Quantitative photoacoustic computed tomography (qPACT) is an emerging medical imaging modality that carries the promise of high-contrast, fine-resolution imaging of clinically relevant quantities like hemoglobin concentration and blood-oxygen saturation. However, qPACT image reconstruction is governed by a multiphysics, partial differential equation (PDE) based inverse problem that is highly non-linear and severely ill-posed. Compounding the difficulty of the problem is the lack of established design standards for qPACT imaging systems, as there is currently a proliferation of qPACT system designs for various applications and it is unknown which ones are optimal or how to best modify the systems under various design constraints. This work introduces a novel computational approach for the optimal experimental design (OED) of qPACT imaging systems based on the Bayesian Cram\'er-Rao bound (CRB). Our approach incorporates several techniques to address challenges associated with forming the bound in the infinite-dimensional function space setting of qPACT, including priors with trace-class covariance operators and the use of the variational adjoint method to compute derivatives of the log-likelihood function needed in the bound computation. The resulting Bayesian CRB based design metric is computationally efficient and independent of the choice of estimator used to solve the inverse problem. The efficacy of the bound in guiding experimental design was demonstrated in a numerical study of qPACT design schemes under a stylized two-dimensional imaging geometry. To the best of our knowledge, this is the first work to propose Bayesian CRB based design for systems governed by PDEs.

翻译：定量光声计算机断层扫描（qPACT）是一种新兴的医学成像技术，有望实现对血红蛋白浓度与血氧饱和度等临床相关参数的高对比度、精细分辨率成像。然而，qPACT图像重建受控于一个基于多物理场偏微分方程（PDE）的反问题，该问题具有高度非线性与严重的不适定性。该问题的复杂性因qPACT成像系统缺乏成熟的设计标准而加剧：目前针对不同应用场景涌现出多种qPACT系统设计方案，但尚未明确何种方案最优，亦不知如何在各类设计约束下对系统进行最佳改进。本研究提出一种基于贝叶斯克拉默-拉奥界（CRB）的qPACT成像系统最优实验设计（OED）计算新方法。为应对在qPACT无限维函数空间框架下构建该界限所面临的挑战，我们的方法整合了多项技术，包括采用具有迹类协方差算子的先验分布，以及运用变分伴随法计算界限求解所需的似然函数对数导数。所构建的基于贝叶斯CRB的设计度量具有计算高效性，且独立于求解反问题所采用的估计器选择。通过二维理想化成像几何下的qPACT设计方案数值研究，验证了该界限在指导实验设计方面的有效性。据我们所知，这是首个针对PDE约束系统提出基于贝叶斯CRB设计方法的研究。