发表机构
The University of Utah; Virginia Tech（犹他大学; 弗吉尼亚理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出混合CNN-伴随优化框架，利用CNN提供初始重建并初始化PDE约束优化，以高效准确地重建磁共振弹性成像中的粘弹性组织性质。
AI 中文摘要
磁共振弹性成像（MRE）是一种非侵入性成像方式，通过剪切波传播量化软组织的粘弹性质。从测量的位移场恢复复值剪切模量导致严重不适定的逆问题，特别是在存在噪声和有限边界激励的情况下。我们研究了基于伴随的优化、卷积神经网络（CNN）重建以及结合两种方法的混合框架。前向模型基于具有复剪切模量的修正稳态Stokes系统的标量形式。我们建立了前向问题的适定性、极小值的存在性以及基于伴随公式的一阶最优性条件，并实现了带有Armijo线搜索的非线性共轭梯度方法。虽然PDE约束优化可以精确细化系数重建，但其性能强烈依赖于初始化。因此，我们构建了一个二维CNN，将复值位移测量映射到空间变化的复剪切模量场，并提供快速、信息丰富的初始重建。所提出的混合方法使用CNN重建来初始化基于伴随的优化，从而实现更快的收敛和更高的精度。CNN在包含单个扰动的系数场上训练，并在单个和先前未见过的组合配置上进行测试。数值实验表明，CNN能够泛化到这些更具挑战性的配置，而随后的PDE约束优化进一步细化了重建系数。这些结果展示了将数据驱动初始化与基于物理的优化相结合用于高效准确的MRE重建的潜力。
英文摘要
Magnetic resonance elastography (MRE) is a noninvasive imaging modality for quantifying the viscoelastic properties of soft tissues from shear wave propagation. Recovering the complex-valued shear modulus from measured displacement fields leads to a severely ill-posed inverse problem, particularly in the presence of noise and limited boundary excitations. We investigate adjoint-based optimization, convolutional neural network (CNN) reconstruction, and a hybrid framework combining both approaches. The forward model is based on a scalar form of the modified stationary Stokes system with a complex shear modulus. We establish well-posedness of the forward problem, existence of minimizers, and first-order optimality conditions for the adjoint-based formulation, and implement a nonlinear conjugate-gradient method with Armijo line search. While PDE-constrained optimization can accurately refine coefficient reconstructions, its performance depends strongly on initialization. We therefore construct a two-dimensional CNN that maps complex-valued displacement measurements to spatially varying complex shear modulus fields and provides rapid, informative initial reconstructions. The proposed hybrid method uses the CNN reconstruction to initialize the adjoint-based optimization, yielding faster convergence and improved accuracy. The CNN is trained on coefficient fields containing individual perturbations and tested on both individual and previously unseen combined configurations. Numerical experiments demonstrate that the CNN generalizes to these more challenging configurations, while subsequent PDE-constrained optimization further refines the reconstructed coefficient. These results demonstrate the potential of combining data-driven initialization with physics-based optimization for efficient and accurate MRE reconstruction.
