Diffusion weighted imaging (DWI) is a non-invasive magnetic resonance imaging (MRI) method that detects the free diffusion of water molecules (Jones, 2010), offering better sensitivity for tumors, edema, and other conditions compared to T1-weighted and T2-weighted MRI (Fliedner et al., 2020). Currently, the commonly used DWI includes single-shot echo-planar imaging (ss-EPI) and multi-shot echo-planar imaging (ms-EPI). Traditional ss-EPI has the advantage of fast sampling and insensitivity to motion but suffers from poor resolution and significant image distortion because of inhomogeneous fields (Frost et al., 2015). In contrast, the ms-EPI reduces the length of the echo train, which can decrease the impact of inhomogeneous fields, resulting in images with higher resolution and less distortion (Engström and Skare, 2013). However, due to the influence of diffusion gradients, there are severe phase errors between different shots, leading to serious image artifacts when combining multi-shot data (Madore et al., 2014). Therefore, artifact removal is important for multi-shot DWI. To achieve this goal, two main categories can be roughly identified: navigator echo-based methods (Anderson and Gore, 1994, Guo et al., 2018, Jeong et al., 2013, Ma et al., 2016, Liu et al., 2016) and non-navigator echo-based methods (Mani et al., 2017, Skare et al., 2007, Mani et al., 2020, Huang et al., 2020, Chen et al., 2013, Chu et al., 2015, Guo et al., 2016).

Navigator echo-based methods require additional data acquisition to estimate the phase between shots (Tournier, 2019). This category has two limitations: (1) It prolongs the acquisition time; (2) It presents image artifacts introduced by the mismatch between the navigator echo and each shot due to inhomogeneous magnetic fields or eddy current effects during the acquisition process.

Non-navigator echo-based methods do not acquire additional phase information estimated from navigator echoes, thus requiring alternative approaches to correct phase discrepancies between different shots. Primary non-navigator echo methods include implicit phase reconstruction methods (Mani et al., 2017, Skare et al., 2007, Mani et al., 2020, Huang et al., 2020), explicit phase reconstruction methods (Chen et al., 2013, Chu et al., 2015, Guo et al., 2016, Hu et al., 2017, Zhang et al., 2015), and deep learning reconstruction methods (Aggarwal et al., 2020, Mani et al., 2021, Wang et al., 2022, Zhang et al., 2021).

Implicit phase reconstruction methods avoid estimating the phase generated by each shot. Instead of solving for phase and magnitude separately during modeling, these methods restore the images sampled after each shot and then combine the images from different shots using the square root of the sum of squares. Typical implicit phase reconstruction methods are MUSSELS (Mani et al., 2017) and PLRHM (Huang et al., 2020). MUSSELS constructs a low-rank matrix by leveraging the annihilation relations between different phases, transforming k-space into a Hankel matrix, and establishing an optimization model by constraining the low-rankness of the Hankel matrix. PLRHM (Huang et al., 2020) assumes that smooth phase maps in the image domain have limited support in k-space (Haldar, 2013), resulting in another low-rank optimization model in the k-space domain.

Explicit phase reconstruction methods estimate the phase generated by different shots and reconstruct the phase and magnitude images separately. Once the phase is estimated, these methods only need to estimate fewer unknowns than implicit phase reconstruction methods, thus benefiting image reconstruction (Qian et al., 2023b). This approach offers advantages in imaging scenarios with low signal-to-noise-ratio (SNR) (Chu et al., 2015). Explicit phase reconstruction methods are exemplified by MUSE (Chen et al., 2013), POCS-ICE (Guo et al., 2016), and PAIR (Qian et al., 2023b). MUSE is a basic method that treats each shot as an instance of traditional under-sampled single coil data and then performs image reconstruction using a conventional approach, such as SENSE (Pruessmann et al., 1999). While MUSE provides robust multi-shot diffusion reconstruction, it faces practical limitations including longer scan times that potentially increase motion artifacts (Wang et al., 2024), computational complexity requiring specialized motion correction approaches (Chu et al., 2015), and hardware constraints related to coil configurations. POCS-ICE assumes that different shots share the same magnitude image and iteratively updates the magnitude and phase in the reconstruction, thereby improving the performance of phase correction. PAIR proposes a joint estimation model with paired phase and magnitude priors. It applies two constraints: the low-rankness in the k-space, which is introduced by the smooth phase, and shared edges among DWI in the image domain. PAIR has demonstrated better noise suppression and robustness in challenging scenarios, such as ultra-high b-value or high shot number DWI (Qian et al., 2023b).

These conventional methods, however, require long computational time due to the iterative reconstruction process and need to set many empirical parameters such as the matrix rank and the number of iterations to achieve optimal performance (Karimi et al., 2021). To address these limitations, deep learning has been introduced into multi-shot DWI reconstruction (Aggarwal et al., 2020, Mani et al., 2021, Wang et al., 2022, Zhang et al., 2021). Among them, MRON proposed by Wang et al. (2022) is based on residual learning and requires multi-b-value inputs to enhance the accuracy and robustness of image reconstruction. DL-MUSE (Zhang et al., 2021), a deep learning method based on MUSE, uses fully sampled ss-EPI data as ground truth for training. The U-net learns the mapping from under-sampled data to phase information, enabling phase estimation during inference for traditional reconstruction. However, obtaining the required paired training labels can be challenging in clinical settings. M-MUSSELS (Aggarwal et al., 2020) is a typical approach that unrolls the iterative reconstruction process into a network structure, making it easy to use valuable image priors (Pietsch et al., 2021). However, M-MUSSELS struggles to maintain consistency in magnitude across different shots during reconstruction. If a single shot exhibits significant artifacts in the reconstructed magnitude, this may compromise the final combined magnitude image (Qian et al., 2023b).

Our work will inherit the advantage of fast image reconstruction from deep learning (Aggarwal et al., 2020), and also explicitly estimate the shot phase and magnitude image (Qian et al., 2023b) with neural network. Besides, an attention module is designed to incorporate a high SNR b0 image with small geometric distortions to assist the image reconstruction. Results will be conducted on simulated and in vivo brain DWI data and 6 radiologists will be invited to blindly score the image quality.