In an EISP system, the scatterer in the enclosed space \( D \) is first illuminated by incoming electromagnetic waves emitted by transmitters and generates scattered fields. Then, the scattered fields measured by receivers are used to determine the scatterer's relative permittivity. We show results obtained by our method and baselines.
Abstract
Electromagnetic Inverse Scattering Problems (EISP) have gained wide applications in computational imaging. By solving EISP, the internal relative permittivity of the scatterer can be non-invasively determined based on the scattered electromagnetic fields. Despite previous efforts to address EISP, achieving better solutions to this problem has remained elusive, due to the challenges posed by inversion and discretization. This paper tackles those challenges in EISP via an implicit approach. By representing the scatterer's relative permittivity as a continuous implicit representation, our method is able to address the low-resolution problems arising from discretization. Further, optimizing this implicit representation within a forward framework allows us to conveniently circumvent the challenges posed by inverse estimation. Our approach outperforms existing methods on standard benchmark datasets.
Framework
Overview of our implicit method. Two MLPs, \(F_\theta\) and \(H_\phi\), are used to implicitly represent relative permittivity \(\varepsilon_r\) and induced current \(J\), respectively. Random sampling is applied for comprehensive optimization. The predicted induced current \(\hat{\mathbf{J}}\) is calculated based on relative permittivity \(\varepsilon_r\) queried from \(F_\theta\) and induced current \(J\) directly queried from \(H_\phi\). Then the state loss \(\mathcal{L}_{\text{state}}\) is calculated by comparing the predicted \(\hat{\mathbf{J}}\) and directly queried \(\mathbf{J}\). Besides, the directly queried induced current \(\mathbf{J}\) is used to compute the scattered fields \(\hat{\mathbf{E}}^{\text{s}}\). Data loss function \(\mathcal{L}_{\text{data}}\) is constructed to evaluate the difference between predicted scattered fields \(\hat{\mathbf{E}}^{\text{s}}\) and the measured values \(\mathbf{E}^{\text{s}}\).
