  Hyperspectral remote sensing images (HSIs) are characterized by having a low
spatial resolution and a high spectral resolution, whereas multispectral images
(MSIs) are characterized by low spectral and high spatial resolutions. These
complementary characteristics have stimulated active research in the inference
of images with high spatial and spectral resolutions from HSI-MSI pairs.
  In this paper, we formulate this data fusion problem as the minimization of a
convex objective function containing two data-fitting terms and an
edge-preserving regularizer. The data-fitting terms are quadratic and account
for blur, different spatial resolutions, and additive noise; the regularizer, a
form of vector Total Variation, promotes aligned discontinuities across the
reconstructed hyperspectral bands.
  The optimization described above is rather hard, owing to its
non-diagonalizable linear operators, to the non-quadratic and non-smooth nature
of the regularizer, and to the very large size of the image to be inferred. We
tackle these difficulties by tailoring the Split Augmented Lagrangian Shrinkage
Algorithm (SALSA)---an instance of the Alternating Direction Method of
Multipliers (ADMM)---to this optimization problem. By using a convenient
variable splitting and by exploiting the fact that HSIs generally "live" in a
low-dimensional subspace, we obtain an effective algorithm that yields
state-of-the-art results, as illustrated by experiments.
