磁声层析成像（Magnetoacoustic Tomography, MAT）是一种耦合电磁激励与声学检测的新型无创成像方法，可实现对生物组织电特性分布的高分辨率、高对比度成像，在早期疾病诊断和生理学研究中展现出巨大潜力。在MAT的实际应用中，磁声信号信噪比低，波形叠加平均处理耗时且数据量大，而使用稀疏采样策略能够有效降低数据采集对通道数量的需求，从而简化系统设计并降低硬件成本，同时有助于缓解存储压力，并加速后续的图像重建进程。然而，稀疏采样不可避免地导致所采集数据的严重不完备性，使得图像重建存在严重的不适定逆问题。传统的解析重建方法难以有效抑制由数据缺失引入的伪影；常规的迭代重建算法虽在一定程度上提升了图像质量，但普遍面临计算效率偏低、对物理模型精确性依赖过高以及先验信息融合困难等问题；而深度学习方法往往受限于配对实验数据集的匮乏，以及仿真数据与实验数据之间存在显著域差异等问题。因此，本论文针对稀疏采样MAT重建中面临的伪影严重、精度低、效率低以及数据依赖性强等问题，分别从模型驱动的优化迭代和数据驱动的深度学习两条主要技术路径展开了系统性研究。

对于模型驱动方法，本研究首先构建了基于换能器的空间指向性、声衰减及脉冲响应等关键物理因素的精确MAT离散化物理正向模型。在此基础之上，提出了一种基于优越化共轭梯度的迭代重建算法（Superiorized Magnetoacoustic Reconstruction, SMAR）。该算法将优越化理论框架与共轭梯度法相结合，通过在迭代过程中引入非二次正则化及背景约束等先验信息作为算法的扰动项，使得在保持原有收敛特性的同时，显著增强了对目标图像复杂结构的表征能力。数值仿真与仿体实验结果表明，SMAR及其施加背景约束的变体在重建精度、噪声鲁棒性及稀疏视角伪影抑制方面，均显著优于传统的解析方法和迭代方法，并通过GPU并行技术实现了数量级的计算效率提升，为高质量稀疏MAT重建提供了高效且可靠的模型驱动计算方法。

对于数据驱动方法，本研究提出了一种基于原始信号域数据的间接无监督稀疏重建网络（Sparse Magnetoacoustic Reconstruction Network, SMART-Net）。为克服MAT深度学习应用中普遍存在的实验数据有限以及模拟与实验之间的域差异问题，SMART-Net框架采用两阶段学习策略：首先，设计并实现了一个基于对比学习的无监督模拟-实验域适应网络（Simulation-to-Experiment Domain Adaptation Network, SEDAN），该网络能够从未配对的模拟与实验信号中学习跨域映射关系，从而生成了大规模的与真实特征相匹配的类实验信号数据集；其次，利用SEDAN生成的数据，以监督学习方式训练第二阶段的基于U-Net架构的全采样信号预测网络，使其能从输入的稀疏MAT测量信号中精确恢复因稀疏采样而丢失的完整信号信息。数值仿真、仿体、离体生物组织以及在体小鼠胃部成像实验结果表明，SMART-Net在不同稀疏采样条件下的伪影抑制能力和重建准确性等方面，均优于传统解析方法、模型驱动算法以及其他深度学习基准方法，并展现出良好的跨组织类型与激励模式的泛化能力和极高的在线重建效率。

本论文对稀疏MAT重建算法进行了系统性研究，分别在模型驱动和数据驱动两个方向上开发了重建算法。模型驱动的SMAR算法为高精度的MAT重建提供了可解释的优化迭代方案；数据驱动的SMART-Net算法能在缺乏实验数据集的情况下实现高质量、高效率的稀疏磁声重建，尤其在处理复杂实验数据以及面临极端稀疏采样条件时，展现出更强的鲁棒性。这些方法为提升稀疏采样MAT的成像质量和成像速度提供有力手段，也为基于数据稀疏采样条件下实现多模态医学成像提供了重要参考。

