Hierarchical Fourier encoding for spatially-adaptive continuous super-resolution

Continuous image super-resolution (CISR) necessitates reconstruction at arbitrary scales; however, current implicit neural representation (INR) approaches frequently depend on fixed bilinear interpolation and exhibit spectral bias, leading to excessively smooth results. In this study, we introduce a spatially adaptive coordinate-shifting framework that integrates hierarchical Fourier encoding with dynamic coordinate adjustment. By re-localizing query points, our approach adaptively fuses neighboring features guided by semantic and spatial information rather than predetermined weights. The hierarchical Fourier encoding supplies multi-frequency positional cues, thereby improving the recovery of high-frequency details, while a lightweight multi-head linear attention mechanism captures long-range contextual relationships. Experimental evaluations conducted on the DIV2K dataset and several benchmark datasets, employing various backbone architectures, indicate that our method achieves improvements of up to 0.12 dB in PSNR and 0.002 in SSIM within the training scale range relative to current state-of-the-art techniques. Furthermore, the proposed framework is designed for flexible integration into any CISR network architecture.