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Low-rank Constrained Reacquired-navigator reconstruction of multi-shot diffusion weighted image

Jiantai Zhou¹, Huabin Zhang¹, Penghui Luo¹, Changliang Wang¹, Fulang Qi¹, Kecheng Yuan¹, Jiaojiao Hu ¹, and Bensheng Qiu¹
¹Medical Imaging Center, Department of Electronic Engineering and Information Science, University of Science and Technology of China, Hefei, China

Synopsis

Keywords: Diffusion Reconstruction, Diffusion/other diffusion imaging techniques, Low-rank, Phase correction,Reacquired-navigator

Motivation: Multi-Shot Diffusion-Weighted Imaging (MS-DWI) requires additional phase correction data and parallel imaging prescans to respectively suppress artifacts caused by positive-negative readout gradient and motion-induced phase variation.

Goal(s): Our objective is to mitigate two common artifacts without the need for additional linear-phase corrections and parallel imaging prescans.

Approach: We propose subtle modifications to the dual spin-echo DW sequence ¹, where positive and negative gradients are employed to separately acquire complete navigator-echo data for low-rank constrained reconstruction.

Results: Simulation studies and in vivo brain imaging experiments demonstrate that the proposed method effectively mitigates image artifacts caused by phase variations, resulting in better image quality.

Impact: This paper presents a novel artifact correction method applied to spin-echo DW sequence, offering an effective prescan-free acquisition and reconstruction strategy that mitigates the impact of prescan data mismatch and additional prescan time consumption.

Introduction

MSDWI uses multi-shot acquisitions to fill the k-space batch and reduce the echo train length, which is essential for high-resolution imaging and mitigating image blurring. However, there are two significant challenges. Firstly, it leads to more severe artifacts due to a mismatch between positive and negative echoes ². Secondly, even minimal non-rigid motions can introduce phase differences between different shots, resulting in prominent image artifacts ^3-4. The low-rank constrained technique has demonstrated considerable success in suppressing these artifacts in magnetic resonance reconstruction tasks ^5-9. By transforming the causes of artifacts into the problem of annihilating low-rank matrices, a convex optimization problem is then formulated and solved using the iterative optimization algorithm. In this work, we unify the mismatch between positive-negative echoes, as well as motion-induced phase variation, into a cohesive optimization problem. By incorporating low-rank constraints, we apply this unified framework to MSDWI reconstruction.

Theory

Pulse design
Single-shot DWI (SS-DWI) has an exceptionally rapid acquisition speed. Following the acquisition of imaging echo, navigator-echo is collected using SSDWI, which has similar motion-induced phase variations as imaging echo ¹⁰. Several reconstruction methods based on navigator-echo have already been applied in MSDWI research to rectify phase discrepancies ^11-14. Fig. 1 illustrates subtle modifications in the dual spin-echo DWI sequence, where two complete navigator-echo data (k+ and k-) are acquired during each phase-encoding step using positive and negative gradients, respectively. Fig. 2 demonstrates that, within each acquisition shot, k+ and k- encompass phase errors induced by gradients, while in different shots the same polarity navigator-echo exhibits varying motion-induced phase errors. This navigator-echo can be concurrently employed to rectify the two primary sources of phase errors in MSDWI.

Low-rank Constraints for MSDWI Reconstruction
The problem of artifact removal can be reformulated as a uniform under-sampling reconstruction. Some methods have incorporated parallel imaging techniques into MSDWI reconstruction^12-13,15-16 or combined with low-rank constraints ^6-7,9,17 to achieve improved image quality. In this study, we partition each echo into shots ro+ and ro-. Subsequently, we treat these separated undersampled data as a new virtual channel dimension. Considering the added complexity of ro+ and ro- echo separation exacerbating the undersampling challenge, we stack the navigator-echo into the virtual channel for the estimation of null space, as depicted in Fig 3. Finally, we formulate the following optimization problem.

$$\hat{s}=\mathop{argmin}\limits_{s}\frac{1}{2}\mid\mid\mathcal{P}s-d\mid\mid_{2}^2+\lambda\mid\mid\mathcal{H}sV_{null}\mid\mid_{F}^2,$$

Where $$$\mathcal{H}$$$ is an operator that converts $$$s$$$ into the Hankel matrix, $$$\mathcal{P}$$$ is the sampling operator, $$$V_{null}$$$ is the basis for the null space of the Hankel matrix, and $$$\lambda$$$ is the regularization parameter for the low-rank constraint.

