Non-negative Einstein tensor factorization for unmixing hyperspectral images

TL;DR

This paper introduces a novel tensor-based non-negative factorization method using the Einstein product, improving hyperspectral image unmixing and denoising with a new optimization algorithm and convergence guarantees.

Contribution

It presents a new tensor factorization approach leveraging the Einstein product, with an optimization algorithm and convergence methods, for hyperspectral image processing.

Findings

Effective in denoising hyperspectral images

Accurate unmixing of hyperspectral data

Validated on synthetic and real datasets

Abstract

In this manuscript, we introduce a tensor-based approach to Non-Negative Tensor Factorization (NTF). The method entails tensor dimension reduction through the utilization of the Einstein product. To maintain the regularity and sparsity of the data, certain constraints are imposed. Additionally, we present an optimization algorithm in the form of a tensor multiplicative updates method, which relies on the Einstein product. To guarantee a minimum number of iterations for the convergence of the proposed algorithm, we employ the Reduced Rank Extrapolation (RRE) and the Topological Extrapolation Transformation Algorithm (TEA). The efficacy of the proposed model is demonstrated through tests conducted on Hyperspectral Images (HI) for denoising, as well as for Hyperspectral Image Linear Unmixing. Numerical experiments are provided to substantiate the effectiveness of the proposed model for both synthetic and real data.