In this study, we extend the contrast source inversion to a fully differentiable, unsupervised framework based on a neural implicit representation of the contrast source. Specifically, instead of a pixel-wise discrete representation, the contrast source is parameterized by a lightweight residual multilayer perceptron (ResMLP) as a continuous neural field conditioned on spatial coordinates and transmitter settings. This continuous parameterization provides a more flexible representation of the contrast source and improves reconstruction accuracy and robustness under noisy measurements. Building on this representation, the state equation and data equation are combined with total-variation regularization to form a differentiable objective function. By reformulating the VIE-constrained inversion as an end-to-end differentiable optimization problem, the network parameters and the medium contrast are jointly optimized via automatic differentiation. Within the same framework, both full and phaseless data inversion are accommodated by only modifying the data misfit function. Numerical experiments demonstrate that this scheme yields higher reconstruction accuracy and robustness than conventional CSI across a range of noise levels and measurement settings. The continuous neural field further enables super-resolution inference at resolutions finer than the training grid, decoupling inversion cost from reconstruction fidelity. Ablation studies and comparisons with alternative neural architectures further confirm that the contrast source parameterization and VIE-based formulation are both essential to the observed improvements.

翻译：在本研究中，我们将对比源反演扩展为一个完全可微、无监督的框架，该框架基于对比源的神经隐式表示。具体而言，对比源并非采用逐像素离散表示，而是通过一个轻量级残差多层感知器（ResMLP）参数化为连续神经场，该场以空间坐标和发射器设置为条件。这种连续参数化提供了对比源更灵活的表示，并提高了噪声测量下的重建精度和鲁棒性。基于该表示，状态方程和数据方程与全变差正则化相结合，构成可微目标函数。通过将VIE约束的反演问题重新表述为端到端可微优化问题，网络参数与介质对比度通过自动微分联合优化。在同一框架内，仅通过修改数据失配函数即可同时容纳全数据和无相位数据反演。数值实验表明，与常规CSI相比，该方案在多种噪声水平和测量设置下具有更高的重建精度和鲁棒性。连续神经场还能在比训练网格更精细的分辨率下实现超分辨率推理，将反演成本与重建保真度解耦。消融实验及与其他神经架构的比较进一步证实，对比源参数化与基于VIE的表述对于观察到的改进均至关重要。