ContinuousSR: Reconstructing Continuous High-Resolution Signals from Discrete Low-Resolution Images

Traditional super‑resolution methods are limited to fixed up‑sampling factors (e.g., ×2, ×4), which restricts their applicability. Recent research on arbitrary‑scale super‑resolution (ASSR) using implicit neural representations such as LIIF and CiaoSR has made progress, but these approaches often require multiple up‑sampling and decoding steps, leading to inefficiency and quality loss.

Pixel‑to‑Gaussian Paradigm

The ContinuousSR framework redefines the problem by converting pixel data into a continuous Gaussian field. Each 2D Gaussian kernel encodes position, color, and covariance parameters, and the model optimizes these parameters to construct a continuous high‑resolution representation that can be sampled at any scale without additional up‑sampling.

Three Innovative Modules

DGP‑Driven Covariance Weighting : Statistical analysis of 40,000 natural images reveals a Deep Gaussian Prior (DGP) governing kernel covariance. By sampling kernels from this distribution and applying dynamic weighting, the optimization difficulty in Gaussian space is greatly reduced.

Adaptive Position Drifting : A dynamic offset strategy adjusts kernel positions based on image content, allowing more kernels to populate complex texture regions and thereby enhancing detail reconstruction.

Color Gaussian Mapping : An efficient multi‑layer perceptron (MLP) learns RGB color parameters, improving color fidelity in the reconstructed images.

Ultra‑Fast Rendering and High‑Quality Reconstruction

After building the Gaussian field, ContinuousSR can generate a high‑resolution image at any scale in approximately 1 ms per scale, achieving a 19.5× speedup over prior ASSR methods. Experiments on multiple benchmark datasets show a 0.9 dB increase in PSNR, with especially strong performance at high magnification factors.