用泰勒展开优化Transformer，实现高效图像修复

Recently, Transformer networks have demonstrated outstanding performance in the field of image restoration due to the global receptive field and adaptability to input. However, the quadratic computational complexity of Softmax-attention poses a significant limitation on its extensive application in image restoration tasks, particularly for high-resolution images. To tackle this challenge, we propose a novel variant of the Transformer. This variant leverages the Taylor expansion to approximate the Softmax-attention and utilizes the concept of norm-preserving mapping to approximate the remainder of the first-order Taylor expansion, resulting in a linear computational complexity. Moreover, we introduce a multi-branch architecture featuring multi-scale patch embedding into the proposed Transformer, which has four distinct advantages: 1) various sizes of the receptive field; 2) multi-level semantic information; 3) flexible shapes of the receptive field; 4) accelerated training and inference speed. Hence, the proposed model, named the second version of Taylor formula expansion-based Transformer (for short MB-TaylorFormer V2) has the capability to concurrently process coarse-to-fine features, capture long-distance pixel interactions with limited computational cost, and improve the approximation of the Taylor expansion remainder. Experimental results across diverse image restoration benchmarks demonstrate that MB-TaylorFormer V2 achieves state-of-the-art performance in multiple image restoration tasks, such as image dehazing, deraining, desnowing, motion deblurring, and denoising, with very little computational overhead. The source code is available at https://github.com/FVL2020/MB-TaylorFormerV2.