非线性阻尼粘性光声断层扫描中基于卷积神经网络引导的无梯度优化框架的初始条件恢复
Initial condition recovery in nonlinear damped viscous photoacoustic tomography using a convolutional neural network-guided gradient-free optimization framework
- University of Utah（犹他大学）
- The University of Texas at Arlington（德克萨斯大学阿灵顿分校）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究提出一种结合卷积神经网络与基于序贯二次哈密顿方法的无梯度优化框架，用于非线性阻尼粘性光声断层扫描中的初始压力分布恢复，数值实验表明其显著提升了重建质量、对比度和鲁棒性。
AI中文摘要：
光声断层扫描（PAT）是一种混合成像模态，结合了高光学对比度与高超声分辨率，用于生物医学成像应用。在本工作中，我们研究了在非线性声传播和粘性衰减效应存在的情况下，从边界测量中恢复初始压力分布的逆问题。为了更准确地模拟这些现象，我们考虑了一个非线性阻尼粘弹性波动方程，该方程包含空间变化的声速、时间衰减和非线性传播机制。我们首先通过伽辽金近似结合能量估计和不动点论证，建立了相应正问题的适定性。对于逆问题，我们在适当假设下，通过调和延拓约简、谱拉普拉斯变换技术和可观测性估计，推导了存在性、唯一性和局部唯一性结果。为了数值重建初始压力场，我们开发了一种混合重建框架，该框架将卷积神经网络（CNN）与基于庞特里亚金最大值原理推导的序贯二次哈密顿（SQH）方法的无梯度优化策略相结合。CNN用于生成信息丰富的初始猜测，而SQH框架在重建过程中强制执行控制偏微分方程动力学。数值实验表明，与独立的时间反转和基于CNN的方法相比，所提出的混合策略显著提高了重建质量、对比度和鲁棒性。
英文摘要：
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.
