Water-Fat Separation using a Locally Low-Rank Enforcing Reconstruction

Felix Lugauer1, Dominik Nickel2, Jens Wetzl1, Berthold Kiefer2 and Joachim Hornegger1

1 Pattern Recognition Lab, Friedrich-Alexander Universität Erlangen-Nürnberg, Germany

2 Siemens Healthcare GmbH, MR, Erlangen, Germany

ISMRM 2015 | Felix Lugauer (felix.lugauer@fau.de)

Water-Fat Separation using a Locally Low-Rank Enforcing Reconstruction #3652

Motivation

Acceleration of Multi-Echo Dixon Imaging

● Abdominal breath-hold examinations suffer from

● Limited SNR

● Residual motion artifacts

● Accelerated acquisition desirable

● Less motion artifacts

● Shorter breath-holds or higher resolution

Multi-echo Compressed Sensing reconstruction

● Exploit redundant contrast information during reconstruction

● 6-echo acquisitions are standard for water-fat-iron separation[1]

2

1. Yu, H. et al., JMRI 26:1153-1161, (2007)

ISMRM 2015 | Felix Lugauer (felix.lugauer@fau.de)

Water-Fat Separation using a Locally Low-Rank Enforcing Reconstruction #3652

…

Motivation – Current Work-Flow

3

contrast

Echo1 Echo2 Echo …

PAT/CS Acquisition

(k-space)

Separate

Reconstructions

(image-space) …

Fitting

(image-space) W F PDFF/R2*

Separate reconstruction:

+ Spatial sparsity regularization

– No usage of shared information

ISMRM 2015 | Felix Lugauer (felix.lugauer@fau.de)

Water-Fat Separation using a Locally Low-Rank Enforcing Reconstruction #3652

…

Motivation – Proposed Work-Flow

4

contrast

Echo1 Echo2 Echo …

PAT/CS Acquisition

(k-space)

TE-Coupled

Reconstruction

(image-space) …

Fitting

(image-space) W F PDFF/R2*

TE-Coupled reconstruction:

+ Spatial sparsity regularization

+ Echo sparsity regularization

ISMRM 2015 | Felix Lugauer (felix.lugauer@fau.de)

Water-Fat Separation using a Locally Low-Rank Enforcing Reconstruction #3652

● Signal is superposition from water and fat

● Spectral components determine rank of echo-train: 2

● Phase evolution (field inhomogenity) violates rank constraint

● But assumed to be smooth or locally constant[2]

Low-rank property of locally correlated contrasts

Theory - Water-Fat Imaging

5

Vector Notation:

: Echo image

: Water

: Fat

: Multi-peak fat phasor

: # voxel

: # echo

: Phase evolution (field

inhomogeneity, gradient

delays, R2* relaxation, …)

2. Doneva, M. et al. MRM 64:1749-1759, (2010)

ISMRM 2015 | Felix Lugauer (felix.lugauer@fau.de)

Water-Fat Separation using a Locally Low-Rank Enforcing Reconstruction #3652

● Image patches stacked as column vectors from all contrasts: Casorati matrix[3]

● SVD analysis confirms the low-rank property for sufficiently small patches

Suppression of noise and sampling artifacts via low-rank promoting reconstruction

Theory - Local Low-Rank (LLR) Property

6

… # Contrasts

# L

ocal sam

ple

s

SVD

Casorati matrix

3. Trazko, J. et al. Proc. ISMRM:4371, (2011)

ISMRM 2015 | Felix Lugauer (felix.lugauer@fau.de)

Water-Fat Separation using a Locally Low-Rank Enforcing Reconstruction #3652

TE-Coupled Reconstruction with LLR Regularization

● LLR Regularizer[3,4]

● Nuclear norm (closest convex relaxation of rank minimization) = sum of singular values

● Involves iterative singular-valaue thresholding: averaging of contrast images

● Robustness through overlapping blocks

● Solve via ADMM / Bregman variable splitting approach

● Additional spatial regularizers possible

7

Data fidelity: multi-contrast Locally low-rank regularizer

Nuclear norm of Casorati blocks

Notation:

: Measured data

: Concatenation of all echos

: Casorati block operator

: System matrix inc. coil

sensitivities, Fourier- and

(TE-dependent)

undersampling matrix

4. Candes, E. et al. Proc. IEEE 98:925-936, (2010)

ISMRM 2015 | Felix Lugauer (felix.lugauer@fau.de)

Water-Fat Separation using a Locally Low-Rank Enforcing Reconstruction #3652

Experiments

● Abdominal acquisition

● Prototype 3D spoiled GRE (VIBE) with bipolar readout, 3 T clinical MR scanner

(MAGNETOM Skyra, Siemens GmbH, Erlangen, Germany)

● FoV: 40 x 28 x 22 cm3, matrix: 256 x 176 x 64

● Flip angle = 15°, TR = 8.48 ms, TEs = 1.19, 2.32, 3.45, 4.58, 5.71, 6.84 ms

● Retrospective undersampling of fully measured data

● Variable density Poisson mask with factor 6 undersampling

● Coil sensitivity reference region 24 x 24

● Reconstructions

● TE-Coupled: 2D+TE (readout decoupled) using LLR regularization (1 patch per pixel of size 5 x 5)

● Decoupled: 2D (readout dec.) regularized total variation (TV) and discrete wavelet transform (DWT)

ISMRM 2015 | Felix Lugauer (felix.lugauer@fau.de)

Water-Fat Separation using a Locally Low-Rank Enforcing Reconstruction #3652

Results – LLR vs Conventional Reco

Reference Coupled LLR Decoupled TV+DWT

1st Echo

Water

ISMRM 2015 | Felix Lugauer (felix.lugauer@fau.de)

Water-Fat Separation using a Locally Low-Rank Enforcing Reconstruction #3652

Discussion & Conclusion

● Image quality improvements by promoting the limited spectral components in contrast series

● LLR regularization performs effective averaging during reconstruction

● Better noise and artifact suppression than conventional reconstructions

● Well-suited for water-fat imaging

● Enables further acceleration for parallel imaging and compressed sensing acquisition

● Applicable to other multi-echo acquisitions and/or dynamic imaging

● Next: Further validation on prospectively undersampled and patient data

Thank you for your attention!