Hyperspectral pan-sharpening: a variational convex constrained formulation to impose parallel level lines, solved with ADMM

TL;DR

This paper proposes a variational convex constrained approach for hyperspectral pan-sharpening, utilizing ADMM to efficiently fuse low-resolution hyperspectral data with high-resolution panchromatic images, ensuring high-quality high-resolution hyperspectral outputs.

Contribution

It introduces a novel convex constrained formulation that enforces parallel level lines and employs ADMM for efficient optimization in hyperspectral pan-sharpening.

Findings

Effective fusion of hyperspectral and panchromatic images achieved.

The method handles data noise statistics explicitly.

High-resolution hyperspectral images with preserved spectral and spatial features.

Abstract

In this paper, we address the issue of hyperspectral pan-sharpening, which consists in fusing a (low spatial resolution) hyperspectral image HX and a (high spatial resolution) panchromatic image P to obtain a high spatial resolution hyperspectral image. The problem is addressed under a variational convex constrained formulation. The objective favors high resolution spectral bands with level lines parallel to those of the panchromatic image. This term is balanced with a total variation term as regularizer. Fit-to-P data and fit-to-HX data constraints are effectively considered as mathematical constraints, which depend on the statistics of the data noise measurements. The developed Alternating Direction Method of Multipliers (ADMM) optimization scheme enables us to solve this problem efficiently despite the non differentiabilities and the huge number of unknowns.