Regularization method study in ultrasound inverse scattering imaging 超声逆散射成像问题中的正则化方法研究
Microwave is the information carrier . both amplitude and phase of the measured scattering data can be used in microwave imaging 微波成像是指以微波作为信息载体的一种成像手段,实质属于电磁逆散射问题。
The electromagnetic inverse scattering is one of most difficult problem due partly to its ill - posed , nonlinear and instablity nature 由于逆散射问题的求解存在病态性、非唯一性以及不稳定性,这给它的求解带来很大困难。
The relating to methods based on the research on international and domestic electromagnetic wave ( elastic wave , acoustic wave ) for the identification of flaws are all - round viewed 本文对国际和国内基于电磁波(声波,弹性波)逆散射理论研究缺陷识别的有关方法给予了全面的评述。
Electromagnetic inverse scattering aims to reconstruct the distribution of the dielectric characteristics of unknown inhomogeneous dielectric object by scattering wave . in the near thirty years , it has been extensively used in military , medical imaging and nondestructive testing field 电磁逆散射(又称为电磁反演或电磁成像)是对接收到的未知物体的散射信号进行分析处理从而重建未知物体的几何形状和内部结构。
In my artice , positive scattering problem is solved by fdtd method and inverse scattering problem is sovled by genetic algorithm ( ga ) ga is a kind of searching method which simulates the normal evolution . in the solution of inverse problem convergence speed is significent and parameter setting has much effect on it 在采用遗传算法求解逆散射的问题时,收敛速度是非常重要的。不同的参数设置会影响到它的收敛速度和结果。因此参数的设置在遗传算法中有很重要的作用。
From mathematical models for inverse scattering in two dimensional inho - mogenous media including variable impedance , all kinds of probable mixed variable impedance boundaries and cracks , from interior and exterior trans - mission problems and radiation condition , ill - posed integral equation and indicator function method are formulated for the diverse of boundary iden - tification . it is shown that the kernel of the integral equation characters the boundary of scatterer , which is determined by solving it by virtual of regularity method , meanwhile , some numerical tests are given . 3 在二维非均匀介质逆散射边界识别的数学模型(包括一般的非均匀介质,正交各向异性介质,变阻抗介质,各种可能的混合变阻抗边界问题)下,由内透射问题和外透射问题以及辐射条件,推导了上述介质的边界识别的积分方程和指示函数方法,由于积分方程的核充分表征了散射物的边界,由此说明只要利用正则化方法求解该积分方程,就可以确定散射物的边界。
First , in virtual of identification of flaws is a typical of in - verse problems , proceeding from time - harmonic electromagnetic maxwell ' s equa - tion and helmholtz equation , the uniqueness and existence of direct scattering problems including the numerical algorithms of diverse of boundary conditions is given . second , the uniqueness and existence of inverse scattering problems and the theory of ill - posed integral equation are briefly looked back upon . finally , indicator function method for boundary identification is set up under all kinds of boundary conditions for inverse scattering of homogenous and inhomogenous objects , meanwhile , the proof of possibility for near - field measurements and nu - merical simulation are given 由于缺陷的识别是一类典型的反问题,因而首先从时谐电磁maxwell方程和helmholz方程出发,具体地阐述了求解正散射问题的有关方法,包括各种(夹杂)边界条件下的数值解法,就解的存在性唯一性给予了肯定的回答;随后对逆散射问题的理论作了简短的回顾,包括解的唯一性以及非线性不适定积分方程的处理等;然后对均匀介质和非均匀介质的逆散射问题建立了在各种边界条件下的边界识别的指示函数方法,鉴于近场数据获得的重要性,对近场测试时边界识别的方法给予了相应的证明,并且实现了数值模拟。
This method is called microwave imaging technique based on rga under frequency domain . after comprehending the principle of the microwave imaging and rga , we present a novel imaging method for the first time . it is a full - time - domain algorithm based on rga , fdtd technique is applied to solve direct problem while the rga is applied to solve inverse problem 在对微波成像的机理和实数遗传算法的工作机制有了初步了解之后,本文首次提出用时域遗传算法来求解导体目标的成像问题,即用时域有限差分法来求解散射问题,而逆散射问题还是采用实数遗传算法,得到了基于实数遗传算法的全时域的微波成像技术。
From mathematical models for inverse scattering in two dimensional homoge - nous media including dirichlet , neumann , robin , all kinds of probable mixed boundaries and cracks , direct and inverse scattering are discussed , and ill - posed integral equation and indicator function method are formulated for the diverse of boundary identification . it is shown that the kernel of the integral equation characters the boundary of scatterer , which is determined by solv - ing it by virtual of regularity method , meanwhile , some numerical tests are given . 2 在二维均匀介质逆散射各种边界识别的数学模型(包括dirichlet , neumann , robin ,各种可能的混合边界问题,裂纹问题)下,分别考虑了正散射问题和逆散射问题,推导了上述各种边界识别的不适定积分方程以及指示函数方法,由于积分方程的核充分表征了散射物的边界,由此说明只要利用正则化方法求解该积分方程,就可以确定散射物的边界,并给出了一些数值实验。