Nonlinear Inverse Scattering Methods for Large Objects

大物体的非线性逆散射方法

• 批准号: 9302145
• 负责人: Weng Chew
• 金额: $ 20.3万
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-03-15 至 1998-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9302145&HistoricalAwards=false
• 关键词: Nonlinear; Inverse; Scattering; Methods; Large

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.

WPC 2 R B J Z X 快递#| 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 @TR & 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 之前 5 年 PYI 资助的支持期使研究人员能够在逆散射和前向散射理论方面取得重大进展。开发了新的非线性逆散射方法来解释散射对象内的多重散射效应。开发了 Born 迭代方法 (BIM) 和扭曲 Born 迭代方法 (DBIM)，证明了物体 对比度高达 10:1，并表现出 0.1 波长量级的超分辨率。 另一种称为局部形状函数（LSF）方法的新技术被开发出来，用于对金属散射进行逆散射，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方法也可以用于介电散射的反演并绕过10:1对比度的限制。需要 反转非常大的散射物体刺激了快速前向散射求解器的研究。 这些快速算法准确地解决了散射问题，并通过利用散射计算中固有的冗余来节省计算量。 这些算法中的第一个（RTMA）解决了？通过利用波现象的平移特性，0 散射问题对 )(N 2.5 ) 操作中的所有入射源都有效。 下一个算法 （RATMA）利用聚合？ 属性导致 O(N 2 ) 算法。 新算法（NEPAL）改为使用表面等效原理，从而产生？ 适合并行处理的 O(N 1.5 ) 算法。目前的建议是继续发展新的非线性逆散射理论。 我们计划放弃 Born 类型方法并开发新的参数化方法 散射物体以实现最佳的重建。 我们将利用我们在快速前向散射求解器方面的进展作为构建块来加速反演并求解更大的物体。 还将研究解决大型物体的其他方法，特别是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度测量的新实验装置，以便能够充分发挥这些新反演方法的潜力。 在实际系统中实现。