论文标题
2.5维反问题的快速数值集成技术
Fast Numerical Integration Techniques for 2.5-Dimensional Inverse Problems
论文作者
论文摘要
涉及微波和超声波的逆散射需要非线性优化问题的数值解。为了减轻整个三维（3-D）逆问题的计算负担，通常将物体近似为二维（2-D），并通过二维散射模式的傅立叶整合来将对象近似为二维（2-D），并将发射器传感器视为3-D。所得积分是奇异的，因此需要大量的集成点，其中每个点对应于2-D溶液。为了降低计算复杂性，本文提出了一组转换的快速整合方法。我们将对象建模为2-D，但传输和接收器对为3-D；因此，我们将解决方案称为2.5-D逆问题。收敛结果表明，所提出的集成技术具有指数收敛，因此具有降低的计算复杂性，以计算2.5-D Green的功能以解决反向散射问题。
Inverse scattering involving microwave and ultrasound waves require numerical solution of nonlinear optimization problem. To alleviate the computational burden of a full three-dimensional (3-D) inverse problem, it is a common practice to approximate the object as two-dimensional (2-D) and treat the transmitter and receiver sensors as 3-D, through a Fourier integration of 2-D modes of scattering. The resulting integral is singular, and hence requires a prohibitively large number of integration points, where each point corresponds to a 2-D solution. To reduce the computational complexity, this paper proposes fast integration approaches by a set of transformations. We model the object in 2-D but the transmit and receiver pairs as 3-D; hence, we term the solution as a 2.5-D inverse problem. Convergence results indicate that the proposed integration techniques have exponential convergence and hence have a reduces the computational complexity to compute 2.5-D Green's function to solve inverse scattering problems.
