## 1 Introduction
Such an approach is particularly beneficial for tackling the \"one-to-many\" FSR problem [16] and finally yielding superior outcomes (Figure 1h). _(3)_ Most previous research [15; 17; 18] favors improving the transformer module for the transformer-based encoder-decoder FSR approaches. However, matching a compatible strong up/downsample module and transformer module is crucial; otherwise, some of the system potential could be wasted on either side. In this work, we aim to address all the limitations mentioned above and propose a novel attention-guided transformer with pixel-related deconvolution network for face super-resolution. The proposed method utilizes a multi-scale connected encoder-decoder architecture as the backbone. In encoder-decoder branches, we carefully design an Attention-Guided Transformer Module (AGTM), which is composed of an Attention Guiding Block (AGB) and a Channel-wise Multi-head Transformer Block (CMTB). AGB aims to guide the transformer block in learning about essential facial components. Different from previous transformer-based methods [15; 17] which utilized the same transformer structure for different feature layers, AGB is further divided into two subdivision modules to adapt different levels of features: AGTM at the top of the encoder-decoder network (AGTM-T) which promotes both local facial details and global facial structures, while AGTM at the bottleneck side (AGTM-B) which optimizes the encoded low-level features. Noting the problem that the usual spatial-wise transformers are limited to position-specific windows and their partition strategy may potentially alter the structure of the facial image [19], the Channel-wise Multi-head Transformer Block (CMTB) is introduced to achieve an image-size receptive field by utilizing feature map channels. The AGB and CMTB are complementary and can simultaneously enhance local facial details and global facial structures. Furthermore, considering that face images are highly structured, we design a Pixel-Related Deconvolution (PRD) layer to establish direct relationships among adjacent pixels in the upsampling process for better face structure preservation. Moreover, different from the pyramid network [13; 20] that progressively reconstructs high-resolution face images, we have also developed a Multi-scale Feature Fusion Module (MFFM) to wisely fuse multi-scale features for better network flexibility and reconstruction results. To sum up, this work has four main contributions:  
* We devise an attention-guided transformer with pixel-related deconvolution network for face super-resolution. To the best of our knowledge, neither the guiding block that mines potential inner feature map information nor the pixel-related deconvolution that  
Figure 1: Visual analysis of the pixel-related deconvolution and the guiding block for transformer-based FSR methods: (**a**) is the input face image; (**b**) is the conventional pixel deconvolutional and pixel shuffle upsampling layer that neglects the relationship between adjacent pixels; (**c**) is the proposed pixel-related deconvolution that establishes direct relationships among adjacent pixels; (**d**) is the inner feature map outputs with corresponding upsampling methods; (**e–g**) are self-attention heatmaps, correlation maps [21] between input and output feature maps, and inner feature maps without and with guiding blocks, respectively (please note that five different images are tested in the correlation map instead of one for fair comparison); (**h**) is the output images (the top one is trained without pixel-related deconvolution and guiding blocks, while the bottom one is trained with them). Moreover, subfigure (**f**) represents the correlations between input and output feature maps. The more the output feature maps squeeze together, the more the input and output feature maps are suited and correlated, and the better it benefits the “one-to-many” FSR problem to obtain fine-grained FSR results. Please refer to Section 2.2 for more detailed information and related works.