# Spectral Variability Aware Blind Hyperspectral Image Unmixing Based on Convex Geometry

## TL;DR

This paper investigates the limitations of convex geometry-based hyperspectral unmixing methods under spectral variability and proposes an integrated unmixing approach that addresses these issues, validated on simulated and real data.

## Contribution

It introduces a new unmixing chain that accounts for spectral variability within the convex geometry framework, based on an extended linear mixing model.

## Key findings

- The proposed method improves unmixing accuracy under spectral variability.
- Validation on datasets shows better performance than classical convex geometry methods.
- The approach effectively handles endmember variability in hyperspectral data.

## Abstract

Hyperspectral image unmixing has proven to be a useful technique to interpret hyperspectral data, and is a prolific research topic in the community. Most of the approaches used to perform linear unmixing are based on convex geometry concepts, because of the strong geometrical structure of the linear mixing model. However, two main phenomena lead to question this model, namely nonlinearities and the spectral variability of the materials. Many algorithms based on convex geometry are still used when considering these two limitations of the linear model. A natural question is to wonder to what extent these concepts and tools (Intrinsic Dimensionality estimation, endmember extraction algorithms, pixel purity) can be safely used in these different scenarios. In this paper, we analyze them with a focus on endmember variability, assuming that the linear model holds. In the light of this analysis, we propose an integrated unmixing chain which tries to adress the shortcomings of the classical tools used in the linear case, based on our previously proposed extended linear mixing model. We show the interest of the proposed approach on simulated and real datasets.