Compressed Sensing for Chemical Shift-Based Water-Fat Separation Doneva M., Bornert P., Eggers H., Mertins A., Pauly J., and Lustig M., Magnetic Resonance in Medicine (64) (2010)

Background Fat often appears bright in MR images: may obscure pathology; Reliable fat suppression methods is needed. Common fat suppresion techniques: Spectral-spatial water excitation Spectral selective fat saturation Short TI inversion recovery Water-fat separation Based on chemical shift induced phase difference between fat/water

Water-Fat Signal Model Single peak fat model Multi peak fat model

Two-Point Dixon RF G Partition G Phase G Readout In-phase Read out Op-phase water fat water fat

Multi-Point Acquisition RF G Partition G Phase G Readout In-phase Read out Op-phase 1 water fat water fat Op-phase 2 water fat

Water-Fat Separation Methods Image at echo time t l Multi peak fat model

Water Fat Separation Require the acquisition of two or more images at different TE Long scan time needed Compressed sensing can be combined with water-fat separation to improve sampling efficiency

Compressed Sensing Key elements of a successful compressed sensing reconstruction: Signal sparsity Incoherent sampling Nonlinear, sparsity promoting reconstruction

Signal Sparsity

Incoherent Sampling

Nonlinear Reconstruction Iterative reconstruction needed Optimization based on minimizing l 1 norm works well:

Image Acquisition

Imaging Parameters 1.5 T scanner (Phillips Healthcare) Retrospective under-sampling (Poisson-disk) Knee images Turbo spin echo, TR=500 ms, TE = 21 ms FOV 160 mm x 160 mm Matrix size 256 x 256, slice thickness 3mm, voxel size 0.6 mmx0.6 mmx3 mm Echo time -0.4, 1.1, 2.6 ms (relative to spin echo)

Imaging Parameters 1.5 T scanner (Phillips Healthcare) Abdominal images 3D gradient echo, TR=6.9 ms, TE1 = 1.66 ms,  TE = 1.66 ms,  =15  FOV 400 mm x 320 mm x 216 mm Matrix size 240 x 192 x 54, bandwidth 833 Hz/pix

Fat Signal Model Single Peak Fat Model Chemical shift of fat: -220 Hz Multi Peak Fat Model Three peak fat model: -30 Hz, -165 Hz, -210 Hz Relative amplitude (0.15, 0.1, 0.75)

CS-WF Reconstruction Initial field map estimation Initialization: Low-resolution: center k-space High-resolution: perform CS reconstruction for each echo Compute possible field map values for each pixel and estimate initial field map using region growing, and Estimate initial water and fat images

CS-WF Reconstruction Similar to Gauss-Newton algorithm Iteratively and simultaneously update the water and fat images and the field map, using the update as:

CS-WF Reconstruction Given the final estimate x n, compute a projection on k-space y n =g(x n ), set the measured data at the sampling location y n =y| acq and perform one last iteration.

2D Knee Images Single peak fat model

2D Knee Images Error seems to have some texture

2D Knee Images Multi peak fat model (three peaks, three echoes)

3D Abdominal Images

CS-WF Reconstruction Low-resolution initialization: 50 Gauss- Newton iterations High-resolution initialization: 5 iteration One Gauss-Newton step for 3D data: 9 min (This is slow!)

Discussion Nice and uniform water fat separation Good field map estimation Clean image without noticable artifact Slow reconstruction Moderate reduction factor High reduction factor results in loss of contrast

Study Based on This Paper Silver HJ, et al. Comparison of gross body fat-water magnetic resonance imaging at 3 Tesla to dual-energy X-ray absorptiometry in obese women. Obesity (Silver Spring) Apr;21(4): Pang Y, Zhang X. Interpolated compressed sensing for 2D multiple slice fast MR imaging. PLoS One. 2013; 8(2) Pang Y, et al. Hepatic fat assessment using advanced Magnetic Resonance Imaging.Quant Imaging Med Surg Sep;2(3):213-8 Sharma SD, et al. Chemical shift encoded water-fat separation using parallel imaging and compressed sensing. Magn Reson Med Feb;69(2):

Study Based on This Paper Li W, et al. Fast cardiac T1 mapping in mice using a model-based compressed sensing method. Magn Reson Med Oct;68(4): Sharma SD,et al. Accelerated water-fat imaging using restricted subspace field map estimation and compressed sensing. Magn Reson Med Mar;67(3):650-9

Thank you!