A convex formulation for hyperspectral image superresolution via subspace-based regularization

TL;DR

This paper introduces a convex optimization framework for hyperspectral image superresolution that leverages subspace-based regularization and an efficient ADMM algorithm, improving upon existing methods in accuracy and robustness.

Contribution

The authors propose a novel convex formulation incorporating a vector Total Variation regularizer and tailored ADMM algorithm for hyperspectral superresolution, handling large-scale data and complex degradations.

Findings

Outperforms state-of-the-art methods in simulated experiments

Effectively estimates spatial blur and spectral operators

Achieves high-quality superresolved hyperspectral images

Abstract

Hyperspectral remote sensing images (HSIs) usually have high spectral resolution and low spatial resolution. Conversely, multispectral images (MSIs) usually have low spectral and high spatial resolutions. The problem of inferring images which combine the high spectral and high spatial resolutions of HSIs and MSIs, respectively, is a data fusion problem that has been the focus of recent active research due to the increasing availability of HSIs and MSIs retrieved from the same geographical area. We formulate this problem as the minimization of a convex objective function containing two quadratic data-fitting terms and an edge-preserving regularizer. The data-fitting terms account for blur, different resolutions, and additive noise. The regularizer, a form of vector Total Variation, promotes piecewise-smooth solutions with discontinuities aligned across the hyperspectral bands. The downsampling operator accounting for the different spatial resolutions, the non-quadratic and non-smooth nature of the regularizer, and the very large size of the HSI to be estimated lead to a hard optimization problem. We deal with these difficulties by exploiting the fact that HSIs generally "live" in a low-dimensional subspace and by tailoring the Split Augmented Lagrangian Shrinkage Algorithm (SALSA), which is an instance of the Alternating Direction Method of Multipliers (ADMM), to this optimization problem, by means of a convenient variable splitting. The spatial blur and the spectral linear operators linked, respectively, with the HSI and MSI acquisition processes are also estimated, and we obtain an effective algorithm that outperforms the state-of-the-art, as illustrated in a series of experiments with simulated and real-life data.