Generative Simplex Mapping: Non-Linear Endmember Extraction and Spectral Unmixing for Hyperspectral Imagery

We introduce a new model for non-linear endmember extraction and spectral unmixing of hyperspectral imagery called Generative Simplex Mapping (GSM). The model represents endmember mixing using a latent space of points sampled within a <inline-formula><math xmlns="http://www.w3.org/1998...

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Bibliographic Details
Main Authors: John Waczak, David J. Lary
Format: Article
Language:English
Published: MDPI AG 2024-11-01
Series:Remote Sensing
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Online Access:https://www.mdpi.com/2072-4292/16/22/4316
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Summary:We introduce a new model for non-linear endmember extraction and spectral unmixing of hyperspectral imagery called Generative Simplex Mapping (GSM). The model represents endmember mixing using a latent space of points sampled within a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>n</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></inline-formula>-simplex corresponding to <i>n</i> unique sources. Barycentric coordinates within this simplex are naturally interpreted as relative endmember abundances satisfying both the abundance sum-to-one and abundance non-negativity constraints. Points in this latent space are mapped to reflectance spectra via a flexible function combining linear and non-linear mixing. Due to the probabilistic formulation of the GSM, spectral variability is also estimated by a precision parameter describing the distribution of observed spectra. Model parameters are determined using a generalized expectation-maximization algorithm, which guarantees non-negativity for extracted endmembers. We first compare the GSM against three varieties of non-negative matrix factorization (NMF) on a synthetic data set of linearly mixed spectra from the USGS spectral database. Here, the GSM performed favorably for both endmember accuracy and abundance estimation with all non-linear contributions driven to zero by the fitting procedure. In a second experiment, we apply the GTM to model non-linear mixing in real hyperspectral imagery captured over a pond in North Texas. The model accurately identified spectral signatures corresponding to near-shore algae, water, and rhodamine tracer dye introduced into the pond to simulate water contamination by a localized source. Abundance maps generated using the GSM accurately track the evolution of the dye plume as it mixes into the surrounding water.
ISSN:2072-4292