Optimized CS-Wave imaging with tailored sampling and efficient reconstruction
Berkin Bilgic1, Huihui Ye1, Lawrence L Wald1, and Kawin Setsompop1

1Martinos Center for Biomedical Imaging, Charlestown, MA, United States


Wave-CAIPI utilizes additional gradients during the readout to improve controlled aliasing and fully harness coil sensitivity encoding. Recently proposed CS-Wave extended Wave-encoding with Poisson sampling and wavelet regularization. This work proposes optimized CS-Wave with i) tailored data-sampling and ii) highly efficient reconstruction. At 15-fold acceleration, proposed CS-Wave provides 20% RMSE improvement over Wave-CAIPI, which nearly doubles the improvement achieved with previously proposed CS-Wave. This permits single head-orientation Quantitative Susceptibility Mapping at 1×1×2mm3 resolution in 25s. Combining CS-Wave with SMS Echo-Shift strategy further increases the acceleration to 30-fold, thus enabling multi-orientation QSM at long-TE from three head-rotations at 1.5mm isotropic in 72s.


Wave-CAIPI utilizes sinusoidal gradients during each readout period to traverse a corkscrew trajectory and spreads aliasing in all spatial directions. This allows 10-fold acceleration in 3D (1,2) and Simultaneous MultiSlice (SMS) imaging (3) with low image artifacts. CS-Wave was recently proposed (4), which extended Wave-encoding through Poisson sampling and wavelet regularization to achieve further accelerations. In this work, we propose an optimized CS-Wave with hybrid sampling that synergistically combines controlled aliasing at low spatial frequencies with incoherent aliasing at high frequencies. This is inspired by the performance gain of hybrid undersampling in (5). Additionally, efficient reconstruction via variable splitting of consistency and regularization terms is developed. At 15-fold acceleration, proposed CS-Wave provides 20% RMSE improvement over Wave-CAIPI, which nearly doubles the improvement from previous CS-Wave approach. This permits whole-brain QSM at 1×1×2mm3 resolution in 25s. CS-Wave is also combined with SMS Echo-Shift (6,7) to achieve further increase in acceleration to 30-fold by minimizing sequence dead-time, thus enabling multi-orientation QSM at 1.5mm isotropic resolution in 72s.

Efficient Reconstruction

Despite following a non-Cartesian trajectory, Wave encoding can be expressed in Cartesian k-space through point spread function (psf) formalism: k = MFyzPFxSm, where k is the k-space data, M represents hybrid undersampling, Fyz and Fx denote Fourier transforms along ky-kz and kx. P is the psf in hybrid (kx,y,z) space, S are the coil sensitivities, and m is the unknown image.

Regularization is incorporated via

1/2||MFyzPFxSm k||22 + λ||Rm||1

where R is wavelet or gradient operator. By introducing auxiliary variables c = FyzPFxSm, and r = Rm, and applying ADMM (8,9), closed-form updates are obtained:

c = (MI)–1·[Mk + α(FyzPFxSm+dc)]

r = max(|Rm+dr|–λ/β, 0)·sign(Rm+dr)

where dc and dr are dual variables, and α and β are Lagrangian parameters. Image update is found by solving

SHSRHR)m = αSHFxHPHFyzH(cdc) + βRH(rdr)

This system can be inverted in closed-form for wavelet transform where RHR = I, and solved for gradient transform (TV) using conjugate gradient with the diagonal preconditioner (SHS+6βI)–1.

Data Acquisition

(i) 3D-GRE Wave data were acquired at 3T and 7T using 32-channel receiver with parameters: matrix=224×222×120, resolution=1×1×2mm3. For 3T: TE/TR=13.3/26ms, and for 7T: TE/TR=10.9/27ms.

(ii) SMS Echo-Shift Wave data were acquired at 3T, where 2-fold improvement in encoding efficiency is achieved by echo-shifting even and odd slices data to minimize dead-time from long-TE. Resolution was 1.5mm isotropic with matrix=160×160×96, TE/TR=35/47ms. Three volumes were collected at different head orientations.

Data Reconstruction

For fast computation, SVD coil compression was applied (10). ESPIRiT calibration (11) from the center 16×16×16 k-space was employed for coil sensitivity estimation.

