In this article, a hierarchical stochastic optimization algorithm for profiling of multiple high-contrast buried objects in large investigation domains (IDs) is presented. As this problem is highly nonlinear and ill-posed, a combination of different profiling modalities is required to tackle the challenges. First, an initialization step using the qualitative diffraction tomography (DT) method is performed to not only limit the ID to scatterers’ locations but also obtain an approximation of their dielectric permittivity range. Then, an algorithm that combines the iterative multiscaling approach (IMSA) with the reconstruction capabilities of covariance matrix adaptation evolution strategy (CMA-ES) is implemented. IMSA is a multistep strategy, which starts with coarse meshes in lower frequencies and, then, step by step, tightens the ID to the newly found domain of scatterers and uses finer meshes for partitioning them. This procedure enhances the resolution without increasing the number of unknowns. In each step, the inversion process is executed using the global optimization technique of CMA-ES. The proposed technique uses the full advantages of global optimization technique and at the same time, by executing it on a multiscaling scheme and using the initializing step, reduces the number of unknowns, the degree of freedom in the search space, and the required measured data. The numerical assessments for various scenarios are performed, which clearly shows an acceptable dielectric profile retrieval, even for inhomogeneous dielectric distributions or noisy measurements. Moreover, a comparison between CMA-ES and other global optimization algorithms is performed, which reveals the outperformance of CMA-ES in these scenarios.

中文翻译：

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使用衍射断层扫描和 CMA-ES 优化的多尺度混合重建多个掩埋目标

在本文中，提出了一种分层随机优化算法，用于对大型调查域 (ID) 中的多个高对比度掩埋对象进行剖析。由于这个问题是高度非线性和不适定的，因此需要结合不同的分析模式来应对挑战。首先，使用定性衍射断层扫描 (DT) 方法执行初始化步骤，不仅将 ID 限制在散射体的位置，而且获得其介电常数范围的近似值。然后，实现了一种将迭代多尺度方法（IMSA）与协方差矩阵自适应进化策略（CMA-ES）的重构能力相结合的算法。IMSA 是一种多步策略，它从较低频率的粗网格开始，然后逐步，将 ID 收紧到新发现的散射体域，并使用更精细的网格对它们进行分区。此过程在不增加未知数的情况下提高了分辨率。在每个步骤中，使用 CMA-ES 的全局优化技术执行反演过程。所提出的技术利用了全局优化技术的全部优点，同时通过在多尺度方案上执行它并使用初始化步骤，减少了未知数的数量、搜索空间中的自由度和所需的测量数据. 对各种场景进行了数值评估，清楚地显示了可接受的介电轮廓检索，即使对于不均匀的介电分布或噪声测量也是如此。此外，还进行了 CMA-ES 与其他全局优化算法之间的比较，