论文标题
直接采样方法逆波数依赖性源问题（第I部分）：确定固定源的支持
Direct sampling method to inverse wave-number-dependent source problems (part I): determination of the support of a stationary source
论文作者
论文摘要
本文涉及一种直接采样方法，用于成像嵌入在同质和各向同性培养基中的频率依赖性源项的支持。源项由时间依赖性源的傅立叶变换给出，该源在时间域中的辐射周期已知。 时间依赖的源被认为是固定的，因为它的紧凑支持在时间变量随着时间变化而变化。 通过多频直接采样方法，我们表明，包含源支撑和垂直于观察方向的最小条可以以固定的观察角从远场模式中恢复。有了多个但稀疏的观察方向，可以回收源支撑的凸壳的形状。此处执行的频域分析可用于处理逆时间依赖性源问题。 我们的算法的计算开销较低，可抵抗噪声。两个维度和三个维度的数值实验证明了我们的理论发现。
This paper is concerned with a direct sampling method for imaging the support of a frequency-dependent source term embedded in a homogeneous and isotropic medium. The source term is given by the Fourier transform of a time-dependent source whose radiating period in the time domain is known. The time-dependent source is supposed to be stationary in the sense that its compact support does not vary along the time variable. Via a multi-frequency direct sampling method, we show that the smallest strip containing the source support and perpendicular to the observation direction can be recovered from far-field patterns at a fixed observation angle. With multiple but sparse observation directions, the shape of the convex hull of the source support can be recovered. The frequency-domain analysis performed here can be used to handle inverse time-dependent source problems. Our algorithm has low computational overhead and is robust against noise. Numerical experiments in both two and three dimensions have proved our theoretical findings.
