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 data matrix in the logarithmic domain, extracts the common vignette component through low-rank decomposition, and further recovers a smooth vignette field by polynomial fitting. Experiments were conducted using real remote sensing images, simulated vignetted images, and star images. On simulated vignetted datasets, the proposed full method achieved the best overall performance, with mean absolute error (MAE), mean absolute deviation (MAD), center-region MAE, and edge-region MAE of 0.482%, 3.646%, 0.138%, and 0.519%, respectively. Compared with the low-rank-only method, these four metrics were reduced by 22.9%, 32.9%, 71.7%, and 19.9%, respectively. For star images, the method reduced image-plane nonuniformity from 1.39-1.92 to 0.59-0.80 while preserving the stability of background-subtracted stellar DN values. These results demonstrate that the proposed method effectively suppresses image-plane nonuniformity while maintaining radiometric consistency, thereby providing an effective solution for remote sensing image vignetting correction.