(i) 3D-GRE Wave data: were retrospectively undersampled using

i) Wave-CAIPI under-sampling at R=5×3,

ii) Poisson CS-Wave sampling at R=15 (4), and

iii) Proposed hybrid CS-Wave sampling with controlled aliasing at R=3×3 in central 25% k-space and variable-density Poisson mask (12) at outer k-space for R=15-fold total acceleration (Fig.1).

Generalized SENSE was used for Wave-CAIPI reconstruction (1,13) and proposed efficient algorithm was employed for CS-Wave reconstruction.

(ii) Echo-Shift Wave data: were undersampled to provide 30-fold total acceleration (Rcs-wave×Recho-shift=15×2) and reconstructed using proposed algorithm.

Phase & QSM processing

Phase data were processed with BET brain-masking (14), Laplacian unwrapping (15), and harmonic background removal (16,17) to obtain the tissue phase.

(i) QSM for 3D-GRE: employed single-step reconstruction that directly relates the unwrapped phase to the underlying susceptibility via TV regularization.

(ii) QSM for Echo-Shift: combined complementary information in phase images from 3-directions using COSMOS (18), thus obviating the need for regularization.


Fig.1 compares proposed CS-Wave and Wave-CAIPI at 7T. RMSEs were 8.6% for CS-Wave with TV-penalty and hybrid sampling (9.1% with previously proposed wavelet and Poisson sampling, not shown) and 10.2% for Wave-CAIPI.

Fig.2 shows 3T results, where the RMSEs were 7.4% for proposed CS-Wave with TV-penalty and hybrid sampling (7.9% with wavelet and Poisson), and 8.9% for Wave-CAIPI. Processing times in Matlab were 8.4min for TV-regularized CS-Wave (3.8min using wavelet) and 1.8min for Wave-CAIPI.

Figs.3&4 demonstrate tissue phase and QSM images, derived from these accelerated 3D-GRE reconstructions.

Fig.5 presents Echo-Shift CS-Wave reconstructions at 3-orientations, and high quality QSM and phase images.

Discussion & Conclusion

The proposed CS-Wave enables improved mitigation of artifacts and noise amplification. This was made possible by efficient ADMM reconstruction, and hybrid sampling that simultaneously accommodates sensitivity encoding and sparsity prior. Compared to previous CS-Wave that achieves 12% improvement over Wave-CAIPI, proposed strategy attains 20% RMSE reduction. This leads to improved phase and QSM from single-orientation at 1×1×2mm3 resolution in 25s. Combining CS-Wave with Echo-Shift permits 30-fold acceleration for multi-orientation QSM, enabling a 72s protocol with 3-rotations. Future work will explore complementary sampling across orientations with joint reconstruction for further gain.


NIH NIBIB P41-EB015896, 1U01MH093765, R24MH106096, 1R01EB01943701A1


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Proposed CS-Wave employs hybrid sampling with controlled aliasing at R=3×3 in central 25% k-space and Poisson sampling at higher frequencies for R=15-fold total acceleration. Using efficient ADMM reconstruction with TV regularization enables 20% RMSE improvement over Wave-CAIPI to provide a 25sec whole-brain acquisition with 1x1x2mm3 resolution at 7T.

CS-Wave provides a rapid 24sec 3D-GRE acquisition at 3T upon R=15-fold acceleration. Hybrid sampling and TV regularization allows better mitigation of aliasing artifacts and noise amplification relative to Wave-CAIPI.

Tissue phase and susceptibility maps derived from the 15-fold accelerated reconstructions with Wave encoding at 7T. Proposed CS-Wave provided better artifact mitigation than Wave-CAIPI, yielding higher quality phase and QSM images. Raw phase images were processed with RESHARP background removal to obtain the tissue phase, and TV-regularized single-step algorithm was employed for QSM reconstruction.

CS-Wave provided higher quality tissue phase and susceptibility maps at 3T from a 24sec, whole brain 3D-GRE acquisition.

Combining Echo-Shift strategy with CS-Wave provides R=30-fold total acceleration. SMS Echo-Shift minimizes the sequence dead-time present in long-TE acquisitions by encoding even and odd slice groups within a single TR. The 2-fold efficiency gain provided by Echo-Shift was combined with R=15-fold CS-Wave acceleration to enable whole-brain, long-TE GRE acquisition in 24sec. Sampling three head orientations allowed high quality QSM in 72sec, obviating the need for regularized dipole inversion.

Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)