Gabriel Varela-Mattatall^{1,2,3}, Tae Hyung Kim^{3}, Jaejin Cho^{3}, Wei-Ching Lo^{4}, Borjan A. Gagoski^{5,6}, Ravi S. Menon^{1,2}, and Berkin Bilgic^{3,7}

^{1}Centre for Functional and Metabolic Mapping (CFMM) | Robarts Research Institute | Western University, London, ON, Canada, ^{2}Department of Medical Biophysics | Schulich School of Medicine and Dentistry | Western University, London, ON, Canada, ^{3}Department of Radiology | Athinoula A. Martinos Center for Biomedical imaging | Massachusetts General Hospital & Harvard Medical School, Charlestown, MA, United States, ^{4}Siemens Medical Solutions USA, Inc., Charlestown, MA, United States, ^{5}Department of Radiology | Harvard Medical School, Boston, MA, United States, ^{6}Fetal-Neonatal Neuroimaging & Developmental Science Center | Boston Children's Hospital, Boston, MA, United States, ^{7}Harvard-MIT Division of Health Sciences and Technology, Massachusetts Institute of Technology, Cambridge, MA, United States

Wave encoding mitigates g-factor noise amplification in highly accelerated parallel imaging but achieving ultra-high acceleration factors is precluded by the intrinsic “√R” SNR penalty. To overcome this limitation, we propose a compressed sensing-based reconstruction with automatic selection of the regularization weighting. Moreover, we show that CS-Wave is flexible enough to perform well with uniform undersampling. We compare reconstruction performance of CS-Wave against the state-of-art Wave-LORAKS which requires parameter tuning, and evaluate different undersampling patterns at R=12-fold acceleration. Results indicate higher reconstruction quality and showcase the feasibility of ultra-fast Wave-MPRAGE acquisitions.

An important limitation of both CS-Wave and Wave-LORAKS is the need for appropriate selection of the regularization weighting. To circumvent time-consuming manual tuning, a novel CS reconstruction with automatic parameter selection was recently presented

Cartesian fully sampled MPRAGE data were acquired using a 3T system (Skyra, Siemens) with 32 receiver coils. Sequence parameters were 1mm isotropic resolution, FOV of 256x256x192 mm, and TE/TI/TR = 3.49/1100/2500 ms. From the fully sampled acquisition, wave encoding was simulated with sinusoidal wave gradients G

We replicated the previous sequence parameters to acquire Wave-MPRAGE data using 2x1, 3x3 and 4x3 uniform undersampling (5:28, 1:23 and 1:03 acquisition times, respectively). Sinusoidal wave gradients were with G

For both retrospective and prospective acquisitions an external GRE reference scan was used to estimate sensitivity coil maps with ESPIRIT

Standard Wave-CAIPI reconstruction minimizes

$$\hat{x}=\textrm{argmin}_x\hspace{1mm}\|Ax-y\|_2^2,\hspace{3mm}\textrm{(1)}$$

where $$$x$$$ is the unknown image, $$$y$$$ are the acquired data, and $$$A=SF_{jk}PF_{i}C$$$ is the forward model. This forward model is composed of sensitivity profiles, $$$C$$$, a Fourier transform in the frequency-encoding direction, $$$F_i$$$, wave point-spread-function, $$$P$$$, a Fourier transform in phase- and partition-encoding directions, $$$F_{jk}$$$, and the undersampling operator, $$$S$$$.

To improve the reconstruction, Wave-LORAKS includes a regularizer that promotes support, smooth phase, and parallel imaging constraints simultaneously (S-based LORAKS formulation

$$\hat{x}=\textrm{argmin}_x\hspace{1mm}\|Ax-y\|_2^2+\lambda J(P(x)),\hspace{3mm}\textrm{(2)} $$

where $$$P(*)$$$ constructs a structured matrix out of the data for those constraints, and $$$J(*)$$$ is the cost function that penalizes matrices with large rank. Wave-LORAKS requires tuning the radius of the LORAKS kernel, the rank for the S-matrix, and the regularization weighting, $$$\lambda$$$

The proposed CS-Wave includes a regularizer that promotes sparsity,

$$ \hat{x} = \textrm{argmin}_x\hspace{1mm}\| Ax - y \|_2^2+\lambda_{\textrm{auto}}\|\Psi x\|_1,\hspace{3mm}\textrm{(3)}$$

with a novel method to automatically select the regularization weighting, $$$\lambda_{\textrm{auto}}$$$, which determines the regularization weighting for each decomposition level, $$$L$$$, of the wavelet transform, $$$W$$$

Figure 2 shows that CS-Wave reconstruction from uniform sampling provides better performance than Poisson undersampling (6.2% vs 6.8% NRMSE). Furthermore, CS-Wave is as good as Wave-CAIPI at 9-fold acceleration (6.2% vs 6.3% NRMSE).

Figure 3 shows the comparison between CS-Wave, Wave-LORAKS and wave-CAIPI reconstructions for uniform undersampling at 12-fold acceleration. From the reconstructions and the error maps, Wave-LORAKS and -CAIPI are noisier than CS-Wave, which is reflected in the NRMSE values. Panel (H) shows reconstruction performance that favors CS-Wave with automatic selection of the decomposition level over the other methods.Figure 4 compares CS-Wave with 4x3 uniform sampling to Wave-CAIPI with uniform 3x3 and 2x1. There is high similarity between Wave-CAIPI at 9-fold acceleration with CS-Wave at 12-fold acceleration.

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Figure 1- Effect of wave encoding and undersampling. Panel (A) shows the original TPSF from the fully sampled case. Panels (B-E) show the TPSF, the sidelobe-to-peak ratio (SPR), and the zero-filled reconstruction for each combination. Panel (B) shows the well-known aliasing effect. Panel (C) shows how random undersampling in Cartesian acquisitions generates incoherence. Panels (D-E) show how wave encoding generates incoherence due to its trajectory and spreads out the signal across the entire wavelet transform. Panels (B-C) are conceptual images.

Figure 2- CS-Wave reconstruction using different undersampling patterns. The first row shows the reference and the reconstructions for each case. The second row shows the difference ($$$5|x-\hat{x}|$$$) between the reference and each reconstruction. The fourth column corresponds to Wave-CAIPI reconstruction at 9-fold acceleration.

Figure 3- Comparison between auto CS-Wave, Wave-LORAKS and standard wave-CAIPI reconstructions from uniform 4x3 undersampling. First row shows the reference and the reconstructions for each reconstruction method. Second row shows the difference ($$$5|x-\hat{x}|$$$) between each reconstruction with the reference. Panel (H) shows the NRMSE for the 3 methods and for the 2 undersampling patterns (CS-Wave does automatic selection of $$$L$$$ but can also be user-defined).

Figure 4- Comparison between CS-Wave and Wave-CAIPI. The columns indicate the method and total acquisition time (TA).

DOI: https://doi.org/10.58530/2022/1604