Spectral image fusion from compressive measurements using spectral unmixing

This work aims at reconstructing a high-spatial high-spectral image from the complementary information provided by sensors that allow us to acquire compressive measurements of different spectral ranges and different spatial resolutions, such as hyperspectral (HS) and multi-spectral (MS) compressed images. To solve this inverse problem, we investigate a new optimization algorithm based on the linear spectral unmixing model and using a block coordinate descent strategy. The non-negative and sum to one constraints resulting from the intrinsic physical properties of abundance and a total variation penalization are used to regularize this ill-posed inverse problem. Simulations results conducted on realistic compressive hyperspectral and multispectral images show that the proposed algorithm can provide fusion and unmixing results that are very close to those obtained when using uncompressed images, with the advantage of using a significant reduced number of measurements.