Multiple Buried Target Reconstruction Using a Multiscale Hybrid of Diffraction Tomography and CMA-ES Optimization

Abstract

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 non-linear and ill-posed, a combination of different profiling modalities is required to tackle the challenges. First, an initialization step using 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 which combines the iterative multi-scaling 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, 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 multi-scaling 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 that 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.