LaST-SR：用于单图像超分辨率的拉普拉斯启发稳态-瞬态复频分解
LaST-SR: Laplace-Inspired Steady-Transient Complex-Frequency Decomposition for Single Image Super-Resolution
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中文总结 AI 辅助
本研究针对单图像超分辨率的结构与细节恢复问题，提出LaST-SR模型，通过复频分解与稳态-瞬态协同聚合模块，在×2和×4超分辨率任务的五个基准上实现了最优PSNR/SSIM。
中文摘要 AI 辅助
单图像超分辨率（SISR）需要全局上下文建模以实现结构一致的重建。傅里叶算子越来越多地被用于全局特征建模，但它们的周期性频谱基函数限制了对局部非周期变化的表示，从而影响了不规则结构和精细细节的恢复。在动力学系统中，拉普拉斯神经算子将傅里叶模式扩展到复频，并将输出信号分解为互补的稳态和瞬态响应，以共同建模周期和非周期信息。我们首次推导了二维特征图的近似稳态-瞬态分解，为所提出的复频分解提供了分析基础。据此，我们提出了LaST-SR，其核心是复频分解模块，该模块耦合了用于图像范围依赖和长程结构一致性的全局全谱傅里叶分支，以及用于局部、内容依赖的非周期变化的窗口条件局部复频分支。为融合所得特征，我们进一步设计了稳态-瞬态协同聚合模块，用于跨分支交互和联合聚合。在五个基准上的实验表明，对于×2和×4 SISR，LaST-SR在对比方法中取得了最佳的PSNR/SSIM。消融研究进一步验证了所提出架构及其关键建模机制的有效性。
英文摘要
Single-image super-resolution (SISR) requires global context modeling for structurally consistent reconstruction. Fourier operators are increasingly adopted for global feature modeling. However, their periodic spectral bases constrain the representation of localized aperiodic variations, limiting the recovery of irregular structures and fine details. In dynamical systems, the Laplace neural operator extends Fourier modes to complex frequencies and decomposes the output signal into complementary steady-state and transient responses to jointly model periodic and aperiodic information. We derive, for the first time, an approximate steady-transient decomposition for two-dimensional feature maps, providing an analytical basis for the proposed complex-frequency decomposition. Accordingly, we propose LaST-SR, centered on a Complex-Frequency Decomposition module that couples a global full-spectrum Fourier branch for image-wide dependencies and long-range structural consistency with a window-conditioned local complex-frequency branch for localized, content-dependent aperiodic variations. To fuse the resulting features, we further design a Steady-Transient Collaborative Aggregation module for cross-branch interaction and joint aggregation. Experiments on five benchmarks show that LaST-SR achieves the best PSNR/SSIM among the compared methods for $\times2$ and $\times4$ SISR. Ablation studies further validate the effectiveness of the proposed architecture and its key modeling mechanisms.
发表机构
- School of Mathematics（数学学院）
- Southeast University（东南大学）
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