arXiv：cs.LG· Anwesa Dey, Johann Rudi, Elena Cherkaev·· 3 小时前AI 评分27
混合 CNN-伴随优化框架：用于磁共振弹性成像中黏弹性组织属性重建
A hybrid CNN-adjoint optimization framework for reconstruction of viscoelastic tissue properties in magnetic resonance elastography
AI 导读
研究提出一种混合框架，将 CNN 重建与伴随优化结合，用于磁共振弹性成像（MRE）中复数剪切模量的重建。CNN 将复数位移测量映射为空间变化的复数剪切模量场，为伴随优化提供快速初始解，从而加快收敛并提升精度。数值实验显示 CNN 可泛化到未见过的组合扰动配置，后续 PDE 约束优化进一步精化重建结果。
正文
Abstract: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.
| Subjects: | Optimization and Control (math.OC); Machine Learning (cs.LG); Numerical Analysis (math.NA) |
| MSC classes: | 68T07, 65K10, 74B05 |
| Cite as: | arXiv:2610.02634 [math.OC] |
| (or arXiv:2610.02634v1 [math.OC] for this version) | |
| https://doi.org/10.48550/arXiv.2610.02634 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Anwesa Dey [view email]
[v1]
Fri, 2 Oct 2026 00:47:56 UTC (1,404 KB)
来源：arXiv：cs.LG · arxiv.org