Multiwave imaging in an enclosure with variable wave speed
Multiwave imaging in an enclosure with variable wave speed
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具有可变波速的外壳中的多波成像
DOI：
10.1088/0266-5611/31/6/065009
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发表时间：
2015
期刊：
影响因子：
2.1
通讯作者：
Carlos Montalto
中科院分区：
文献类型：
--
作者：
Sebastián Acosta;Carlos Montalto
在本文中，我们考虑的数学模型的热声和光声层析成像恢复的初始条件的波场的知识，其边界值。与自由空间的设置，我们认为在一个区域内的波问题所包围的表面施加阻抗边界条件。该条件模拟了物理边界的存在，例如界面或声镜，其将一些波能量反射回封闭域。通过认识到，逆问题是相当于一个声明的边界可观性，我们使用控制算子证明的唯一性和稳定的恢复的初始波剖面的边界测量的知识。由于我们的证明是建设性的，我们明确推导出一个可解方程的未知初始条件。这个方程可以用共轭梯度法数值求解。我们还提出了一种基于稳定波的替代方法。当阻抗系数不恒为零时，这导致指数和一致收敛的Neumann级数重建。在这两种情况下，如果众所周知的几何条件得到满足，我们的方法自然适合于可变的波速和测量的边界的一个子集。
In this paper we consider the mathematical model of thermo- and photo-acoustic tomography for the recovery of the initial condition of a wave field from knowledge of its boundary values. Unlike the free-space setting, we consider the wave problem in a region enclosed by a surface where an impedance boundary condition is imposed. This condition models the presence of physical boundaries such as interfaces or acoustic mirrors which reflect some of the wave energy back into the enclosed domain. By recognizing that the inverse problem is equivalent to a statement of boundary observability, we use control operators to prove the unique and stable recovery of the initial wave profile from knowledge of boundary measurements. Since our proof is constructive, we explicitly derive a solvable equation for the unknown initial condition. This equation can be solved numerically using the conjugate gradient method. We also propose an alternative approach based on the stabilization of waves. This leads to an exponentially and uniformly convergent Neumann series reconstruction when the impedance coefficient is not identically zero. In both cases, if well-known geometrical conditions are satisfied, our approaches are naturally suited for variable wave speed and for measurements on a subset of the boundary.
影响因子：
3.5
作者：
Shah, Jignesh;Park, Suhyun;Emelianov, Stanislav Y.
通讯作者：
Emelianov, Stanislav Y.