School of Computer Science and Engineering, Southeast University, Nanjing, People's Republic of China.
CAS Key Laboratory of Molecular Imaging, Institute of Automation, Chinese Academy of Sciences, Beijing, People's Republic of China.
Phys Med Biol. 2024 Jul 16;69(15). doi: 10.1088/1361-6560/ad56f1.
Magnetic particle imaging (MPI) is an emerging medical tomographic imaging modality that enables real-time imaging with high sensitivity and high spatial and temporal resolution. For the system matrix reconstruction method, the MPI reconstruction problem is an ill-posed inverse problem that is commonly solved using the Kaczmarz algorithm. However, the high computation time of the Kaczmarz algorithm, which restricts MPI reconstruction speed, has limited the development of potential clinical applications for real-time MPI. In order to achieve fast reconstruction in real-time MPI, we propose a greedy regularized block Kaczmarz method (GRBK) which accelerates MPI reconstruction.GRBK is composed of a greedy partition strategy for the system matrix, which enables preprocessing of the system matrix into well-conditioned blocks to facilitate the convergence of the block Kaczmarz algorithm, and a regularized block Kaczmarz algorithm, which enables fast and accurate MPI image reconstruction at the same time.We quantitatively evaluated our GRBK using simulation data from three phantoms at 20 dB, 30 dB, and 40 dB noise levels. The results showed that GRBK can improve reconstruction speed by single orders of magnitude compared to the prevalent regularized Kaczmarz algorithm including Tikhonov regularization, the non-negative Fused Lasso, and wavelet-based sparse model. We also evaluated our method on OpenMPIData, which is real MPI data. The results showed that our GRBK is better suited for real-time MPI reconstruction than current state-of-the-art reconstruction algorithms in terms of reconstruction speed as well as image quality.Our proposed method is expected to be the preferred choice for potential applications of real-time MPI.
磁共振粒子成像（MPI）是一种新兴的医学层析成像方式，能够实现实时高灵敏度、高空间和时间分辨率成像。对于系统矩阵重建方法，MPI 重建问题是一个不适定的反问题，通常使用 Kaczmarz 算法求解。然而，Kaczmarz 算法的计算时间较高，限制了 MPI 重建速度，这限制了实时 MPI 在潜在临床应用中的发展。为了在实时 MPI 中实现快速重建，我们提出了一种贪婪正则化块 Kaczmarz 方法（GRBK），用于加速 MPI 重建。GRBK 由系统矩阵的贪婪分区策略组成，该策略可以将系统矩阵预处理成条件良好的块，以促进块 Kaczmarz 算法的收敛，以及正则化块 Kaczmarz 算法，该算法可以同时实现快速准确的 MPI 图像重建。我们使用来自三个体模的模拟数据在 20dB、30dB 和 40dB 噪声水平下对我们的 GRBK 进行了定量评估。结果表明，与流行的正则化 Kaczmarz 算法（包括 Tikhonov 正则化、非负融合套索和基于小波的稀疏模型）相比，GRBK 可以将重建速度提高一个数量级。我们还在 OpenMPIData 上评估了我们的方法，这是真实的 MPI 数据。结果表明，与当前最先进的重建算法相比，我们的 GRBK 在重建速度和图像质量方面更适合实时 MPI 重建。我们提出的方法有望成为实时 MPI 潜在应用的首选。
