直接采样法用于成像小介电不均匀体：分析与改进
Direct sampling method for imaging small dielectric inhomogeneities: analysis and improvement
AI总结：
本文分析了直接采样法在成像小介电不均匀体时的行为，并提出改进方法，通过Bessel函数和不均匀体的尺寸、形状和介电常数来表达DSM指示函数，揭示了当一个不均匀体更小或介电常数更低时的局限性，并通过多波入射提出改进方案，与归一化的Kirchhoff迁移密切相关。
摘要：
直接采样法（DSM）已被引入用于非迭代成像小不均匀体，因其快速、稳健且在反散射问题中有效而闻名。然而，到目前为止，尚未对DSM的行为进行全面分析。本文在二维情况下基于渐近假设框架，推导出DSM指示函数的表达式，以Bessel函数零阶和不均匀体的尺寸、形状和介电常数表示。通过这种解析表达式，揭示了当一个不均匀体更小或介电常数更低时DSM方法的局限性，并通过数值模拟和实验数据支持理论分析。
英文摘要：
The direct sampling method (DSM) has been introduced for non-iterative imaging of small inhomogeneities and is known to be fast, robust, and effective for inverse scattering problems. However, to the best of our knowledge, a full analysis of the behavior of the DSM has not been provided yet. Such an analysis is proposed here within the framework of the asymptotic hypothesis in the 2D case leading to the expression of the DSM indicator function in terms of the Bessel function of order zero and the sizes, shapes and permittivities of the inhomogeneities. Thanks to this analytical expression the limitations of the DSM method when one of the inhomogeneities is smaller and/or has lower permittivity than the others is exhibited and illustrated. An improved DSM is proposed to overcome this intrinsic limitation in the case of multiple incident waves. Then we show that both the traditional and improved DSM are closely related to a normalized version of the Kirchhoff migration. The theoretical elements of our proposal are supported by various results from numerical simulations with synthetic and experimental data.
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