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

Self-similarity techniques are booming in blind 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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {O}(N^{2})$</tex-math></inline-formula> to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {O}(N)$</tex-math></inline-formula>. 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. Codes are available at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/GZHU-DVL/STEA-MLFR</uri>.