GB-LSR: Local Spectral Decoding with a Learned Global Bandwidth for Arbitrary-Scale Super-Resolution

We present GB-LSR (Global-Bandwidth Local Spectral Representation), a fixed-grid local spectral representation for continuous image decoding. The image domain is partitioned into non-overlapping square patches. Each patch carries coefficients for a truncated Fourier basis, predicted by a single linear projection from shared convolutional-encoder features, and one trainable scalar bandwidth is shared across every patch and every image. As in earlier local spectral decoders, decoding at a continuous coordinate is a fixed-size basis contraction whose cost is set by the spectral cutoff; GB-LSR learns the bandwidth of that basis instead of fixing it. We evaluate an arbitrary-scale super-resolution extension, GB-LSR-Scalar-ASR, against the authors' released LIIF, LTE, and SRNO checkpoints on the same RDN encoder, with every method scored under one protocol and timed in one session per scale, each on one GPU. It runs 1.25x faster than LIIF-RDN at x4 and as fast as SRNO-RDN, whose released code uses 15 times as much peak memory on Urban100. It trails the three encoder-matched baselines by 0.07 to 0.79 dB PSNR-Y in distribution, SRNO-RDN by 0.35 dB on average. Removing the local ensemble raises the speedup to 2.41x over LIIF-RDN and 1.95x over SRNO-RDN at x4, and to 3.00x and 2.41x at x8, without changing PSNR-Y beyond seed variation, at the cost of value jumps at cell boundaries of 0.22 gray levels (of 255) on average at x4. Against the EDSR-baseline checkpoints of five recent methods at x4, GB-LSR-Scalar-ASR scores above or within 0.17 dB on PSNR-Y of LMF, SRNO-EDSR, and OPE-SR-EDSR (1.39 to 6.43 million parameters against 22.02) and 0.14 to 0.57 dB below GSASR and Thera (20.44 and 5.85 million), and has a higher mean LPIPS at x4 than every baseline.