考虑热力学衰减的光声成像
Photoacoustic imaging taking into account thermodynamic attenuation
摘要：
在本文中，我们考虑了光声成像的数学模型，它考虑了由于热力学耗散衰减。声（压缩）波的传播是由标量波方程耦合到热方程的过度温度。我们试图从边界处的声学测量知识中恢复初始声学剖面。我们认识到，这个反问题是一个特殊的情况下，边界可观的热弹性系统。这导致使用控制/可观测性工具来证明在弱热弹性耦合制度的初始声学剖面的独特和稳定的恢复。这种方法是建设性的，产生一个可解方程的未知的声学剖面。此外，可以使用共轭梯度法数值地近似该重建方程的解。如果满足某些几何条件的波速，这种方法是非常适合于可变介质和测量的边界的一个子集。我们还提出了一个建议的重建算法的数值实现。
英文摘要：
In this paper we consider a mathematical model for photoacoustic imaging which takes into account attenuation due to thermodynamic dissipation. The propagation of acoustic (compressional) waves is governed by a scalar wave equation coupled to the heat equation for the excess temperature. We seek to recover the initial acoustic profile from knowledge of acoustic measurements at the boundary. We recognize that this inverse problem is a special case of boundary observability for a thermoelastic system. This leads to the use of control/observability tools to prove the unique and stable recovery of the initial acoustic profile in the weak thermoelastic coupling regime. This approach is constructive, yielding a solvable equation for the unknown acoustic profile. Moreover, the solution to this reconstruction equation can be approximated numerically using the conjugate gradient method. If certain geometrical conditions for the wave speed are satisfied, this approach is well--suited for variable media and for measurements on a subset of the boundary. We also present a numerical implementation of the proposed reconstruction algorithm.
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