S3D-Mosaic: Subgradient-Guided Cross-Band Structure Transfer for Spectral Demosaicing
Abstract: Multispectral filter array (MSFA) imaging enables snapshot spectral acquisition, but its per-band sparse sampling causes severe spatial aliasing. Although missing spatial structures can be inferred across bands, wavelength-dependent contrast variations make direct cross-band transfer unreliable. Existing model-based methods lack explicit magnitude-invariant mechanisms, and learning-based methods require layout-specific training or per-image tuning, limiting generalization. To address these issues, we propose S3D-Mosaic, a model-based spectral demosaicing method built upon a subgradient-guided cross-band structure transfer framework. We first establish a subgradient-guided regularization framework with a generalized cosine-similarity interpretation, providing a convex mechanism for magnitude-invariant information transfer. Then we design a compact Directional Sparse Equivariant Difference Convolution (DSE-DConv) for band-level extraction of orientation-selective, high-frequency structure features at low computational cost. Instantiating the framework with DSE-DConv on spectrally adjacent bands yields a cross-band self-structure similarity regularizer for spectral demosaicing, which we optimize via a dual-scan ADMM algorithm that decouples the bidirectional dependency while propagating magnitude-robust structural information across bands. With DSE-DConv's two parameters trained once via self-supervision, S3D-Mosaic outperforms state-of-the-art unsupervised methods on CAVE and NTIRE 2022, and generalizes robustly to varying MSFA layouts, pan-mosaic fusion, and real-world UAV data with fixed reconstruction hyperparameters. The source code is available at \url{https://github.com/bestwishes43/S3D-Mosaic}.