## 1 Introduction
Furthermore, the performance of transformers has already been proven and widely applied in computer vision tasks, such as image recognition [34; 35] and image restoration [28; 36; 37]. The core of the transformers is a self-attention mechanism that can capture both long- and short-range correlations between words/pixels [38]. Therefore, transformer-based methods have gained dramatic attention for their high ability to capture both local and global dependencies. While transformer-based methods have led to significant improvements in FSR performance, they have a number of limitations that need to be addressed. First, there is a lack of sufficient discussion regarding the inner feature maps. As shown in Figure 1b, without guidance, the features of the inner feature maps may not always be detail-rich, and may even be buried in gray. This restricts the transformer block to selecting only a limited number of feature maps based on the self-attention matrix (Figure 1c), while leaving others untouched. On the contrary, from Figure 1d it can be seen that utilizing a guiding block to enhance essential facial components results in more correlated output feature maps, benefiting the \"one-to-many\" FSR problem [39] and yielding superior outcomes (Figure 1e). Therefore, it is crucial to have a guiding block that can identify the essential facial component for inner feature maps in transformer-based methods. Second, most previous transformer-based methods [28; 37] have utilized the same transformer structure for different feature layers. However, the transformer structure on high-level features cannot be thoroughly applied to low-level features [40], and vice versa, otherwise resulting in unsatisfactory FSR performance. Lastly, the usual spatial-wise transformers are limited to position-specific windows, meaning that the partition strategy may potentially alter the structure of the facial image [15]. Based on the above analysis, we propose a spatial-channel mutual attention-guided transformer network for face super-resolution, which explores the potential of inner feature maps for reconstructing plausible face images. The proposed method is a multi-scaleconnected encoder-decoder network. In the encoder-decoder branches, a Spatial-Channel Mutual Attention-guided Transformer Module (SCATM) is carefully designed to extract more detailed features by enhancing the relationship between inner feature maps. It is composed of a Spatial-Channel Mutual Attention Guiding Block (SCAGB) and a Channel-wise Multi-head Transformer Block (CMTB). Among them, SCAGB aims to guide the transformer block in identifying the essential facial component. SCAGB on the top layer (SCAGB-T) aims to guide and promote both local facial details and global facial structures, while SCAGB on the bottom layer (SCAGB-B) seeks to identify the crucial encoded features. Unlike the usual spatial-wise transformersm which are limited to position-specific windows, the CMTB utilizes feature map channels to achieve image-size receptive fields. The combination of SCAGB and CMTB is complementary, and can simultaneously promote both local facial details and global facial structures. Meanwhile, unlike pyramid super-resolution networks [41; 42], which progressively reconstruct high-resolution images, we further develop a Multi-scale Feature Fusion Module (MFFM) which fuses features from all layers, making for network flexibility and better restoration performance. In summary, the main contributions of this work are four-fold:  
* We devise a spatial-channel mutual attention-guided transformer network for face super-resolution. To the best of our knowledge, this is the first paper to explore the potential of inner feature maps in reconstructing plausible face images in the transformer-based FSR area. * We carefully design a Spatial-Channel Mutual Attention-guided Transformer Module (SCATM) to extract more detailed features by enhancing the relationship between inner feature maps.