Temporal illumination variation compensation using perpendicular whisk-broom hyperspectral scans

This study introduces a novel method to mitigate temporal illumination variations in whisk-broom hyperspectral imaging under varying environmental illumination conditions. Whisk-broom hyperspectral imaging captures high resolution spectra pixel-by-pixel sequentially, a process susceptible to sunlight fluctuations over time, particularly when imaging cultural artifacts outdoors. Despite sunlight's broad spectrum, its variability over time can compromise the quality of hyperspectral images, affecting data analysis. Prior strategies suggested a supplementary single compensating vertical scan alongside the standard row-wise raster scan. However, this strategy fails when the additional single vertical scan is performed near or on a black frame. Building on this, our study proposes using two scans, one performed orthogonally to the traditional row-wise scan, to counteract illumination variations. Furthermore, we formulate the compensation problem in logarithmic space, exploiting the low-dimensional structure of the reflectance and illumination spectra. Using total variation penalization in the cost function enhances smoothness. Our method achieves robust compensation for changes in environmental illumination. We also demonstrate that we can use multiple columns from the column-wise scan without significantly decreasing the compensation quality while reducing acquisition time. We illustrate the application of our methods to hyperspectral images of stained-glass windows of the historic Cathédrale Notre-Dame d'Amiens in France.