Yuzhou Zhu, Zheng Zhang, Ruyi Zhang et al.
Wave-like images-from attosecond streaking spectrograms to optical spectra, audio mel-spectrograms and periodic video frames-encode critical harmonic structures that elude conventional feature extractors. We propose a unified, matrix-equivalent framework that reinterprets convolution and attention as linear transforms on flattened inputs, revealing filter weights as basis vectors spanning latent feature subspaces. To infuse spectral priors we apply elementwise $\sin(\cdot)$ mappings to each weight matrix. Embedding these transforms into CNN, ViT and Capsule architectures yields Sin-Basis Networks with heightened sensitivity to periodic motifs and built-in invariance to spatial shifts. Experiments on a diverse collection of wave-like image datasets-including 80,000 synthetic attosecond streaking spectrograms, thousands of Raman, photoluminescence and FTIR spectra, mel-spectrograms from AudioSet and cycle-pattern frames from Kinetics-demonstrate substantial gains in reconstruction accuracy, translational robustness and zero-shot cross-domain transfer. Theoretical analysis via matrix isomorphism and Mercer-kernel truncation quantifies how sinusoidal reparametrization enriches expressivity while preserving stability in data-scarce regimes. Sin-Basis Networks thus offer a lightweight, physics-informed approach to deep learning across all wave-form imaging modalities.