GB-LSR’s 3.6 dB Gain Isn’t Just a Record — It Makes Continuous Image Reconstruction 4x Faster

GB-LSR (Global-Bandwidth Local Spectral Representation) tackles continuous image reconstruction and arbitrary-scale super-resolution by combining local Fourier basis functions with a single trainable global bandwidth. The image is divided into non-overlapping square patches, each carrying coefficients for a truncated Fourier series predicted from shared convolutional-encoder features. A single scalar bandwidth is learned globally across all patches and images, making reconstruction at any continuous coordinate a fixed-size basis contraction independent of image resolution. The authors evaluated three bandwidth variants—trainable global, fixed global, and per-patch adaptive—and found that a single global scalar suffices empirically, with per-patch alternatives offering no improvement on either a closed-form locality diagnostic or end-to-end ablation.

On a native-reconstruction benchmark across Kodak, Set14, and Urban100, the main variant outperforms matched-budget amortized LIIF/LTE/WIRE re-implementations by 2.8–3.6 dB PSNR and 0.11–0.15 LPIPS, while running at roughly one-quarter of the slowest baseline's inference cost. In a separate arbitrary-scale super-resolution (ASR) extension, GB-LSR achieves competitive PSNR-Y and runs 1.44× faster than LIIF-RDN and 3.25× faster than LTE-SwinIR at 4× scale. Further optimizations—removing 4-corner local-ensemble averaging—give a 1.77× speedup with 35% lower peak memory and negligible PSNR change, while widening the RDN encoder from 64 to 96 channels yields a small positive PSNR shift with a 1.58× speedup and 31% lower peak memory.