A Vignetting Correction Method for Remote Sensing Images Based on Low-Rank Modeling and Polynomial Fitting

Vignetting introduces spatial radiometric nonuniformity into remote sensing images and degrades subsequent radiometric analysis, image interpretation, and calibration-related applications. To address this problem, this paper proposes a vignetting correction method based on low-rank modeling and polynomial fitting. The method constructs a multi-frame data matrix in the logarithmic domain, extracts the shared vignette component through rank-1 low-rank modeling, and further recovers a smooth vignette field through polynomial fitting. Experiments were conducted using real remote sensing images, simulated vignetted images, and star images. Among the three ablation variants, the proposed full method achieved the best performance, with MAE, MAD, Center-MAE, and Edge-MAE values of 0.48%, 3.65%, 0.14%, and 0.52%, respectively. Compared with the low-rank-only method, these metrics were reduced by 23.8%, 32.8%, 71.4%, and 20.0%, respectively. An additional all-frame comparison across 28 dataset settings showed that the proposed rank-1 model achieved mean accuracy comparable to nuclear-norm-based standard RPCA, while exhibiting lower cross-dataset variability in MAE, MAD, and Edge-MAE. For star images, the method reduced image-plane nonuniformity from 1.39-1.92% to 0.59-0.80% while preserving background-subtracted stellar DN values. These results demonstrate that the proposed method provides physically interpretable and stable vignetting correction while maintaining radiometric consistency.