SUnAA: Sparse Unmixing using Archetypal Analysis

TL;DR

SUnAA introduces a robust, archetypal analysis-based sparse unmixing method that effectively estimates mineral abundances in hyperspectral data, outperforming traditional techniques in accuracy and detection capabilities.

Contribution

The paper presents a novel non-convex optimization approach for sparse unmixing using archetypal analysis, requiring only the number of endmembers and demonstrating improved performance.

Findings

Better signal-to-reconstruction error on simulated data

Successful mineral abundance estimation on Cuprite dataset

Enhanced mineral detection compared to conventional methods

Abstract

This paper introduces a new sparse unmixing technique using archetypal analysis (SUnAA). First, we design a new model based on archetypal analysis. We assume that the endmembers of interest are a convex combination of endmembers provided by a spectral library and that the number of endmembers of interest is known. Then, we propose a minimization problem. Unlike most conventional sparse unmixing methods, here the minimization problem is non-convex. We minimize the optimization objective iteratively using an active set algorithm. Our method is robust to the initialization and only requires the number of endmembers of interest. SUnAA is evaluated using two simulated datasets for which results confirm its better performance over other conventional and advanced techniques in terms of signal-to-reconstruction error. SUnAA is also applied to Cuprite dataset and the results are compared visually with the available geological map provided for this dataset. The qualitative assessment demonstrates the successful estimation of the minerals abundances and significantly improves the detection of dominant minerals compared to the conventional regression-based sparse unmixing methods. The Python implementation of SUnAA can be found at: https://github.com/BehnoodRasti/SUnAA.