论文标题
两光子光声断层扫描的基于稀疏性的非线性重建方法
A sparsity-based nonlinear reconstruction method for two-photon photoacoustic tomography
论文作者
论文摘要
我们提出了一种新的非线性优化方法，用于在光声断层扫描（PAT）中稀疏重建单光子吸收和两光子吸收系数。该框架包括最大程度地减少目标功能，涉及与两个边界源函数相对应的内部压力场数据的最小二乘拟合，其中吸收系数和光子密度通过PAT中产生的半线性椭圆形偏微分方程（PDE）相关。此外，该目标功能由$ l^1 $正则化项组成，该项促进了吸收系数的稀疏模式。该框架的动机主要来自一些与解决声学层析成像和当前密度阻抗断层扫描中的反相反问题有关的作品。我们为半线性PDE的解决方案提供了新的证明。此外，涉及半线性PDE的PICARD求解器及其伴随的近端方法用于解决优化问题。提出了几个数值实验，以证明所提出的框架的有效性。
We present a new nonlinear optimization approach for the sparse reconstruction of single-photon absorption and two-photon absorption coefficients in photoacoustic tomography (PAT). This framework comprises of minimizing an objective functional involving a least squares fit of the interior pressure field data corresponding to two boundary source functions, where the absorption coefficients and the photon density are related through a semi-linear elliptic partial differential equation (PDE) arising in PAT. Further, the objective functional consists of an $L^1$ regularization term that promotes sparsity patterns in absorption coefficients. The motivation for this framework primarily comes from some recent works related to solving inverse problems in acousto-electric tomography and current density impedance tomography. We provide a new proof of existence and uniqueness of a solution to the semi-linear PDE. Further, a proximal method, involving a Picard solver for the semi-linear PDE and its adjoint, is used to solve the optimization problem. Several numerical experiments are presented to demonstrate the effectiveness of the proposed framework.
