematicsMagnetic resonance in medicine
- 2007

FOCUSS is effective for projection reconstruction MRI, since medical images are usually sparse in some sense and the center region of the undersampled radial k‐space samples still provides a low resolution, yet meaningful, image essential for the convergence of FOCUSS.

k‐t BLAST and k‐t SENSE: Dynamic MRI with high frame rate exploiting spatiotemporal correlations

- MathematicsMagnetic resonance in medicine
- 2003

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.