# Sparsity Constrained Distributed Unmixing of Hyperspectral Data

## TL;DR

This paper introduces a novel distributed optimization algorithm for hyperspectral spectral unmixing that incorporates sparsity constraints, improving the estimation of endmembers and abundances in hyperspectral images.

## Contribution

It proposes a sparsity constrained distributed unmixing algorithm using diffusion LMP strategy, with analysis for various LMP powers and norms, advancing hyperspectral data analysis methods.

## Key findings

- The proposed algorithm outperforms existing methods in spectral unmixing accuracy.
- Distributed approach effectively handles large hyperspectral datasets.
- Sparsity constraints improve endmember and abundance estimation.

## Abstract

Spectral unmixing (SU) is a technique to characterize mixed pixels in hyperspectral images measured by remote sensors. Most of the spectral unmixing algorithms are developed using the linear mixing models. To estimate endmembers and fractional abundance matrices in a blind problem, nonnegative matrix factorization (NMF) and its developments are widely used in the SU problem. One of the constraints which was added to NMF is sparsity, that was regularized by Lq norm. In this paper, a new algorithm based on distributed optimization is suggested for spectral unmixing. In the proposed algorithm, a network including single-node clusters is employed. Each pixel in the hyperspectral images is considered as a node in this network. The sparsity constrained distributed unmixing is optimized with diffusion least mean p-power (LMP) strategy, and then the update equations for fractional abundance and signature matrices are obtained. Afterwards the proposed algorithm is analyzed for different values of LMP power and Lq norms. Simulation results based on defined performance metrics illustrate the advantage of the proposed algorithm in spectral unmixing of hyperspectral data compared with other methods.