# Nonparametric Detection of Nonlinearly Mixed Pixels and Endmember Estimation in Hyperspectral Images

arXiv: https://arxiv.org/abs/1503.05521 · HTML: https://mlsanity.com/paper/1503.05521/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Mar 2015.

## Built on by (most cited first, 3 of 3)

- [Model-Based Deep Autoencoder Networks for Nonlinear Hyperspectral Unmixing](https://mlsanity.com/paper/2104.08409/) (2021)
- [Hybrid Neural Network Augmented Physics-based Models for Nonlinear Filtering](https://mlsanity.com/paper/2204.06471/) (2022)
- [DTU-Net: A Multi-Scale Dilated Transformer Network for Nonlinear Hyperspectral Unmixing](https://mlsanity.com/paper/2503.03465/) (2025)

## Abstract (arXiv)

Mixing phenomena in hyperspectral images depend on a variety of factors such as the resolution of observation devices, the properties of materials, and how these materials interact with incident light in the scene. Different parametric and nonparametric models have been considered to address hyperspectral unmixing problems. The simplest one is the linear mixing model. Nevertheless, it has been recognized that mixing phenomena can also be nonlinear. The corresponding nonlinear analysis techniques are necessarily more challenging and complex than those employed for linear unmixing. Within this context, it makes sense to detect the nonlinearly mixed pixels in an image prior to its analysis, and then employ the simplest possible unmixing technique to analyze each pixel. In this paper, we propose a technique for detecting nonlinearly mixed pixels. The detection approach is based on the comparison of the reconstruction errors using both a Gaussian process regression model and a linear regression model. The two errors are combined into a detection statistics for which a probability density function can be reasonably approximated. We also propose an iterative endmember extraction algorithm to be employed in combination with the detection algorithm. The proposed Detect-then-Unmix strategy, which consists of extracting endmembers, detecting nonlinearly mixed pixels and unmixing, is tested with synthetic and real images.