  Spectral imaging enables spatially-resolved identification of materials in
remote sensing, biomedicine, and astronomy. However, acquisition times require
balancing spectral and spatial resolution with signal-to-noise. Hyperspectral
imaging provides superior material specificity, while multispectral images are
faster to collect at greater fidelity. We propose an approach for fusing
hyperspectral and multispectral images to provide high-quality hyperspectral
output. The proposed optimization leverages the least absolute shrinkage and
selection operator (LASSO) to perform variable selection and regularization.
Computational time is reduced by applying the alternating direction method of
multipliers (ADMM), as well as initializing the fusion image by estimating it
using maximum a posteriori (MAP) based on Hardie's method. We demonstrate that
the proposed sparse fusion and reconstruction provides quantitatively superior
results when compared to existing methods on publicly available images.
Finally, we show how the proposed method can be practically applied in
biomedical infrared spectroscopic microscopy.
