# Hyperspectral Unmixing with 3D Convolutional Sparse Coding and Projected Simplex Volume Maximization

arXiv: https://arxiv.org/abs/2512.05674 · HTML: https://mlsanity.com/paper/2512.05674/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 50 references that are in the map.
- First posted on arXiv 5 Dec 2025.

## Builds on (most cited first, 14 of 14)

- [Spectral Variability in Hyperspectral Data Unmixing: A Comprehensive Review](https://mlsanity.com/paper/2001.07307/) (2020)
- [Maximal Sparsity with Deep Networks?](https://mlsanity.com/paper/1605.01636/) (2016)
- [EndNet: Sparse AutoEncoder Network for Endmember Extraction and Hyperspectral Unmixing](https://mlsanity.com/paper/1708.01894/) (2017)
- [Nonlinear unmixing of hyperspectral images: models and algorithms](https://mlsanity.com/paper/1304.1875/) (2013)
- [Learned Convolutional Sparse Coding](https://mlsanity.com/paper/1711.00328/) (2017)
- [Hyperspectral unmixing with spectral variability using a perturbed linear mixing model](https://mlsanity.com/paper/1502.01260/) (2015)
- [Hyperspectral Unmixing via Deep Autoencoder Networks for a Generalized Linear-Mixture/Nonlinear-Fluctuation Model](https://mlsanity.com/paper/1904.13017/) (2019)
- [Spectral Unmixing via Data-guided Sparsity](https://mlsanity.com/paper/1403.3155/) (2014)
- [Revisiting Sparse Convolutional Model for Visual Recognition](https://mlsanity.com/paper/2210.12945/) (2022)
- [Integration of Physics-Based and Data-Driven Models for Hyperspectral Image Unmixing](https://mlsanity.com/paper/2206.05508/) (2022)
- [Hyperspectral unmixing with spectral variability using adaptive bundles and double sparsity](https://mlsanity.com/paper/1804.11132/) (2018)
- [SINET: Sparsity-driven Interpretable Neural Network for Underwater Image Enhancement](https://mlsanity.com/paper/2409.01022/) (2024)
- [Unrolling Plug-and-Play Network for Hyperspectral Unmixing](https://mlsanity.com/paper/2409.04719/) (2024)
- [l0-Regularized Sparse Coding-based Interpretable Network for Multi-Modal Image Fusion](https://mlsanity.com/paper/2411.04519/) (2024)

## Abstract (arXiv)

Hyperspectral unmixing (HSU) aims to separate each pixel into its constituent endmembers and estimate their corresponding abundance fractions. This work presents an algorithm-unrolling-based network for the HSU task, named the 3D Convolutional Sparse Coding Network (3D-CSCNet), built upon a 3D CSC model. Unlike existing unrolling-based networks, our 3D-CSCNet is designed within the powerful autoencoder (AE) framework. Specifically, to solve the 3D CSC problem, we propose a 3D CSC block (3D-CSCB) derived through deep algorithm unrolling. Given a hyperspectral image (HSI), 3D-CSCNet employs the 3D-CSCB to estimate the abundance matrix. The use of 3D CSC enables joint learning of spectral and spatial relationships in the 3D HSI data cube. The estimated abundance matrix is then passed to the AE decoder to reconstruct the HSI, and the decoder weights are extracted as the endmember matrix. Additionally, we propose a projected simplex volume maximization (PSVM) algorithm for endmember estimation, and the resulting endmembers are used to initialize the decoder weights of 3D-CSCNet. Extensive experiments on three real datasets and one simulated dataset with three different signal-to-noise ratio (SNR) levels demonstrate that our 3D-CSCNet outperforms state-of-the-art methods.