Compressed sensing for body MRI

Abstract

The introduction of compressed sensing for increasing imaging speed in magnetic resonance imaging (MRI) has raised significant interest among researchers and clinicians, and has initiated a large body of research across multiple clinical applications over the last decade. Compressed sensing aims to reconstruct unaliased images from fewer measurements than are traditionally required in MRI by exploiting image compressibility or sparsity. Moreover, appropriate combinations of compressed sensing with previously introduced fast imaging approaches, such as parallel imaging, have demonstrated further improved performance. The advent of compressed sensing marks the prelude to a new era of rapid MRI, where the focus of data acquisition has changed from sampling based on the nominal number of voxels and/or frames to sampling based on the desired information content. This article presents a brief overview of the application of compressed sensing techniques in body MRI, where imaging speed is crucial due to the presence of respiratory motion along with stringent constraints on spatial and temporal resolution. The first section provides an overview of the basic compressed sensing methodology, including the notion of sparsity, incoherence, and nonlinear reconstruction. The second section reviews state-of-the-art compressed sensing techniques that have been demonstrated for various clinical body MRI applications. In the final section, the article discusses current challenges and future opportunities.

Level of evidence: 5 J. Magn. Reson. Imaging 2017;45:966-987.

Keywords: MRI; body imaging; compressed sensing; rapid imaging; sparsity.

Figure 1

Comparison of standard image compression (a) and compressed sensing (b). Image compression first acquires a fully-sampled image and then compresses it in the second step. Compressed sensing, on the other hand, builds the compression into the encoding process, thus acquiring only a subset of the encoding steps in a random pattern. The image is subsequently reconstructed from undersampled data with a suitable nonlinear algorithm. F: Fourier transform; T: sparsifying transform; CS: compressed sensing.

Figure 2

MR images can be considered sparse in an appropriate transform domain. A liver image has as parse representation (i.e. a representation with a small number of high-value coefficients) in the wavelet space (a), and a dynamic contrast-enhanced image series has a sparse representation in the x-y-f (two spatial dimensions + temporal frequency dimension) space, with a FFT (fast Fourier transform) performed along the temporal dimension (b).

Figure 3

(a) Regular undersampling generates coherent replicas of the signal structure; (b) Random undersampling generates incoherent artifacts that appear like added noise; (c) radial sampling permits undersampling along both spatial dimensions and thus enables a higher level of incoherence.

Figure 4

(a) 2D Cartesian undersampling pattern, where undersampling is only performed along the phaseencoding dimension (ky); (b) 3D Cartesian undersampling pattern, where undersampling can be performed along two spatial dimensions (ky and kz); (c) 3D Cartesian undersampling pattern based on the Poisson-disc distribution, which limits the distances between samples across the entire k-space, with full sampling in a small central region; (d) 2D dynamic Cartesian undersampling pattern, where a different sampling pattern can be employed in each temporal frame to provide additional temporal incoherence. White lines or points indicate acquired data.

Figure 5

Various 3D golden-angle sampling schemes. (a) Stack-of-stars scheme, in which radial sampling is implemented in the kx–ky plane and Cartesian sampling is implemented in the kz plane; (b) Stack-of-spiral scheme, in which spiral sampling is implemented in the kx–ky plane and Cartesian sampling is implemented in the kz plane; (c) 3D Cartesian sampling, in which the k-space sampling in the ky–kz plane is segmented into multiple interleaves rotated by a golden-angle.

Figure 6

Comparison of soft-gating with XD-GRASP sorting. Soft-gating (a) reduces motion blurring by binning the acquired k-space and then weighting them according to their motion state in the reconstruction process. XD-GRASP (b) sorts the acquired k-space data into multiple separated motion states and creates an additional motion dimension. Compressed sensing is performed to exploit correlations along the new dimension.

Figure 7

L₁-ESPIRiT with either soft-gating or autofocusing achieved better image quality of the portal vein than L₁-ESPIRiT without motion compensation (yellow dashed arrows). A combination of soft-gating and autofocusing enabled further improvement in delineation of the liver dome (white arrow) and the hepatic vessels (yellow dashed arrows) compared to L₁-ESPIRiT with soft-gating or autofocusing alone, and also achieved better delineation of the hepatic vessels than the respiratory triggered reference. (Images were obtained from the Figure 4 in Cheng JY et al. J Magn Reson Imaging. 2015 2015 Aug;42(2):407–20 and were reproduced with permission from the authors and the journal.)

Figure 8

Comparison of maximum intensity projection (MIP) images between breath-held SPARSE-MRCP (MR Cholangiopancreatography) and respiratory-triggered MRCP in two patients. In patient 1, breath-held SPARSE-MRCP achieved better image quality (despite approximately 17-fold acceleration) than freebreathin respiratory-triggered MRCP, which showed significant residual motion blurring due to poor respiratory triggering. In patient 2, breath-held SPARSE-MRCP demonstrated image quality comparable to that of the respiratory-triggered MRCP. (Images were modified from the Figure 2 and Figure 4 in Chandarana H et al. Radiology. 2016 Aug;280(2):585–94 and were reproduced with permission from the authors and the journal.)

Figure 9

(a) L₁-ESPIRiT reconstruction with no motion weighting (left) and with soft respiratory gating (right). Soft-gating improves the delineation of the liver edge (dashed arrows) and the hepatic vessels (solid arrows). (b) Zoomed and cropped image of the spleen and kidney at different contrast enhancement phases with a spatial resolution of 1.1x1.1 mm2. The time of acquisition is shown on top of each contrast phase. Images show the progressive enhancement from cortical to medullary region of the kidney, as well as the perfusion pattern of the spleen. (Images were obtained from the Figure 2c and Figure 5a in Zhang T et al. J Magn Reson Imaging. 2015 Feb;41(2):460–73 and were reproduced with permission from the authors and the journal.)

Figure 10

Comparison of conventional breath-hold VIBE (left) with free-breathing GRASP (right) in the arterial phase (top row) and the venous phase (bottom row). GRASP achieved image quality comparable to that of the breath-hold references in healthy volunteers who have excellent breath-holding capacity. (Images were obtained from the Figure 4 and Figure 5 in Chandarana H et al. Invest Radiol. 2013 Jan;48(1):10–6 and were reproduced with permission from the authors and the journal.)

Figure 11

Comparison of GRASP without motion compensation to XD-GRASP with reconstruction of an extra respiratory motion for three image slices. XD-GRASP achieved improved vessel-tissue contrast and vessel sharpness (white arrows in slice 1 and slice 2), and better delineation of hepatocellular carcinoma previously treated with chemoembolization (white arrow in slice 3).

Figure 12

Representative results obtained with Cartesian (A–D, I) and spiral (E–H, J) 4D flow imaging techniques. Magnitude images are shown in A and E and phase-difference images are shown in B–D and F–H. VX, VY, and VZ correspond to velocity measured with motion-encoding gradients in right-left, anteriorposterior, and foot-head directions, respectively. I and J are 3D angiograms showing segmented view of portal, splenic, and superior mesenteric veins with comparable quality and conspicuity. Dark lines proximal to spleen on Cartesian series (yellow arrow) show cross-beam navigator used for respiratory gating in Cartesian acquisition. (Images were obtained from the Figure 2 in Dyvorne H et al. Radiology 2015 Apr;275(1):245–54 and were reproduced with permission from the authors and the journal.)