Structured Multi-Level-Set Inversion for 3-D Electromagnetic Inverse Scattering

Many dielectric targets encountered in 3-D electromagnetic inverse scattering exhibit piecewise-homogeneous material distributions, which provide useful structural information for inversion. To exploit this property, this paper proposes a structured multi-level-set inversion (SMLSI) method within a physics-driven neural network (PDNN) framework. Instead of directly parameterizing the contrast distribution, SMLSI represents it in terms of object support and material distribution. Multiple level-sets are mapped to soft-support functions and combined through a soft-union operation to construct the object support. The normalized contributions of these soft-support functions, together with trainable complex relative permittivities, determine the material distribution within the support. The level-set residuals are parameterized by a coordinate-based neural network, and the trainable parameters are optimized from scattered field data. Structure-aware regularization terms are introduced to promote binary object support and spatially coherent material regions while reducing material mixing and redundant activation of level-set supports. Adaptive regularization weighting is further employed to reduce the dependence on manual parameter tuning. Numerical experiments demonstrate that SMLSI improves reconstruction accuracy over direct contrast parameterization and enables the recovery of irregular 3-D geometries, closely spaced objects, and multiple material regions. Compared with CSI and L2/3-FBE-WCIE, SMLSI achieves more accurate reconstructions on representative synthetic targets. Experimental validation using 3-D Fresnel data further demonstrates its applicability to measured scattering data.