Nonlinear Inverse Scattering Methods for Large Objects

WPC 2 R B J Z X Courier#|x x 6 X@K X@QMS JetScript QMSJETSC.PRS x@h}X@T？X x 6 X@K X@T R&amp；H H 6 X@K h@2 u 6~；)！T-S：t@，`；&amp；%t：u 2 4“u$u t 3 y u O t 2 9302145咀嚼5年期PYI资助下的前一个支持期，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)，证明了对比度高达10：1的物体的反演，并显示出0.1波长数量级的超分辨率。另一种被称为局部形状函数(LSF)的新技术被发展用于对金属散射体进行逆散射，以前的方法由于极强的非线性而无法产生收敛解。最近发现，LSF方法也可以用于介质散射的反演，并且绕过了10：1的对比度限制。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。第一种算法(RTMA)利用波现象的平移性质，解决了)(N2.5)运算中所有入射源的？0散射问题。Next算法(RATMA)是否利用了聚合？属性导致O(N 2)算法。新的算法(尼泊尔)改为使用表面等效原理，从而产生？一种适用于并行处理的O(N 1.5)算法。目前的建议是继续在发展新的非线性逆散射理论方面取得进展。我们计划取代Born类型的方法，并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。我们将使用我们在快速向前散射解算器方面的进展作为构建块来加速反演并求解更大的对象。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，我们希望开发能够实现高保真测量的新的实验装置，以便在实际系统中充分发挥这些新的逆方法的潜力。

WPC 2 R B J Z X Courier #| x x 6 X @ K X @ QMS JetScript QMSJETSC.PRS x @ h h h h }X @T ? x x x x 6 X @ K X @ T R & H H H H 6 X @ K h @ 2 u 6~ ; ) ! t - S :t @ ,` ; & % t : u 2 4 " u$ u t 3 y u O t 2 9302145 Chew The previous support period under the 5 year PYI grant enabled the investigator to make significant progress in both inverse and forward scattering theory. New non linear 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. Another new technique known as the local shape function (LSF) method was developed to perform inverse scattering on metallic scatters where previous methods failed to produce a convergent solution due to extremely strong nonlinearities. Recently it was found that the LSF method could also be used for the inversion of dielectric scatters and bypass the 10:1 contrast limitation. 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 algorithms (RTMA) solved the ? 0 scattering problem valid for all incidence sources in )(N 2.5 ) operations by exploiting translational properties of wave phenomenon. T he next algorithm (RATMA) exploited an aggregation ? property resulting in an O(N 2 ) algorithm. The new algorithm (NEPAL) instead uses the surface equivalence principle resulting in ? an O(N 1.5 ) algorithm that is amenable to parallel processing. The current proposal is to continue progress in developing new nonlinear inverse scattering theories. We plan to move away for the Born type methods and exploit new ways of parameterizing the scattering object in order to achieve the best possible reconstruction. We will use our progress in fast forward scattering solvers as building blocks to speed up the inversion and solve much larger objects. Other means of solving large objects, particularly objects buried in a slowly varying inhomogeneous background would be investigated as well. Finally, we wish to develop new experimental apparatus that can achieve high fidelity measurements so that the full potential of these new inverse methods could be achieved in a practical system.