Hyperspectral image superresolution: An edge-preserving convex formulation

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.

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.

Miguel Simões

Miguel Simões was born in Lisbon, Portugal, in 1987. He received the M.Sc. degree in electrical and computer engineering from the Instituto Superior Técnico, University of Lisbon, Lisbon, in 2010. He is currently working toward the joint Ph.D. degree in electrical and computer engineering, and signal and image processing at the Instituto de Telecomunicações, Instituto Superior Técnico, University of Lisbon, Lisbon, and at the Grenoble Images Parole Signal Automatique (GIPSA-lab), University of Grenoble, Grenoble, France, respectively. Previously, he has worked as an Information Technology (IT) consultant in the field of telecommunications. His main areas of research interest are image processing, optimization, and remote sensing.IT