Image Super-Resolution With Taylor Expansion Approximation and Large Field Reception

Self-similarity techniques are booming in no-reference super-resolution (SR) due to accurate estimation of the degradation types involved in low-resolution images. However, high-dimensional matrix multiplication within self-similarity computation prohibitively consumes massive computational costs. We find that the high-dimensional attention map is derived from the matrix multiplication between query and key, followed by a softmax function. This softmax makes the matrix multiplication inseparable, posing a great challenge in simplifying computational complexity. To address this issue, we first propose a second-order Taylor expansion approximation (STEA) to separate the matrix multiplication of query and key, resulting in the complexity reduction from $\mathcal {O}(N^{2})$ to $\mathcal {O}(N)$. Then, we design a multi-scale large field reception (MLFR) to compensate for the performance degradation caused by STEA. Finally, we apply these two core designs to laboratory and real-world scenarios by constructing LabNet and RealNet, respectively. Extensive experimental results tested on five synthetic datasets demonstrate that our LabNet sets a new benchmark in qualitative and quantitative evaluations. Tested on the real-world dataset, our RealNet achieves superior visual quality over existing methods. Ablation studies further verify the contributions of STEA and MLFR towards both LabNet and RealNet frameworks.