Methods

Data acquisition
We generated 4-shot images by applying smooth phase variations to a $$$192\times192$$$ digital brain phantom ¹⁸. Subsequently, we transformed them into hybrid (x-ky) space, and introducing phase offsets in the frequency-encoding direction, and then added Gaussian noise (expectation $$$\mu=0$$$, standard deviation $$$\sigma=0.01$$$) in k-space. Additionally, navigator-echo data were acquired from the central k-space data with same expectation but higher standard deviation Gaussian noise.
To evaluate the effect in in-vivo imaging, two volunteers‘ brains were scanned on 1.5 Tesla Climber148 system (supported by Anhui Fuqing Medical Technology Company) using 16-channel head receive-only coil with 4 shots. Acquired matrix=$$$168\times168$$$, FOV (field-of-view)=$$$230\times230mm^2$$$, in-plane resolution=$$$1.5mm$$$, slice thickness=$$$6mm$$$,b-value= $$$1000 s/mm^2$$$ and NEX (number of repetitions) = 1.

Data preprocessing and reconstruction
All acquired data were reconstructed by compact kernel grappa ¹³ and the proposed method using Augmented Lagrangian algorithm with 300 iterations, a regularization parameter of 0.1 and $$$5\times 5$$$ patches for the Hankel matrix. Additionally, a comparison was made with the linear phase correction (LPC) method ¹⁹, which involves the acquisition of additional prescan data.

Results and discussion

In numerical simulation (Fig. 4), as the standard deviation in navigator-echo increases, compact kernel grappa has peak signal-to-noise ratio (PSNR) decreases and increases the residual artifacts compared with the proposed method shown in (Fig. 4h).
For in vivo data, there is no golden standard for reference. Thus, we combine LPC with the proposed method to reconstruct an image as reference. Fig. 5 shows a 4-shot head DWI image, where the proposed method exhibits fewer noise and residual artifacts.
The proposed method can also be applied to sense-based reconstructions, such as MUSSELS ⁶ and MUSE ¹⁵, to achieve higher PSNR. However, further efforts are required to address potential residual artifacts caused by distortion in navigator-echo.

Conclusion

By utilizing navigator-echo data acquired with different polarity readout gradients, it is possible to simultaneously correct two common phase variations in MSDWI without the need for additional prescan. The proposed method, incorporating low-rank constraints, proves to be robust in artifact removal and noise suppression.

Acknowledgements

We acknowledge the equipment support provided by "Anhui Fuqing Medical Equipment Company." The authors express their gratitude to the Information Science Laboratory Center at the University of Science and Technology of China for their measurement services.

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Figures

Figure 1. A typical dual spin-echo DW sequence diagram. Dashed boxes represent diffusion-sensitizing gradients. A 180° RF refocusing pulse is applied after the imaging echo to acquire the navigator-echo. Two navigator-echoes are acquired at each phase-encoding step, with a shortened acquisition window to maintain the phase variation of the image-echo.

Figure 2. Example of a 4-shot brain single-channel naviagtor-echo phase image acquired with positive readout gradient (top row) and negative readout gradient (bottom row). The acquired matrix for the navigation echo is $$$16\times16$$$, zero-padded to $$$256\times256$$$ for reconstruction.

Figure 3. An illustrative diagram shows the acquisition of null space bases using navigator echoes. The echo in each excitation with positive and negative readout gradients in a single channel is separated to create a new dimension, as shown in the figure. Multi-channel data follows the same stacking format within this new dimension，and then the stacked navigation echo data is constructed into a Hankel matrix. A zoomed view of the V matrix of the SVD and a plot of the singular vectors show that the calibration matrix has a null space $$$V_{null}$$$.

Figure 4. Reconstructed images of simulated digital brain phantom. (a) Original image, (b) compact kernel grappa, (c) the proposed method, (d) direct reconstruction without any correction, (e)-(f) error map of (b)-(c)，(g) Image PSNR for different reconstruction methods various levels of Gaussian noise standard deviation.

Figure 5. Reconstructed brain DWI by different methods. (a) Direct reconstruction without any correction, (b) the proposed methods with LPC, (c) compact kernel grappa without LPC, (d) the proposed methods without LPC，(e)-(h) Scale the intensity of the image for (a)-(d) by a factor of 5, (i-l) error maps obtained by subtracting image (b).

Proc. Intl. Soc. Mag. Reson. Med. 32 (2024)

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DOI: https://doi.org/10.58530/2024/2447