Interpretable Operator Learning for Inverse Problems via Adaptive Spectral Filtering: Convergence and Discretization Invariance
Solving ill-posed inverse problems necessitates effective regularization strategies to stabilize the inversion process against measurement noise. While classical methods like Tikhonov regularization require heuristic parameter tuning, and standard deep learning approaches often lack interpretability and generalization across resolutions, we propose SC-Net (Spectral Correction Network), a novel operator learning framework. SC-Net operates in the spectral domain of the forward operator, learning a pointwise adaptive filter function that reweights spectral coefficients based on the signal-to-noise ratio. We provide a theoretical analysis showing that SC-Net approximates the continuous invers...
| Authors | Hang-Cheng Dong, Pengcheng Cheng, Shuhuan Li |
|---|---|
| Primary category | stat.ML |
| Published | 21 March 2026 |
| Last updated at source | 21 March 2026 |
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