Hyperspectral and Multispectral Image Fusion With Functional Data Analysis Techniques

The fusion of hyperspectral images (HSIs) and multispectral images (MSI) aims to synthesize high-resolution hyperspectral image (HR-HSI) from observable low-resolution hyperspectral image (LR-HSI) and high-resolution multispectral image (HR-MSI) data. Existing methodologies often overlook the importance of the degradation model within imaging systems and the inherent spectral and spatial smoothness properties of hyperspectral data, resulting in suboptimal outcomes in real-world applications. We introduce a novel approach that utilizes functional data analysis (FDA) techniques to precisely estimate degradation parameters and effectively fuse HSI-MSI pairs. Based on the physical generation mechanisms of both HSI and MSI, alongside the intrinsic smoothness of degradation parameters, we propose an iterative function estimation technique to recover the spectral response function (SRF) and point spread function (PSF). Additionally, we introduce a spatial content-aware spectral subspace regularizer (SSR) that promotes low-dimensional functional subspaces for spectral data within similar spatial contexts. Implemented within an alternating direction method of multipliers (ADMM) optimization framework, our fusion model integrates the precisely estimated degradation parameters and SSR to accurately construct the target HR-HSI data. Extensive experimental evaluations on multiple public datasets demonstrate that our approach achieves superior performance in both quantitative metrics and qualitative assessments. The code for this work is available at https://github.com/lingxingongye/FDAssr.git.