# Compressed Sensing MRI

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Home / Compressed Sensing MRI#### Project Summary

Compressed sensing exploits the compressibility of medical images to reconstruct undersampled data (below the Nyquist rate) without loss of information. The technique can be applied to MRI to increase imaging speed or to CT to reduce radiation dose. Compressed sensing is based on three major components: (1) sparsity of representation is some known domain, (2) incoherent measurements, which are usually achieved by irregular sampling patterns such as random sampling, and (3) sparsity-constrained non-linear reconstruction. In practice, about four incoherent samples are required for each sparse coefficient. If the total number of points in the image is larger than four times the number of sparse coefficients, which is usually the case in practice due to extensive signal correlations, reconstruction of undersampled data is feasible

MRI is a particular good candidate for the application of compressed sensing since data acquisition is performed in a transform domain (k-space) instead of the image domain, which facilitates the generation of incoherent aliasing artifacts. Moreover, compressed sensing can be combined with parallel imaging to increase the acceleration or undersampling rate. We have developed general methods that combine compressed sensing and parallel imaging to speed up MRI, such as k-t SPARSE-SENSE and GRASP, which have been applied to a variety of clinical studies.

Compressed sensing and parallel imaging can be combined using the notion of joint sparsity in the multicoil image ensemble. Using this approach, the additional spatial encoding capabilities of multiple receiver coils can be exploited to reduce the incoherent aliasing artifacts and thus enable higher acceleration rates. The joint reconstruction is given by:

*min||Wx||*

_{1}subject to ||Ex - y||_{2}< ε

Where W is the sparsifying transform, x is the image to reconstruct, E is the multicoil acquisition operator (undersampled Fourier transform + coil sensitivities), y is the undersampled k-space data, is the p-norm and ε is a data fidelity threshold (usually set to the noise level). The l1-norm term enforces joint multicoil sparsity, since x represents the contributions from all coils, and the l2-norm term enforces multicoil data consistency

We have implemented this combination of compressed sensing and parallel imaging for Cartesian and radial sampling of k-space. The Cartesian version (named k-t SPARSE-SENSE for the case of dynamic MRI) uses random undersampling patterns and the radial version (GRASP: Golden-angle RAdial Sparse Parallel) uses golden-angle radial sampling. Radial trajectories are an attractive alternative for compressed sensing, due to the inherent presence of incoherent aliasing artifacts in multiple dimensions, even for regular undersampling, which enables us to exploit additional sparsity and incoherence along frequency-encoding dimensions (not feasible in Cartesian sampling). The use of golden-angle acquisition schemes in dynamic radial MRI, where uniform coverage of k-space is obtained by grouping consecutive spokes, further increases incoherence and allows for continuous data acquisition and reconstruction with arbitrary temporal resolution at arbitrary time points.

#### Example: Whole Heart Perfusion

8-fold accelerated cardiac perfusion using k-t SPARSE-SENSE. The technique enabled the acquisition of 10 slices/heartbeat which cover most of the heart with temporal resolution of 60ms/slice and in-plane resolution of 1.67 mm

#### Example: Whole Liver Perfusion

Free-breathing 3D dynamic liver imaging using GRASP. Only 13 radial spokes were employed to reconstruct each temporal frame resulting in a temporal resolution of about 1.5 sec to image the entire liver with a spatial resolution of 1×1×3 mm3

Otazo R, Kim D, Axel L, Sodickson DK. Combination of compressed sensing and parallel imaging for highly accelerated first-pass cardiac perfusion MRI. Magn Reson Med. 2010; 64(3):767-76.

Kim D, Dyvorne HA, Otazo R, Feng L, Sodickson DK, Lee VS. Accelerated phase-contrast cine MRI using k-t SPARSE-SENSE. Magn Reson Med. 2012;67(4):1054-64.

Feng L, Srichai MB, Lim RP, Harrison A, King W, Adluru G, Dibella EV, Sodickson DK, Otazo R, Kim D. Highly accelerated real-time cardiac cine MRI using k-t SPARSE-SENSE. Magn Reson Med. 2012 Aug 6.

Feng L, Chandarana H, Xu J, Block T, Sodickson DK, Otazo R. k-t radial SPARSE-SENSE: Combination of compressed sensing and parallel imaging with golden angle radial sampling for highly accelerated volumetric dynamic MRI. 20th Annual ISMRM Meeting, Melbourne, Australia, 2012, p. 81.

Chandarana H, Feng L, Block TK, Rosenkrantz AB, Lim RP, Babb JS, Sodickson DK, Otazo R. Free-breathing contrast-enhanced multiphase MRI of the liver using a combination of compressed sensing, parallel imaging, and golden-angle radial sampling. Invest Radiol. 2013;48(1):10-6.

Otazo R, Feng L, Chandarana H, Block KT, Sodickson DK. Combination of compressed sensing and parallel imaging for highly-accelerated dynamic MRI. 9th IEEE International Symposium on Biomedical Imaging (ISBI), Barcelona, Spain, 2012, pp. 980-3.

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#### Philanthropic Support

We gratefully acknowledge generous support for radiology research at NYU Langone Health from:

• The Big George Foundation

• Raymond and Beverly Sackler

• Bernard and Irene Schwartz

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