Clinical Applications of Compressed Sensing
Akira Yamamoto1

1Department of Diagnostic Imaging and Nuclear Medicine, Kyoto University, Graduate School of Medicine, Kyoto, Japan


Through these clinical MR images, we try to explain three key elements essential for compressed sensing. The first is sparsity, the second is random sampling, and the third is nonlinear iterative image reconstruction. Since all of these keywords are unfamiliar to clinicians, we will try a simple and intuitive explanation that clinicians can understand necessity of these three elements by using MR image obtained with compressed sensing.


In clinical MRI practice, the technique to obtain MR images at high speed is one of very important methods. For example, MR imaging under sedation may be necessary for examination of children, MR imaging of abdominal organs may require holding of brth, and dynamic contrast enhanced MRI may require high temporal resolution. One of the emerging high-speed MR imaging techniques in clinical practice is compressed sensing. As a high-speed MR imaging method, parallel imaging methods such as SENSE or GRAPPA have been commonly used in clinical MRI. By reconstructing signals obtained with multiple receive coils having different sensitivity profiles, parallel imaging could shorten imaging time, and realize high speed imaging. In addition to this, compressed sensing makes use of a novel algorithm different from the image reconstruction method widely used in the past.

In this education lecture, we introduce three studies at our institution using compressed sensing. The first is the cerebral vascular time-of-flight MR angiography (TOF-MRA), the second is the MR cholangiopancreatography (MRCP), and the third is the breast dynamic contrast enhanced MRI. Through these clinical MR images, we try to explain three key elements essential for compressed sensing. The first is sparsity, the second is random sampling, and the third is nonlinear iterative image reconstruction. Since all of these keywords are unfamiliar to clinicians, we will try a simple and intuitive explanation that clinicians can understand necessity of these three elements by using MR image obtained with compressed sensing.

Three essential elements of compressed sensing

As we mentioned in the INTRODUCTION section above, compressed sensing requires three elements.

(1) Sparsity

"Sparsity" means that the MR image itself, or an MR image that has undergone appropriate transformation contains many zero elements. For example, TOF MR angiography of the brain has relatively few pixels of high signal (i.e. arterial blood) and many pixels with zero or close to zero outside of the brain tissue (i.e. background). For another example, if wavelet transformation, which is widely used for data compression of natural images, is successfully applied to MR images, most of the small coefficients can be eliminated without degrading image quality. It is not easy to obtain sparsely represented images. However, it become possible by making use of random sampling and nonlinear iterative reconstruction, which are mentioned below.

(2) Randomness

In the compressed sensing MRI, randomness is achieved by the semi-random sampling in k-space (i.e. image representation in the frequency domain). When k-space data is collected on a Cartesian grid with equidistant undersampling as is used in SENSE or GRAPPA, due to the periodicity, aliasing artifacts which clinicians are familiar with can be seen. In compressed sensing, it is very important that the observation (i.e. measurement by the MRI) can be "considered as nearly random", so it is desirable to choose an undersampling method that minimizes structural artifacts.

(3) Nonlinear iterative reconstruction

Nonlinear iterative reconstruction in compressed sensing is the unique part from conventional iterative image reconstruction method, such as iterative SENSE. By using a constraint called L1 regularization, image reconstruction by obtaining a sparse solution (in a transform domain such as wavelet) is performed using an iterative algorithm including nonlinear transformation such as soft thresholding. In this method, images are repeatedly calculated so that the L1 norm (sum of absolute values) of the wavelet coefficients is as small as possible while maintaining consistency with the observation (i.e. k-space) data. If sparsity and randomness are appropriate, MR images with similar image quality can be reconstructed with fewer sampling than the conventional method. This small sampling contributes to the high-speed MR imaging technique.

Clinical application of compressed sensing

(1) Cerebral vascular TOF-MRA

Cerebral vascular TOF-MRA is an imaging sequence that is routinely used and is one of imaging sequences essential in the evaluation of stroke. In TOF-MRA, reduction factor = 2 to 3 (speed increase by a factor of 2 to 3) by parallel imaging method using multichannel coils with different sensitivity profiles (e.g. using head 32-channel coil etc.) is possible. To further increase the speed beyond this point, due to the g-factor penalty, image degradation is likely to occur, which is unfeasible for clinical use. By introducing compressed sensing to TOF-MRA, it is possible to speed increase more than by a factor of 3 because g-factor penalty is not so strict in compressed sensing.

