Neural Inverse Scattering with Score-based Regularization

TL;DR

This work tackles the nonlinear inverse-scattering problem by jointly reconstructing the scattering potential $f$ and induced current $J$ using a neural-field framework regularized with a score-based prior. It introduces NF-Score, which integrates a pre-trained denoising score function into the loss and employs two MLPs to estimate $f$ and $J$, with a loss $\oldsymbol{\mathcal{L}}_{ ext{train}} = \alpha_1 L_{img} + \alpha_2 L_{cur} + \alpha_3 L_{scr}$ where $L_{scr} = \tfrac{1}{2} \|S(f;\sigma)\|_2^2$ and $S(\cdot;\sigma) \approx \nabla \log p_\sigma(f)$. Experimental results on three synthetic targets show that NF-Score, particularly using a score network, yields higher SSIM and PSNR than NF and TV-based regularization, with stable convergence. The approach demonstrates the effectiveness of score-based priors in complex, non-convex joint-inference inverse problems and suggests robustness to measurement noise, offering a principled pathway for improved image quality in practical scattering imaging scenarios.

Abstract

Inverse scattering is a fundamental challenge in many imaging applications, ranging from microscopy to remote sensing. Solving this problem often requires jointly estimating two unknowns -- the image and the scattering field inside the object -- necessitating effective image prior to regularize the inference. In this paper, we propose a regularized neural field (NF) approach which integrates the denoising score function used in score-based generative models. The neural field formulation offers convenient flexibility to performing joint estimation, while the denoising score function imposes the rich structural prior of images. Our results on three high-contrast simulated objects show that the proposed approach yields a better imaging quality compared to the state-of-the-art NF approach, where regularization is based on total variation.

Figures (5)

• Figure 1: Left: Visualization of the experimental setup for the inverse scattering problem under consideration. The object within the domain $\Omega$ is illuminated by transmitters and observed by receivers, both distributed along a circular sensor orbit $\Gamma$. Right: Conceptual illustration of the proposed NF-Score method, which employs two MLPs, $\mathcal{M}_f$ and $\mathcal{M}_J$, to estimate $\mathbf{f}$ and $\mathbf{J}$, respectively. A score-based regularization term is added into the loss function to enhance reconstruction quality.
• Figure 2: Visual comparison of the permittivity contrast images reconstructed by the proposed NF-Score method and baseline methods. We present two variants: NF-Score (D), which utilizes a pre-trained DnCNN denoiser, and NF-Score (S), which incorporates a pre-trained score network. Both variants demonstrate superior reconstruction quality and reduced artifacts compared to the baselines, which is also corroborated by the SSIM values attached to each image.
• Figure 3: Visualization of the samples generated by running annealed Langevin dynamics Song.etal2019 equipped with the score networks trained on the synthetic datasets corresponding to Au, Polygon, and Shepp-Logan, respectively.
• Figure 4: Illustration of the convergence of NF-Score (D) and NF-Score (S) during training. The PSNR value are plotted against the iteration number.
• Figure 5: Comparison of the reconstructed permittivity contrast obtained by estimating $\mathbf{J}$ versus $\mathbf{E}$. NF was selected as the reconstruction method to eliminate the influence of regularization.