论文标题
具有理想化的压电传感器的光声成像的可溶性
Solvability for Photoacoustic Imaging with Idealized Piezoelectric Sensors
论文作者
论文摘要
用于光声成像的大多数重建算法都假设压力场是通过放置在检测表面上的超声传感器来测量的。但是，由于其不均匀的定向和频率响应以及分辨率的限制，此类传感器不能准确地测量压力。通常用于光声成像的压电传感器就是这种情况。在本文中，使用匹配的渐近扩展方法和压电性的基本组成关系，我们为压电传感器提出了一个简单的数学模型。该方法同时建模压力波如何诱导压电测量以及传感器的存在如何影响压力波。使用此模型，我们分析了压电传感器收集的数据是否导致光声成像问题的数学解决性。我们得出的结论是，在某些规范空间和几何假设下，这个成像问题在某些规范的空间中得到了很好的影响。我们还提出了一种迭代重建算法，该算法结合了压电测量模型。提出了重建算法的数值实现。
Most reconstruction algorithms for photoacoustic imaging assume that the pressure field is measured by ultrasound sensors placed on a detection surface. However, such sensors do not measure pressure exactly due to their non-uniform directional and frequency responses, and resolution limitations. This is the case for piezoelectric sensors that are commonly employed for photoacoustic imaging. In this paper, using the method of matched asymptotic expansions and the basic constitutive relations for piezoelectricity, we propose a simple mathematical model for piezoelectric transducers. The approach simultaneously models how the pressure waves induce the piezoelectric measurements and how the presence of the sensors affects the pressure waves. Using this model, we analyze whether the data gathered by piezoelectric sensors leads to the mathematical solvability of the photoacoustic imaging problem. We conclude that this imaging problem is well-posed in certain normed spaces and under a geometric assumption. We also propose an iterative reconstruction algorithm that incorporates the model for piezoelectric measurements. A numerical implementation of the reconstruction algorithm is presented.
