# An Augmented Linear Mixing Model to Address Spectral Variability for Hyperspectral Unmixing

arXiv: https://arxiv.org/abs/1810.12000 · HTML: https://mlsanity.com/paper/1810.12000/

## Key facts

- Cited by 66 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Oct 2018.

## Built on by (most cited first, 30 of 66)

- [SpectralFormer: Rethinking Hyperspectral Image Classification with Transformers](https://mlsanity.com/paper/2107.02988/) (2021)
- [Multimodal Fusion Transformer for Remote Sensing Image Classification](https://mlsanity.com/paper/2203.16952/) (2022)
- [Hyperspectral Image Classification-Traditional to Deep Models: A Survey for Future Prospects](https://mlsanity.com/paper/2101.06116/) (2021)
- [Multimodal Remote Sensing Benchmark Datasets for Land Cover Classification with A Shared and Specific Feature Learning Model](https://mlsanity.com/paper/2105.10196/) (2021)
- [Deep Learning for UAV-based Object Detection and Tracking: A Survey](https://mlsanity.com/paper/2110.12638/) (2021)
- [Endmember-Guided Unmixing Network (EGU-Net): A General Deep Learning Framework for Self-Supervised Hyperspectral Unmixing](https://mlsanity.com/paper/2105.10194/) (2021)
- [Dynamic-Group-Aware Networks for Multi-Agent Trajectory Prediction with Relational Reasoning](https://mlsanity.com/paper/2206.13114/) (2022)
- [A Comprehensive Survey for Hyperspectral Image Classification: The Evolution from Conventional to Transformers and Mamba Models](https://mlsanity.com/paper/2404.14955/) (2024)
- [Decoupled-and-Coupled Networks: Self-Supervised Hyperspectral Image Super-Resolution with Subpixel Fusion](https://mlsanity.com/paper/2205.03742/) (2022)
- [Multi-Content Complementation Network for Salient Object Detection in Optical Remote Sensing Images](https://mlsanity.com/paper/2112.01932/) (2021)
- [Semantic-aware Dense Representation Learning for Remote Sensing Image Change Detection](https://mlsanity.com/paper/2205.13769/) (2022)
- [Exploring Multi-Timestep Multi-Stage Diffusion Features for Hyperspectral Image Classification](https://mlsanity.com/paper/2306.08964/) (2023)
- [Pansharpening by convolutional neural networks in the full resolution framework](https://mlsanity.com/paper/2111.08334/) (2021)
- [3D Instance Segmentation of MVS Buildings](https://mlsanity.com/paper/2112.09902/) (2021)
- [Convolutional Neural Networks Rarely Learn Shape for Semantic Segmentation](https://mlsanity.com/paper/2305.06568/) (2023)
- [Image Processing and Machine Learning for Hyperspectral Unmixing: An Overview and the HySUPP Python Package](https://mlsanity.com/paper/2308.09375/) (2023)
- [Rotation Equivariant Feature Image Pyramid Network for Object Detection in Optical Remote Sensing Imagery](https://mlsanity.com/paper/2106.00880/) (2021)
- [Entropic Descent Archetypal Analysis for Blind Hyperspectral Unmixing](https://mlsanity.com/paper/2209.11002/) (2022)
- [Tensor Decompositions for Hyperspectral Data Processing in Remote Sensing: A Comprehensive Review](https://mlsanity.com/paper/2205.06407/) (2022)
- [Full-resolution quality assessment for pansharpening](https://mlsanity.com/paper/2108.06144/) (2021)
- [Dynamical Hyperspectral Unmixing with Variational Recurrent Neural Networks](https://mlsanity.com/paper/2303.10566/) (2023)
- [Multi-patch Feature Pyramid Network for Weakly Supervised Object Detection in Optical Remote Sensing Images](https://mlsanity.com/paper/2108.08063/) (2021)
- [PromptHSI: Universal Hyperspectral Image Restoration with Vision-Language Modulated Frequency Adaptation](https://mlsanity.com/paper/2411.15922/) (2024)
- [Using Low-rank Representation of Abundance Maps and Nonnegative Tensor Factorization for Hyperspectral Nonlinear Unmixing](https://mlsanity.com/paper/2103.16204/) (2021)
- [Attention Mechanism Meets with Hybrid Dense Network for Hyperspectral Image Classification](https://mlsanity.com/paper/2201.01001/) (2022)
- [Integrating Multiple Sources Knowledge for Class Asymmetry Domain Adaptation Segmentation of Remote Sensing Images](https://mlsanity.com/paper/2305.09893/) (2023)
- [Distributed Learning over Networks with Graph-Attention-Based Personalization](https://mlsanity.com/paper/2305.13041/) (2023)
- [Incomplete Multimodal Industrial Anomaly Detection via Cross-Modal Distillation](https://mlsanity.com/paper/2405.13571/) (2024)
- [Universal Adversarial Defense in Remote Sensing Based on Pre-trained Denoising Diffusion Models](https://mlsanity.com/paper/2307.16865/) (2023)
- [Deep Class Incremental Learning from Decentralized Data](https://mlsanity.com/paper/2203.05984/) (2022)

## Abstract (arXiv)

Hyperspectral imagery collected from airborne or satellite sources inevitably suffers from spectral variability, making it difficult for spectral unmixing to accurately estimate abundance maps. The classical unmixing model, the linear mixing model (LMM), generally fails to handle this sticky issue effectively. To this end, we propose a novel spectral mixture model, called the augmented linear mixing model (ALMM), to address spectral variability by applying a data-driven learning strategy in inverse problems of hyperspectral unmixing. The proposed approach models the main spectral variability (i.e., scaling factors) generated by variations in illumination or typography separately by means of the endmember dictionary. It then models other spectral variabilities caused by environmental conditions (e.g., local temperature and humidity, atmospheric effects) and instrumental configurations (e.g., sensor noise), as well as material nonlinear mixing effects, by introducing a spectral variability dictionary. To effectively run the data-driven learning strategy, we also propose a reasonable prior knowledge for the spectral variability dictionary, whose atoms are assumed to be low-coherent with spectral signatures of endmembers, which leads to a well-known low coherence dictionary learning problem. Thus, a dictionary learning technique is embedded in the framework of spectral unmixing so that the algorithm can learn the spectral variability dictionary and estimate the abundance maps simultaneously. Extensive experiments on synthetic and real datasets are performed to demonstrate the superiority and effectiveness of the proposed method in comparison with previous state-of-the-art methods.