Illumination and reflectance spectra separation of a hyperspectral image meets low-rank matrix factorization

This paper addresses the illumination and reflectance spectra separation (IRSS) problem of a hyperspectral image captured under general spectral illumination. The huge amount of pixels in a hypersepctral image poses tremendous challenges on computational efficiency, yet in turn offers greater color variety that might be utilized to improve separation accuracy and relax the restrictive subspace illumination assumption in existing works. We show that this IRSS problem can be modeled into a low-rank matrix factorization problem, and prove that the separation is unique up to an unknown scale under the standard low-dimensionality assumption of reflectance. We also develop a scalable algorithm for this separation task that works in the presence of model error and image noise. Experiments on both synthetic data and real images have demonstrated that our separation results are sufficiently accurate, and can benefit some important applications, such as spectra relighting and illumination swapping.