Nonlinear Inverse Scattering Methods for Three Dimensional Objects

9906651周在五年的PYI赠款下的前一个支持期，加上随后的一年和三年的赠款，使研究人员在反向和前向散射理论方面都取得了重大进展。发展了一种新的非线性逆散射方法来考虑散射体内部的多重散射效应。发展了Born迭代法(BIM)和扭曲Born迭代法(DBIM)，对对比度高达10：1的目标进行了反演，对EZ(TM)极化波表现出0.1波长量级的超分辨率。另一种被称为局部形状函数(LSP)的新方法被用来计算金属散射体上的HZ(TE)极化波和变密度声波的逆散射，以前的方法由于极强的非线性和格林函数奇异性而无法产生收敛解。最近，跳频方法已经发展起来，这种方法可以重建具有高对比度的大散射体。此外，还得到了初步的三维逆散射结果。对非常大的散射体进行反演的需求刺激了对快速前向散射解算器的研究。这些快速算法通过利用散射计算中固有的冗余，精确地解决了散射问题，并实现了计算上的节省。第一种是递归算法(RATMA，RTMA)，它利用波现象的平移性质，在0(N2)次运算中解决了对所有入射源有效的散射问题。新的算法(尼泊尔)改为使用表面等价原理，从而得到一个可并行处理的0(N1.5)算法。该算法已推广到三维空间。最近，各种快速迭代求解器已经被开发出来，它们在0(N)次运算和使用0(N)存储器的情况下提供了一次激励的解。它们涉及到快速多极子方法的使用，以及平移算子对角化的各种方法。目前的建议是继续发展新的非线性逆散射理论，特别强调三维散射体。研究人员计划摆脱Born类型的方法，开发新的方法来对散射对象进行参数化，以实现尽可能好的重建。他们将利用他们在快速向前散射解算器方面的进展作为构建块来加快反演速度，并求解更大的对象和三维对象。还将研究解决大型物体的其他方法，特别是掩埋在缓慢变化的不均匀背景中的物体。最后，他们希望开发能够实现高保真测量的新的实验设备，以便从实验上验证超分辨率现象。***

9906651ChewThe previous support period under the five-year PYI grant plus a subsequent one-year and then three-year grant enabled the investigator to make significant progress in both inverse and forward scattering theory. New nonlinear inverse scattering methods were developed to account for multiple scattering effects within the scattering object. The Born-iterative method (BIM) and distorted-Born-iterative method (DBIM) were developed that demonstrated the inversion of objects with contrasts as great as 10:1 and exhibited super-resolution on the order of 0.1 wavelengths for EZ (TM) polarized wave. Another new technique known as the local-shape-function (LSP) method was developed to perform inverse scattering on metallic scatterers, for HZ (TE) polarized waves, and variable density acoustic waves, where previous methods failed to produce a convergent solution due to extremely strong nonlinearities and Green's function singularity. More recently, the frequency hopping approach where large scatterers with high contrasts can be reconstructed, have been developed. Furthermore, preliminary three-dimensional inverse scattering result has been obtained. The need to invert very large scattering objects stimulated research in fast forward scattering solvers. These fast algorithms solve the scattering problem exactly and achieve computational savings by exploiting inherent redundancies in the scattering calculations. The first of these are recursive algorithms (RATMA, RTMA) that solve the scattering problem valid for all incidence sources in 0(N2) operations by exploiting translational properties of wave phenomenon. The new algorithm (NEPAL) instead uses the surface equivalence principle resulting in an 0 (N1.5) algorithm that is amenable to parallel pro-cessing. This algorithm has been generalized to three dimensions. Recently, various fast iterative solvers have been developed that furnish the solution for one excitation in 0(N log N) operations and using 0(N) memory. They involve the use of fast multipole method, and various methods to diagonalize the translation operator.The current proposal is to continue developing new nonlinear inverse scattering theo-ries with special emphasis on three-dimensional scatterers. The investigators plan to move away from the Born-type methods and exploit new ways of parameterizing the scattering object in order to achieve the best possible reconstruction. They will use their progress in fast forward scattering solvers as building blocks to speed up the inversion and solve much larger objects and three-dimension-objects. Other means of solving large objects, particularly objects buried in a slowly varying inhomogeneous background would be investigated as well. Finally, they wish to develop new experimental apparatus that can achieve high-fidelity measurements so that the super-resolution phenomenon can be verified experimentally. ***