FKAN-SR: A Fourier-Kolmogorov-Arnold residual network for lightweight domain-specialized image super-resolution

Abstract Practitioners who must train a compact super-resolution model on a modest, domain-specific dataset with a single GPU are poorly served by benchmark leaderboards, because leaderboard rankings mix the effect of the architecture with the effects of training data, schedule and model capacity. This work separates those factors in a controlled, seed-matched study. The proposed FKAN-SR is a residual network with about 1.18M parameters that couples bicubic-anchored residual learning with a Kolmogorov–Arnold-inspired per-channel Fourier-series (Fourier-KAN) activation. It is compared with six recent backbones, namely HAT, SRFormer, DAT, MambaIR, ATD and SeemoRe, all trained from scratch under one identical protocol for $$\times 4$$ super-resolution. Against conventional direct-regression baselines on Oxford Flowers-102, FKAN-SR leads by 2.16 dB PSNR. The central fair-comparison experiment then applies the same bicubic anchor to every baseline and shows that this margin comes mainly from the learning formulation, not from the architecture: anchoring lifts every backbone by 1.5–1.9 dB, the architectural margin shrinks to 0.30 dB, and it falls to 0.03 dB once parameter budgets are also matched. The fair-arm ranking and its sub-decibel margins replicate on two further narrow domains, Oxford-IIIT Pets and Describable Textures, and are confirmed by full-image evaluation, saturation-free statistics with effect sizes, multi-seed replication and a longer schedule. A sensitivity study shows the Fourier-KAN activation is a real but capacity-dependent refinement: its gain is negligible at the default $$K{=}3$$ harmonics and reaches $$+0.20$$ dB at a validation-selected $$K{=}6$$ . In this lightweight regime, the learning formulation and the model capacity govern reconstruction quality, not the sophistication of the feature mixer.