(2) 3-D MRCP

In the abdominal MR imaging, there is always a problem of motion of the abdominal organs due to respiration. Respiratory gated imaging and breath holding imaging are examples of countermeasures for respiratory movement. However, it cannot be said that the time with a single breath hold is sufficiently long to obtain a good quality 3-D MRCP image, and there is a possibility that the obtained image quality deteriorates to some extent in the breath holding imaging method. 3-D MRCP is an essential imaging sequence in diagnosis of common bile duct disease and pancreatic cancer. Although it is possible to acquire the 3-D MRCP image under single breath hold, image quality deterioration is large, and imaging is often performed by the respiratory gated method. Respiratory gated imaging has a problem that the imaging time is prolonged. By introducing compressed sensing into 3-D MRCP, it is possible to obtain image under single breath hold.

(3) Breast dynamic contrast enhanced MRI

For MRI diagnosis of breast cancer, a dynamic contrast enhance sequence is generally used. In the conventional diagnosis of breast cancer, we created a kinetic curve in dynamic contrast and performed benign / malignant diagnosis of the lesion. In particular, the existence of washout in the delayed phase has been considered important. From recent high-speed imaging method, view-sharing method, by introducing compressed sensing, imaging with even higher temporal resolution became possible while maintaining the spatial resolution of conventional images. In the temporal profile, it is noticed that detailed signal change (wash-in effect) in the very early phase from 1 to 2 minutes after injection of the contrast medium may become a new parameter for diagnosis. By using compressed sensing, time resolution of breast dynamic contrast enhanced MRI can also be increased.


This work was supported by Grant-in-Aid for Scientific Research on Innovative Areas “Initiative for High-Dimensional Data-Driven Science through Deepening of Sparse Modeling (No. 4503)” of The Ministry of Education, Culture, Sports, Science and Technology, Japan.

Support of the Grant-in-Aid for Scientific Research on Innovative Areas, MEXT, Japan (25120002, 25120008) is acknowledged.

I'd like to thank Dr. Koji Fujimoto for his great support in preparing this lecture.


1. Lustig, M., Donoho, D. and Pauly, J. M., Sparse MRI: The application of compressed sensing for rapid MR imaging, Magnetic Resonance in Medicine, 58 (2007), 1182-1195

2. Pruessmann, K. P., Weiger, M., Bornert, P. and Boesiger, P., Advances in sensitivity encoding with arbitrary k-space trajectories, Magnetic Resonance in Medicine, 46 (2001), 638-651

3. Pruessmann KP, Weiger M, Scheidegger MB, Boesiger P. SENSE: Sensitivity encoding for fast MRI. Magnetic Resonance in Medicine, 1999; 42: 952-962.

4. Griswold MA, Jakob PM, Heidemann RM, Nittka M, Jellus V, Wang J, Kiefer B, Haase A. Generalized autocalibrating partially parallel acquisitions (GRAPPA). Magnetic Resonance in Medicine, 2002 Jun;47(6):1202-10.

5. Akasaka T, Fujimoto K, Yamamoto T, Okada T, Fushumi Y, Yamamoto A, et al. Optimization of Regularization Parameters in Compressed Sensing of Magnetic Resonance Angiography: Can Statistical Image Metrics Mimic Radiologists' Perception? PLoS One. 2016;11(1):e0146548.

6. Fushimi Y, Fujimoto K, Okada T, Yamamoto A, Tanaka T, Kikuchi T, et al. Compressed Sensing 3-Dimensional Time-of-Flight Magnetic Resonance Angiography for Cerebral Aneurysms: Optimization and Evaluation. Invest Radiol. 2016;51(4):228-35.

7. Fushimi Y, Okada T, Kikuchi T, Yamamoto A, Yamamoto T, Schmidt M, et al. Clinical evaluation of time-of-flight MR angiography with sparse undersampling and iterative reconstruction for cerebral aneurysms. NMR Biomed. 2017;30(11).

8. Onishi N, Kataoka M, Kanao S, Sagawa H, Iima M, Nickel MD, et al. Ultrafast dynamic contrast-enhanced mri of the breast using compressed sensing: breast cancer diagnosis based on separate visualization of breast arteries and veins. J Magn Reson Imaging. 2018;47(1):97-104.

9. Ono A, Arizono S, Fujimoto K, Akasaka T, Yamashita R, Furuta A, et al. Non-contrast-enhanced 3D MR portography within a breath-hold using compressed sensing acceleration: A prospective noninferiority study. Magn Reson Imaging. 2017;43:42-7.

10. Yamamoto T, Okada T, Fushimi Y, Yamamoto A, Fujimoto K, Okuchi S, et al. Magnetic resonance angiography with compressed sensing: An evaluation of moyamoya disease. PLoS One. 2018;13(1):e0189493.

Proc. Intl. Soc. Mag. Reson. Med. 26 (2018)