ResSR: A Computationally Efficient Residual Approach to Super-Resolving Multispectral Images

Multispectral imaging (MSI) plays a critical role in material classification, environmental monitoring, and remote sensing. However, MSI sensors typically have wavelength-dependent resolution, which limits downstream analysis. MSI super-resolution (MSI-SR) methods address this limitation by reconstructing all bands at a common high spatial resolution. Existing methods can achieve high reconstruction quality but often rely on spatially-coupled optimization or large learning-based models, leading to significant computational cost and limiting their use in large-scale or time-critical settings. In this paper, we introduce ResSR, a computationally efficient, model-based MSI-SR method that achieves high-quality reconstruction without supervised training or spatially-coupled optimization. Notably, ResSR decouples spectral and spatial processing into two sequential steps. ResSR first computes a spectrally-informed high-resolution estimate of the MSI using singular value decomposition together with a spatially-decoupled approximate forward model. It then applies a residual correction step to restore low-frequency spatial consistency while preserving high-frequency detail recovered by the spectral reconstruction. ResSR achieves comparable or improved reconstruction quality relative to existing MSI-SR methods while being 2$\times$ to 10$\times$ faster. Code is available at https://github.com/hdsullivan/ResSR.

💡 Research Summary

The paper introduces ResSR, a computationally efficient, model‑based approach for multispectral image super‑resolution (MSI‑SR) that avoids both supervised deep‑learning training and spatially‑coupled optimization. The method is built on a two‑stage pipeline that completely decouples spectral processing from spatial processing.

In the first stage, the authors exploit the strong inter‑band correlations of MSI by assuming the high‑resolution image lies in a low‑dimensional spectral subspace. They first up‑sample all low‑resolution bands to a common grid using bicubic interpolation, then randomly sample a small set of pixels (Nₛ ≪ Nₚ) to form a compact data matrix D. An SVD on D (truncated to K components, K = 2 in experiments) yields the spectral mean μ, the basis matrix V (size N_b × K), and the singular values Λ. A loss function combines a data‑fitting term—derived from the band‑dependent forward model yᵢ = Aᵢxᵢ + εᵢ—and a regularization term that penalizes coefficients associated with small singular values. The data‑fitting term is weighted by γ_{Lᵢ}, a set of per‑band weights controlled by a single user parameter γ_{HR} that emphasizes high‑resolution bands.

To avoid the costly spatial coupling introduced by the down‑sampling operators Aᵢ, the authors approximate AᵢᵀAᵢ by Lᵢ⁻²I, justified by the smoothness of satellite imagery at the scale of the down‑sampling blocks. This approximation removes spatial coupling from the normal equations, reducing the problem to solving Nₚ independent K × K linear systems. The resulting spectral coefficient matrix Ẑ is then used to reconstruct an initial high‑resolution MSI estimate: X̂_SVD = ẐVᵀ + 1μ.

Because the spatially‑decoupled reconstruction does not enforce low‑frequency consistency, the second stage applies a residual correction. For each band i, the method computes the residual between the measured low‑resolution observation yᵢ and the down‑sampled version of the spectral estimate AᵢX̂_SVD,i, upsamples this residual with Bᵢ (bicubic), and adds it back to the spectral estimate: x̂_norm,i = x̂_SVD,i + Bᵢ(yᵢ − Aᵢx̂_SVD,i). Finally, the original intensity scaling (based on 2nd and 98th percentiles) is restored to obtain the final super‑resolved bands.

Algorithmically, ResSR consists of five steps: (1) intensity normalization and pixel subsampling, (2) SVD‑based subspace estimation, (3) closed‑form solution for Ẑ using the spatially‑decoupled linear systems, (4) construction of the uncorrected high‑resolution image, and (5) per‑band residual correction. The computational complexity is linear in the number of pixels (O(NₚK²)) and independent of the full image size, contrasting sharply with traditional SVD‑based methods that require O(KNₚ³) operations.

Experimental evaluation on simulated and real Sentinel‑2 data shows that ResSR achieves peak signal‑to‑noise ratio (PSNR) and structural similarity (SSIM) comparable to or slightly better than state‑of‑the‑art methods, including deep‑learning models (e.g., DSen2) and iterative SVD approaches (e.g., SupReME). Importantly, ResSR runs 2–10× faster, with the spectral coefficient estimation being up to 1000× quicker than ADMM‑based solvers. Sensitivity analyses demonstrate that a high γ_{HR} (≈ 0.99) preserves fine spatial detail, while the regularization weight λ = 0.5 effectively suppresses noise without sacrificing spectral fidelity.

In summary, ResSR offers a practical solution for large‑scale MSI‑SR tasks: it leverages low‑rank spectral representations, eliminates costly spatial coupling through a principled approximation, and restores low‑frequency accuracy via a lightweight residual step. The method requires no training data, scales linearly with image size, and delivers high‑quality super‑resolved multispectral products suitable for downstream applications such as material classification, environmental monitoring, and rapid remote‑sensing analytics.