Magnetoacoustic Tomography (MAT), an emerging non-invasive biomedical imaging modality coupling electromagnetic excitation with acoustic detection, enables high-resolution, high-contrast imaging of tissue electrical property distributions, crucial for early disease diagnosis and pathophysiological research. In practical applications of MAT, magnetoacoustic signals often exhibit a low signal-to-noise ratio (SNR). The process of waveform-stacking averaging, while employed to enhance SNR, is time-consuming and generates a large volume of data. The adoption of sparse sampling strategies effectively reduces the demand for data acquisition channels, thereby simplifying system design and lowering hardware costs. Furthermore, the reduction in raw data volume also alleviates storage pressure and accelerates subsequent image reconstruction processes. However, sparse sampling inevitably leads to severe incompleteness of the acquired data, rendering image reconstruction a severely ill-posed inverse problem. Traditional analytical reconstruction methods struggle to effectively suppress artifacts introduced by data missing. While conventional iterative reconstruction algorithms offer some improvement in image quality, they generally face challenges such as low computational efficiency, high dependency on physical model accuracy, and difficulties in fusing prior information. Deep learning methods are often limited by the scarcity of paired experimental datasets and significant domain gaps between simulated and experimental data. Therefore, this paper focuses on the critical issues encountered in sparse MAT reconstruction, including severe artifacts, low accuracy, poor efficiency, and strong data dependency, systematically investigating two primary technical pathways: model-driven optimized iteration and data-driven deep learning.

In terms of model-driven methods, this research first constructed a more precise discretized physical MAT forward model, which comprehensively considers critical physical factors in actual imaging systems such as transducer spatial directivity, acoustic attenuation, and impulse response. Based on this foundation, an iterative magnetoacoustic reconstruction algorithm based on superiorized conjugate gradient (SMAR) was proposed. This algorithm integrates the superiorization theoretical framework with the conjugate gradient method, efficiently incorporating prior information such as non-quadratic regularization and background constraints as perturbation terms during the iteration process. This approach significantly enhances the representational capability for complex image structures while maintaining the original convergence characteristics. Results from numerical simulations and physical phantom experiments demonstrate that SMAR and its variant with background constraints markedly outperform traditional analytical and iterative methods in terms of reconstruction accuracy, noise robustness, and sparse-view artifact suppression. Furthermore, a several-fold improvement in computational efficiency was achieved through GPU parallelization, providing an efficient and reliable model-driven computational solution for high-quality sparse MAT reconstruction.

In terms of data-driven methods, this research introduces an indirect unsupervised sparse reconstruction network based on raw signal-domain data-based sparse magnetoacoustic reconstruction network (SMART-Net). To overcome the prevalent challenges of experimental data scarcity and the domain gap between simulation and experiment in MAT applications, the SMART-Net employs a two-stage learning strategy. Firstly, a simulation-to-experiment domain adaptation network (SEDAN), based on contrastive learning, was designed and implemented. This network efficiently learns cross-domain mapping from unpaired simulated and experimental signals, thereby generating a large-scale, pseudo-experimental signal dataset with features highly consistent with real data. Secondly, utilizing the dataset generated by SEDAN, a U-Net-based full-sample signal prediction network was trained via supervised learning in the second stage, enabling it to accurately complete missing signals caused by sparse sampling from the input sparse MAT measurement signals. Experimental results from numerical simulations, physical phantoms, ex vivo biological tissues, and in vivo mouse stomach models indicate that SMART-Net surpasses traditional analytical methods, model-driven algorithms, and other representative deep learning benchmarks in terms of artifact suppression capabilities and reconstruction accuracy under various sparse sampling conditions. It also exhibits good generalization across different tissue types and excitation modes, along with extremely high reconstruction efficiency.

Through systematic research on sparse MAT reconstruction algorithms, this paper has developed novel reconstruction algorithms in both model-driven and data-driven. The model-driven SMAR algorithm provides an interpretable optimized iterative solution for high-precision MAT reconstruction. The data-driven SMART-Net algorithm enables high-quality, high-efficiency sparse magnetoacoustic reconstruction in the absence of experimental datasets, demonstrating enhanced robustness, particularly in processing complex experimental data or under extremely sparse sampling conditions. These methodologies provide robust means for enhancing both the imaging quality and acquisition speed of MAT under sparse sampling conditions. Furthermore, they offer a valuable reference for the realization of multimodal medical imaging under constraints of sparse data acquisition.