Multi-scale design has been considered in recent image super-resolution (SR) works to explore the hierarchical feature information. Existing multi-scale networks aim to build elaborate blocks or progressive architecture for restoration. In general, larger scale features concentrate more on structural and high-level information, while smaller scale features contain plentiful details and textured information. In this point of view, information from larger scale features can be derived from smaller ones. Based on the observation, in this paper, we build a sequential hierarchical learning super-resolution network (SHSR) for effective image SR. Specially, we consider the inter-scale correlations of features, and devise a sequential multi-scale block (SMB) to progressively explore the hierarchical information. SMB is designed in a recursive way based on the linearity of convolution with restricted parameters. Besides the sequential hierarchical learning, we also investigate the correlations among the feature maps and devise a distribution transformation block (DTB). Different from attention-based methods, DTB regards the transformation in a normalization manner, and jointly considers the spatial and channel-wise correlations with scaling and bias factors. Experiment results show SHSR achieves superior quantitative performance and visual quality to state-of-the-art methods with near 34\% parameters and 50\% MACs off when scaling factor is $\times4$. To boost the performance without further training, the extension model SHSR$^+$ with self-ensemble achieves competitive performance than larger networks with near 92\% parameters and 42\% MACs off with scaling factor $\times4$.

翻译：多尺度设计已在近期图像超分辨率（SR）工作中被用于探索分层特征信息。现有多尺度网络旨在构建精细的模块或渐进式架构以实现图像复原。通常，较大尺度特征更关注结构性和高层语义信息，而较小尺度特征则包含丰富的细节与纹理信息。基于此视角，较大尺度特征的信息可从较小尺度特征中推导得出。受此观察启发，本文构建了一种顺序分层学习超分辨率网络（SHSR）以实现高效图像SR。具体而言，我们考虑了特征间的跨尺度相关性，并设计了一种顺序多尺度块（SMB）以逐步探索分层信息。SMB基于卷积的线性特性以递归方式设计，并保持了受限参数规模。除顺序分层学习外，我们还研究了特征图之间的相关性，并设计了分布变换块（DTB）。与基于注意力机制的方法不同，DTB以归一化方式处理变换，并通过缩放因子和偏置因子联合考虑空间与通道维度的相关性。实验结果表明，当缩放因子为$\times4$时，SHSR在参数数量减少约34%、MACs减少约50%的情况下，取得了优于现有方法的定量性能和视觉质量。为进一步提升性能而无需额外训练，扩展模型SHSR$^+$通过自集成在缩放因子为$\times4$时，以参数数量减少约92%、MACs减少约42%的代价，实现了与更大网络相竞争的性能。