# Using Low-rank Representation of Abundance Maps and Nonnegative Tensor Factorization for Hyperspectral Nonlinear Unmixing

arXiv: https://arxiv.org/abs/2103.16204 · HTML: https://mlsanity.com/paper/2103.16204/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 43 references that are in the map.
- First posted on arXiv 30 Mar 2021.

## Builds on (most cited first, 7 of 7)

- [An Augmented Linear Mixing Model to Address Spectral Variability for Hyperspectral Unmixing](https://mlsanity.com/paper/1810.12000/) (2018)
- [Hyperspectral Unmixing: Ground Truth Labeling, Datasets, Benchmark Performances and Survey](https://mlsanity.com/paper/1708.05125/) (2017)
- [Nonlinear unmixing of hyperspectral images: models and algorithms](https://mlsanity.com/paper/1304.1875/) (2013)
- [Robust Collaborative Nonnegative Matrix Factorization For Hyperspectral Unmixing (R-CoNMF)](https://mlsanity.com/paper/1506.04870/) (2015)
- [Simultaneously sparse and low-rank abundance matrix estimation for hyperspectral image unmixing](https://mlsanity.com/paper/1504.01515/) (2015)
- [A Low-rank Tensor Regularization Strategy for Hyperspectral Unmixing](https://mlsanity.com/paper/1803.06355/) (2018)
- [Unsupervised Nonlinear Spectral Unmixing based on a Multilinear Mixing Model](https://mlsanity.com/paper/1604.04293/) (2016)

## Built on by (most cited first, 6 of 6)

- [Image Processing and Machine Learning for Hyperspectral Unmixing: An Overview and the HySUPP Python Package](https://mlsanity.com/paper/2308.09375/) (2023)
- [Tensor Decompositions for Hyperspectral Data Processing in Remote Sensing: A Comprehensive Review](https://mlsanity.com/paper/2205.06407/) (2022)
- [Bidirectional recurrent imputation and abundance estimation of LULC classes with MODIS multispectral time series and geo-topographic and climatic data](https://mlsanity.com/paper/2310.07223/) (2023)
- [Wasserstein Nonnegative Tensor Factorization with Manifold Regularization](https://mlsanity.com/paper/2401.01842/) (2024)
- [Deep Nonlinear Hyperspectral Unmixing Using Multi-task Learning](https://mlsanity.com/paper/2402.03398/) (2024)
- [Overcoming the Identity Mapping Problem in Self-Supervised Hyperspectral Anomaly Detection](https://mlsanity.com/paper/2504.04115/) (2025)

## Abstract (arXiv)

Tensor-based methods have been widely studied to attack inverse problems in hyperspectral imaging since a hyperspectral image (HSI) cube can be naturally represented as a third-order tensor, which can perfectly retain the spatial information in the image. In this article, we extend the linear tensor method to the nonlinear tensor method and propose a nonlinear low-rank tensor unmixing algorithm to solve the generalized bilinear model (GBM). Specifically, the linear and nonlinear parts of the GBM can both be expressed as tensors. Furthermore, the low-rank structures of abundance maps and nonlinear interaction abundance maps are exploited by minimizing their nuclear norm, thus taking full advantage of the high spatial correlation in HSIs. Synthetic and real-data experiments show that the low rank of abundance maps and nonlinear interaction abundance maps exploited in our method can improve the performance of the nonlinear unmixing. A MATLAB demo of this work will be available at https://github.com/LinaZhuang for the sake of reproducibility.