Jaeyeop Choi | Search arXiv

arXiv2026

WaFIR: Wavelet-Fourier Mixture-of-Experts with Subband-Adaptive Routing for Blind All-in-One Image Restoration

Blind all-in-one image restoration must adapt a shared model to heterogeneous and sometimes mixed degradations without a task label at test time. We introduce WaFIR, a decoder module that decomposes features into Haar subbands, summarizes each subband with a compact Fourier descriptor, and routes it to prompt-conditioned spectral modulation experts. Unlike image-level frequency conditioning, WaFIR makes routing decisions at the subband level, enabling frequency-specific processing while retaining the task context learned by the backbone. Under a unified training and evaluation protocol for denoising, deraining, and dehazing, WaFIR improves average PSNR over the three tasks by 0.48 dB over the PromptIR baseline and by 0.38 dB over the recent Up-Restorer. Matched-capacity and routing controls show that the gain is not explained by additional parameters alone. On unseen noise intensities, descriptor-based routing is more robust than a discrete label-conditioned alternative and remains on par under compound degradations, while routing analyses show stable subband-dependent expert use across degradation types. These results support subband frequency structure as an interpretable complement to prompt-based conditioning for blind image restoration. Code is available at https://anonymous.4open.science/r/WaFIR/README.md

cs.CV↗

arXiv2026

Certified Abstention for Provably-Unidentifiable Index-Phase Recovery in Image Registration

Image registration underpins measurement across scanning, camera, and microscopy imaging, yet a fundamental question is rarely posed: when is the sample-to-position map recoverable at all, and when does any estimator that reports a position necessarily fabricate one? We show that in reference-perturbed sampled imaging, where samples are localized through a perturbed reference, position fidelity (where samples land) and phase fidelity (which reference index becomes each block's origin) are logically independent: no policy acting on position information alone can guarantee phase fidelity. We derive a tight resolution threshold separating recoverable from provably-unidentifiable registration, and a recovery framework that certifies identifiable regions--recovering them exactly--while abstaining on provably-unidentifiable regions rather than hallucinating structure. On a deployed scanning system we measure a direction-bimodal registration offset consistent with the theory. Against classical and learned restoration baselines, certificate-free offset estimators fabricate structure on the unidentifiable regime, whereas the certified method abstains rather than fabricating. Finally, the certified-abstention mechanism carries across scanning, rolling-shutter, and cryo-electron-microscopy imaging--declining rather than fabricating on the regime it flags--though how completely it abstains and how tightly it bounds kept-region risk stay modality-specific (at extreme SNR the cryo-EM certificate abstains only partially): a structural-versus-statistical boundary in registration reliability.

cs.CV↗