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Phase Inconsistency Compensated Multi-shot Diffusion Image Reconstruction with Locally Low-Rank Constraint1Radiological Sciences, University of California, Los Angeles, Los Angeles, CA, United States, 2Radiation Oncology, University of California, Los Angeles, Los Angeles, CA, United States
Synopsis
Multi-shot diffusion imaging is a promising technique to achieve high-resolution visualization of the microstructure of the issue. However, phase variations induced by physiological motion among different shots remains to be a challenge. To improve the reconstruction accuracy, we propose a novel reconstruction method that integrates the information of phase variation within a compressed sensing
Introduction
As a noninvasive technique to explore the microstructure of tissue, diffusion imaging has become a powerful tool in many neuro/cardiac applications. In diffusion imaging, conventional single-shot echo planar imaging (SS-EPI) provides stable and repeatable apparent diffusion coefficient (ADC) measurement (1). However, SS-EPI suffers from low spatial resolution, blurring and distortion artifacts. To address these issues, multi-shot diffusion imaging techniques have been proposed. However, shot-to-shot k-space inconsistency is a major challenge to multi-shot diffusion imaging such that severe aliasing artifacts and signal cancellation will occur if inconsistency is not corrected or compensated. Previous literature described methods using motion compensation gradients (2), extra-navigation (3) or self-navigation (4) to correct/compensate for the inconsistency. However, these methods either greatly lengthen TE/TR or are limited to a small number of shots. In this work, we demonstrated an image reconstruction framework that is based on a diffusion prepared bSSFP sequence with built-in navigator. Proposed method does not penalize TE/TR and it integrates the correction of inconsistency into a compressed sensing based reconstruction.Theory and Methods
Theory and Method: The proposed method is based on a multi-shot diffusion prepared bSFFP sequence shown in Figure 1. Eight central k-space lines were acquired during the ramp-up period of bSSFP sequence and used as the navigator for phase inconsistency correction described as follows: define $$$y_i$$$ as the acquired k-space data matrix (size: $$$n_x * n_y$$$) from the $$$i^{th}$$$ shot (within a total of $$$L$$$ shots, i.e. $$$i=1,2,...,L$$$), $$$x_i$$$ as the image matrix (size: $$$n_x * n_y$$$) reconstructed from the $$$i^{th}$$$ shot, $$$x$$$ as the matrix (size: $$$n_x * n_y * L$$$) concatenating all images from different shots, $$$F$$$ as the Fourier transform operator, $$$D_i$$$ as the sampling operator for $$$i^{th}$$$ shot, and $$$P_i$$$ as the phase compensation matrix (size: $$$n_x * n_y$$$) estimated from the low resolution navigator signal for shot $$$i$$$. Our assumption is that: By compensating back the phase differences between different shots, data redundancy exists along the shot dimension in the resulting multi-shot image series. Specifically, the data redundancy can be expressed as the locally low-rank property (5). Let the image series $$$x$$$ be partitioned into a set $$$\Omega$$$ of small image blocks (size: $$$b_x * b_y * L$$$), and define $$$C_b$$$ as the operator that takes image block $$$b$$$ from the set $$$\Omega$$$ and forms its Casorati matrix (size: $$$b_xb_y * L$$$). The optimization problem that we are going to solve is: $$$min_x\sum_{i=1}^L||D_iFP_ix_i-y_i||_2^2+\sum_{b\in\Omega}||C_bx||_*$$$, where $$$||C_bx||_*$$$ is the nuclear norm of $$$C_bx$$$. Reconstructed images from different shots are combined together using sum of square.
To evaluate the performance of the proposed method, in-vivo experiments were performed on two healthy volunteers. The data were acquired on a 3T scanner (Prisma, Siemens, Germany) using the aforementioned multi-shot diffusion prepared bSFFP sequence with the following parameters: number of shots = 4 or 8, number of coils = 8, number of directions = 15, b value = 500 s/mm2, FOV = 230×230 mm2, slice thickness = 5 mm, acquisition matrix = 192×192, TR/TE= 2000/45 ms.Results
Figure 2a shows the phase image of the 4 different shots from central k-space lines (navigator) and after the proposed locally low-rank method. It can be seen that phase variations across different shots were greatly reduced by the proposed method. Figure 2b shows the comparison of direct Fourier transformation reconstruction without any correction and the reconstruction from the proposed method at a single diffusion direction. Aliasing artifact and signal cancellation were effectively removed by the proposed method. Figure 3 compares the reconstruction results of three methods: direct Fourier transform, MUSE (6), and proposed algorithm with 4 and 8 shot acquisitions. As shown, at 4-shot acquisition, both MUSE and the proposed algorithm can recover clean images within the brain region. However, MUSE still suffers from residual aliasing artifacts at background region. At the higher 8-shot acquisition, MUSE reconstruction has higher noise level compared with the proposed algorithm. This is because the underlying SENSE reconstruction in MUSE reconstruction breaks down due to high acceleration factor for each shot. On the contrary, proposed algorithm is still able to provide high-quality reconstruction. Figure 4 the reconstruction results of all 15 diffusion directions with a 4-shot acquisition from direct Fourier transform and the proposed method. Although each individual direction has different inconsistency among shots (and therefore different aliasing artifacts), the proposed method is still able to recover clean images with artifacts removed.Discussion and Conclusion
In-vivo experiments validated the advantages of the proposed method for multi-shot diffusion imaging with improved accuracy and reduced artifacts, benefiting from a better constraint that exploits data redundancy after inconsistency correction. With further validation, the proposed method can be used to reconstruct high-quality multi-shot 3D diffusion imaging.Acknowledgements
No acknowledgement found.References
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