arXiv：cs.LG（机器学习，全量分类）· Madhu Gupta, Anwesa Dey, Prapti Tala, Souvik Roy·· 9 小时前AI 评分29
基于 CNN 引导的无梯度优化框架实现非线性阻尼粘性光声断层成像初始条件恢复
Initial condition recovery in nonlinear damped viscous photoacoustic tomography using a convolutional neural network-guided gradient-free optimization framework
AI 导读
研究提出一种 CNN 与无梯度优化结合的混合重建框架，用于非线性阻尼粘性光声断层成像（PAT）中的初始压力分布反演。该框架用 CNN 生成初始猜测，并以基于 Pontryagin 最大值原理的 SQH 方法约束 PDE 动力学。数值实验显示，其重建质量、对比度与鲁棒性均显著优于单独的时间反演和 CNN 方法。
正文
Abstract:Photoacoustic tomography (PAT) is a hybrid imaging modality that combines high optical contrast with high ultrasonic resolution for biomedical imaging applications. In this work, we investigate the inverse problem of recovering the initial pressure distribution from boundary measurements in the presence of nonlinear acoustic propagation and viscous attenuation effects. To model these phenomena more accurately, we consider a nonlinear damped viscoelastic wave equation incorporating spatially varying sound speed, temporal attenuation, and nonlinear propagation mechanisms. We first establish the well-posedness of the corresponding forward problem using a Galerkin approximation combined with energy estimates and a fixed-point argument. For the inverse problem, we derive existence, uniqueness, and local uniqueness results under suitable assumptions through a harmonic extension reduction, spectral Laplace transform techniques, and observability estimates. To numerically reconstruct the initial pressure field, we develop a hybrid reconstruction framework that combines a convolutional neural network (CNN) with a gradient-free optimization strategy based on the sequential quadratic Hamiltonian (SQH) method derived from Pontryagin's maximum principle. The CNN is used to generate an informative initial guess, while the SQH framework enforces the governing PDE dynamics during the reconstruction process. Numerical experiments demonstrate that the proposed hybrid strategy significantly improves reconstruction quality, contrast, and robustness compared to standalone time-reversal and CNN-based approaches.
| Subjects: | Optimization and Control (math.OC); Machine Learning (cs.LG) |
| Cite as: | arXiv:2610.01015 [math.OC] |
| (or arXiv:2610.01015v1 [math.OC] for this version) | |
| https://doi.org/10.48550/arXiv.2610.01015 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Souvik Roy [view email]
[v1]
Thu, 1 Oct 2026 03:58:47 UTC (932 KB)
来源：arXiv：cs.LG（机器学习，全量分类） · arxiv.org