Abstract：Magnetoacoustic concentration tomography with magnetic induction (MACT-MI) is a new method for imaging the concentration of magnetic nanoparticles (MNPs) based on magnetoacoustic coupling. Existing studies on the inverse problem of MACT-MI have insufficient image resolution and slow reconstruction speed for MNPs. Therefore, this study focuses on the theoretical simplification and algorithmic optimization to simultaneously improve the quality and efficiency of reconstructed images. Firstly, this paper presents a Lorentz force potential acoustic source image reconstruction method based on the transpose-free quasi-minimal residual (TFQMR) algorithm. A possible function is introduced to construct the correlation between the acoustic pressure signal and MNP concentration, effectively circumventing the complexity of the traditional acoustic pressure-concentration solution. The acoustic field data are discretized using the finite element method, transforming the concentration reconstruction into a sparse system of equations. Subsequently, the TFQMR algorithm solves the concentration distribution due to its fast convergence, low memory usage, and the ability to avoid explicitly computing the matrix transpose when dealing with large sparse systems, thereby significantly improving solution efficiency. In addition, a variety of 2D axisymmetric simulation models were constructed in COMSOL. These models cover the distribution of MNPs at different sizes (radii 2 mm to 12.5 mm), geometries (circular, elliptical, triangular, hexagonal), and noise levels (signal-to-noise ratios 5 dB to 20 dB). The TV-MoM method, the regularized pre-optimization LSQR method, and the BICGSTAB method are compared. In the absence of noise interference, the average correlation coefficient is higher than 0.947 6, the average relative error is lower than 0.399 3, the average structural similarity is higher than 0.95, and the average image reconstruction time is reduced to 39.84 s. The shape contours of MNPs can be clearly reconstructed under different noise models, with relative residuals below 0.009 9, thereby maintaining stable imaging quality. The results show that the present method overcomes the boundary-singularity problem in conventional image reconstruction, reduces streak artifacts within the reconstruction, and improves uneven concentration distribution and imaging resolution. The solution complexity is reduced by the Lorentz force potential acoustic source theory, and the matrix equations can be solved efficiently using the TFQMR algorithm, which has strong stability and noise immunity. The computational cost is reduced, and the reconstruction speed is enhanced.
闫孝姮, 付鹏, 陈伟华, 侯潇涵. 基于TFQMR的洛伦兹力势声源MACT-MI图像重建研究[J]. 电工技术学报, 2026, 41(4): 1087-1099.
Yan Xiaoheng, Fu Peng, Chen Weihua, Hou Xiaohan. Research on MACT-MI Image Reconstruction of Lorentz Force Potential Acoustic Source Based on TFQMR. Transactions of China Electrotechnical Society, 2026, 41(4): 1087-1099.
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