The University of Chicago, Department of Radiology, 5841 South Maryland Avenue, Chicago, Illinois 60637, USA.
J Biomed Opt. 2010 Mar-Apr;15(2):021308. doi: 10.1117/1.3333550.
Previous research correcting for variable speed of sound in photoacoustic tomography (PAT) based on a generalized radon transform (GRT) model assumes first-order geometrical acoustics (GA) approximation. In the GRT model, the pressure is related to the optical absorption, in an acoustically inhomogeneous medium, through integration over nonspherical isochronous surfaces. Previous research based on the GRT model assumes that the path taken by acoustic rays is linear and neglects amplitude perturbations to the measured pressure. We have derived a higher-order GA expression that takes into account the first-order effect in the amplitude of the measured signal and higher-order perturbation to the travel times. The higher-order perturbation to travel time incorporates the effect of ray bending. Incorrect travel times can lead to image distortion and blurring. These corrections are expected to impact image quality and quantitative PAT. We have previously shown that travel-time corrections in 2-D suggest that perceivable differences in the isochronous surfaces can be seen when the second-order travel-time perturbations are taken into account with a 10% speed-of-sound variation. In this work, we develop iterative image reconstruction algorithms that incorporate this higher-order GA approximation assuming that the speed of sound map is known. We evaluate the effect of higher-order GA approximation on image quality and accuracy.
先前基于广义 Radon 变换（GRT）模型校正光声断层成像（PAT）中可变声速的研究都假设了一阶几何声学（GA）近似。在 GRT 模型中，通过对非球形等时面进行积分，压力与声速不均匀介质中的光吸收相关。基于 GRT 模型的先前研究假设声射线的路径是线性的，并忽略了对测量压力的幅度扰动。我们已经推导出一个更高阶的 GA 表达式，它考虑了测量信号幅度的一阶效应以及对传播时间的更高阶扰动。传播时间的高阶扰动包含了射线弯曲的影响。不正确的传播时间会导致图像变形和模糊。这些校正有望影响图像质量和定量 PAT。我们之前已经表明，在 2-D 中，当考虑到二阶传播时间扰动时，对于 10%的声速变化，在等时面中可以看到可感知的差异。在这项工作中，我们开发了迭代图像重建算法，假设声速图已知，这些算法包含了这种更高阶的 GA 近似。我们评估了更高阶 GA 近似对图像质量和准确性的影响。
