PhyIR: Physics-Inspired Implicit Representation Method for Inverse Scattering Problems

This study proposes an innovative unsupervised reconstruction approach for solving highly nonlinear and ill-posed inverse scattering problems (ISPs). We establish a novel implicit representation method, termed PhyIR, for two-dimensional ISPs, in which a spectral collocation scheme is adopted to compute the Jacobian of the full forward operator and a physics-inspired neural network is elaborately constructed to impose implicit regularization on the iterative solution. Specifically, to endow the implicit representation with physics-inspired structural priors inherent in ISPs, we build the implicit neural representation by emulating an idealized formulation of the physical parameters. Furthermore, motivated by the key insight that the transformations in the spectral domain are dominant in forward scattering, we harness the spectral-domain parameterization capability of the Fourier neural operator (FNO) to provide global spectral feature coupling within the representation while preserving the resolution flexibility property of the continuous representation. The proposed PhyIR combines a measurement-conditioned learnable encoder with a decoder that integrates global features, achieving remarkable reconstruction performance, particularly in strongly nonlinear scattering regimes. The effectiveness of the proposed method is validated through extensive simulated and real-world data experiments. Comparative analyses underscore its superior reconstruction performance and consistent improvements in sharpness and shape preservation. The advances of PhyIR offer a promising and extendable solution to ISPs, while also providing valuable insights into other imaging modalities and problems exhibiting analogous properties.