# Tech Report: A Fast Multiscale Spatial Regularization for Sparse Hyperspectral Unmixing

arXiv: https://arxiv.org/abs/1712.01770 · HTML: https://mlsanity.com/paper/1712.01770/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Dec 2017.

## Built on by (most cited first, 11 of 11)

- [Image Processing and Machine Learning for Hyperspectral Unmixing: An Overview and the HySUPP Python Package](https://mlsanity.com/paper/2308.09375/) (2023)
- [Dynamical Hyperspectral Unmixing with Variational Recurrent Neural Networks](https://mlsanity.com/paper/2303.10566/) (2023)
- [Model-Based Deep Autoencoder Networks for Nonlinear Hyperspectral Unmixing](https://mlsanity.com/paper/2104.08409/) (2021)
- [SUnAA: Sparse Unmixing using Archetypal Analysis](https://mlsanity.com/paper/2308.04771/) (2023)
- [Spectral Variability Augmented Sparse Unmixing of Hyperspectral Images](https://mlsanity.com/paper/2110.09744/) (2021)
- [Learning Interpretable Deep Disentangled Neural Networks for Hyperspectral Unmixing](https://mlsanity.com/paper/2310.02340/) (2023)
- [A Generalized Multiscale Bundle-Based Hyperspectral Sparse Unmixing Algorithm](https://mlsanity.com/paper/2401.13161/) (2024)
- [Fast Semisupervised Unmixing Using Nonconvex Optimization](https://mlsanity.com/paper/2401.12609/) (2024)
- [Hierarchical Homogeneity-Based Superpixel Segmentation: Application to Hyperspectral Image Analysis](https://mlsanity.com/paper/2407.15321/) (2024)
- [A General Framework for Group Sparsity in Hyperspectral Unmixing Using Endmember Bundles](https://mlsanity.com/paper/2505.14634/) (2025)
- [MiSiSUn: Minimum Simplex Semisupervised Unmixing](https://mlsanity.com/paper/2603.20263/) (2026)

## Abstract (arXiv)

Sparse hyperspectral unmixing from large spectral libraries has been considered to circumvent limitations of endmember extraction algorithms in many applications. This strategy often leads to ill-posed inverse problems, which can benefit from spatial regularization strategies. While existing spatial regularization methods improve the problem conditioning and promote piecewise smooth solutions, they lead to large nonsmooth optimization problems. Thus, efficiently introducing spatial context in the unmixing problem remains a challenge, and a necessity for many real world applications. In this paper, a novel multiscale spatial regularization approach for sparse unmixing is proposed. The method uses a signal-adaptive spatial multiscale decomposition based on superpixels to decompose the unmixing problem into two simpler problems, one in the approximation domain and another in the original domain. Simulation results using both synthetic and real data indicate that the proposed method can outperform state-of-the-art Total Variation-based algorithms with a computation time comparable to that of their unregularized counterparts.