This paper addresses the electromagnetic inverse scattering problem of determining the location and shape of anisotropic objects from near-field data. We investigate both cases involving the Helmholtz equation and Maxwell's equations for this inverse problem. Our study focuses on developing efficient imaging functionals that enable a fast and stable recovery of the anisotropic object. The implementation of the imaging functionals is simple and avoids the need to solve an ill-posed problem. The resolution analysis of the imaging functionals is conducted using the Green representation formula. Furthermore, we establish stability estimates for these imaging functionals when noise is present in the data. To illustrate the effectiveness of the methods, we present numerical examples showcasing their performance.

翻译：本文研究从近场数据确定各向异性物体位置与形状的电磁逆散射问题。针对该逆问题，我们分别探讨了涉及亥姆霍兹方程与麦克斯韦方程组的两种情形。本研究聚焦于开发高效的成像泛函，以实现对各向异性物体的快速稳定复原。该成像泛函的实现方法简洁，无需处理不适定问题。通过格林表示公式对成像泛函进行分辨率分析，并进一步建立了数据含噪条件下成像泛函的稳定性估计。最后通过数值算例展示该方法的有效性。