Coil Compression

MRI using receiver arrays with many coil elements can provide high signal-to-noise ratio and increase parallel imaging acceleration. At the same time, the growing number of elements results in larger datasets and more computation in the reconstruction. This is of particular concern in 3D acquisitions and in iterative reconstructions. Coil compression is effective in mitigating this problem by compressing data from many channels into fewer virtual coils. Among different coil compression methods, data-based coil compression is most effective and does not rely on the explicit knowledge of the coil sensitivities.

In Cartesian sampling there often are fully sampled k-space dimensions. A spatially varying coil compression can therefore be exploited in these fully sampled directions to further reduce the number of virtual coils. A geometric-decomposition coil compression (GCC) is proposed here that includes different coil compressions at individual spatial locations and an alignment of coil compression matrices. The alignment guarantees the smoothness of the virtual coil sensitivites and provides compatibility with autocalibrating parallel imaging reconstructions.

More details of the coil compression algorithm can be found in the references. I have provided a MATLAB example of the algorithm.

MATLAB Example

A complete MATLAB-based coil compression package can be downloaded here.

Dr. Michael Lustig has also provided a nice demo here.

In Vivo Datasets

We have deployed the proposed method clinically at Lucile Packard Children's Hospital at Stanford. The clinical performance is summarized in Ref. 3 below and all evaluated datasets can be found here.

More compressed sensing datasets can be found at


  1. Zhang T, Pauly JM, Vasanawala SS, Lustig M. "Coil Compression for Accelerated Imaging with Cartesian Sampling," Magn Reson Med 2013; 69: 571-582

  2. Huang F, Vijayakumar S, Li Y, Hertel S, Duensing R. "A software channel compression technique for faster reconstruction with many channels," Magn Reson Imaging 2008; 26: 133-141

  3. Zhang T, Chowdhury S, Lusitg M, et al. "Clinical Performance of Contrast Enhanced Abdominal Pediatric MRI with Fast Combined Parallel Imaging Compressed Sensing Reconstruction," J Magn Reson Imaging 2014; 40: 13-25

Dual-Echo Dixon Imaging Using a Projected Power Method

A major challenge in dual-echo Dixon imaging is to estimate the phase error from field inhomogeneity. Due to field inhomogeneity, two ambiguous phase error (a.k.a phasor) candidates can be analytically calculated at each image pixel. Here, a binary quadratic optimization program is formulated to resolve the phase ambiguity in dual-echo Dixon imaging. A projected power method is developed to efficiently solve this optimization problem. Fast and robust water-fat separation can be achieved using this method. More details of the projected power algorithm can be found in the references below.

MATLAB Example

A demonstration of the projected power method can be downloaded here. Note that this package (~380 MB) contains a high-resolution 3D dataset.


  1. Zhang T, Chen Y, Bao S, Alley M, Pauly J, Hargreaves B, Vasanawala S. "Resolving phase ambiguity in dual-echo Dixon imaging using a projected power method," Magn Reson Med 2016. DOI: 10.1002/26287

  2. Eggers H, Brendel B, Duijndam A, Herigault G. "Dual-echo Dixon imaging with flexible choice of echo times," Magn Reson Med 2011; 65:96-107

  3. ISMRM Fat-water toolbox. ISMRM fat-water separation workshop 2012. ""

Fast Dynamic MRI and Parameter Mapping with a Locally Low Rank Constraint

MR parameter mapping (MRPM) is a promising approach to characterize intrinsic tissue-dependent information. Quantitative MRPM requires acquisition of multipart datasets with modulated pulse sequence parameters, e.g. echo time (TE), flip angle (FA), or inversion time (TI). The major limitation of clinical application of MRPM is long scan times due to multiple data acquisitions. This process can be significantly accelerated using a locally low rank method, in which the spatiotemporal correlation is exploited in local image patches. This locally low rank property can also be applied in dynamic MRI.

MATLAB Example

A simple demonstration of accelerating parameter mapping with a locally low rank constraint can be downloaded here.


  1. Zhang T, Pauly JM, Levesque IR. "Accelerating Parameter Mapping with a Locally Low Rank Constraint," Magn Reson Med 2015; 73: 655-661

  2. Trzasko J, Manduca A. "Local versus global low-rank promotion in dynamic MRI series reconstruction," In Proceedings of the 19th Annual Meeting of ISMRM, Montreal, 2011. p.4371.

  3. Zhang T, Cheng JY, Potnick AG, et al. "Fast Pediatric 3D Free-breathing Abdominal Dynamic Contrast Enhanced MRI with High Spatiotemporal Resolution," J Magn Reson Imaging 2015; 41: 460-473

Robust Self-gated Abdominal and Cardiac MRI Using Coil Clustering

By modifying standard MR pulse sequences, motion can be extracted without the use of external motion tracking devices (e.g. respiratory bellows and ECG). For example, Cartesian trajectory can be simply modified, with the prewinder gradients traversing the same trajectory at the beginning of each phase encode. With the traversing trajectory alternating at different directions, translational motion can be estimated in all three directions (superior/inferior, right/left, and anterior/inferior). This self-navigating trajectory is known as Butterfly.

Dense coil arrays with small coil elements and high channel counts can provide additional motion information, as each coil element can generate a motion estimate within a local region. Motion estimates from different coil elements can vary significantly, and do not individually represent the dominant motion within the entire imaging volume. In this work, a robust motion estimation method using coil clustering is proposed to automatically determine a subset of coil elements (a.k.a a coil cluster) that represent the dominant motion.

MATLAB Example

A simple demonstration of coil clustering for 3D abdominal MRI can be downloaded here.

For more information about Butterfly, Dr. Joseph Cheng has provided a nice demo here.


  1. Zhang T, Cheng JY, Chen Y, Nishimura DG, Pauly JM, Vasanawala SS. "Robust Self-Navigated Body MRI Using Dense Coil Arrays," Magn Reson Med 2015. DOI: 10.1002/mrm.25858

  2. Cheng JY, Alley MT, Cunningham CH, Vasanawala SS, Pauly JM, Lustig M. "Nonrigid Motion Correction in 3D Using Autofocusing with Localized Linear Translations," Magn Reson Med 2012; 68: 1785-1797