Spatial Low-Rank Tensor Factorization and Unmixing of Hyperspectral Images

William Navas-Auger,Vidya Manian

doi:10.3390/computers10060078

William Navas-Auger, Vidya Manian

Open Access

https://doi.org/10.3390/computers10060078

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Journal: Computers	Publication Date: Jun 11, 2021
Citations: 2	License type: CC BY 4.0

Affiliation: University of Puerto Rico-Mayaguez

Abstract

This work presents a method for hyperspectral image unmixing based on non-negative tensor factorization. While traditional approaches may process spectral information without regard for spatial structures in the dataset, tensor factorization preserves the spectral-spatial relationship which we intend to exploit. We used a rank-(L, L, 1) decomposition, which approximates the original tensor as a sum of R components. Each component is a tensor resulting from the multiplication of a low-rank spatial representation and a spectral vector. Our approach uses spatial factors to identify high abundance areas where pure pixels (endmembers) may lie. Unmixing is done by applying Fully Constrained Least Squares such that abundance maps are produced for each inferred endmember. The results of this method are compared against other approaches based on non-negative matrix and tensor factorization. We observed a significant reduction of spectral angle distance for extracted endmembers and equal or better RMSE for abundance maps as compared with existing benchmarks.

Highlights

One pervasive problem in remote sensing is the identification of materials based on their spectral signature [1]
Both sets see very low variability when the representation has its lowest spectral angle distance (SAD) and The parameter L was set according to Equation (13) and R is set equal to the number of root mean square error (RMSE)
The second best from the benchmark was negative matrix factorizations (NMF)-L1/2 with RMSE of 0.1567 and RMSE of 0.1789

Summary

Introduction

One pervasive problem in remote sensing is the identification of materials based on their spectral signature [1]. When a pixel is recorded by the sensor, it can gather reflected radiation from more than one material or substance. This happens because there may be an insufficient spatial resolution for the sensor to capture individual materials or the substances in question are mixed uniformly. Hyperspectral images (HSI) are three-dimensional data cubes with two spatial dimensions and one spectral dimension with hundreds of bands. In the resulting data set, every pixel is considered an independent sample of the material. This treatment ignores spatial relationships amongst neighboring pixels that could be exploited.

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