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This paper introduces LaST-SR, a novel approach to single-image super-resolution (SISR) that employs a Laplace-inspired complex-frequency decomposition to effectively model both periodic and aperiodic features in images. By integrating a global Fourier branch for long-range structural consistency with a localized complex-frequency branch for fine details, LaST-SR achieves superior performance in reconstructing irregular structures. Experimental results demonstrate that LaST-SR outperforms existing methods on multiple benchmarks, achieving the highest PSNR and SSIM scores for both 2x and 4x super-resolution tasks.
LaST-SR achieves unprecedented detail recovery in single-image super-resolution by effectively modeling both periodic and aperiodic features through a novel complex-frequency decomposition.
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.