# Target-based Hyperspectral Demixing via Generalized Robust PCA

## TL;DR

This paper introduces a target localization method in hyperspectral images using a generalized robust PCA model that separates the image into low-rank and sparse components based on known spectral signatures, with theoretical guarantees and experimental validation.

## Contribution

It proposes a novel hyperspectral demixing technique leveraging a superposition model with spectral signatures, providing recovery guarantees and demonstrating effectiveness on real data.

## Key findings

- Effective localization of targets based on spectral signatures.
- Theoretical recovery guarantees for the proposed method.
- Superior performance compared to related techniques in experiments.

## Abstract

Localizing targets of interest in a given hyperspectral (HS) image has applications ranging from remote sensing to surveillance. This task of target detection leverages the fact that each material/object possesses its own characteristic spectral response, depending upon its composition. As $\textit{signatures}$ of different materials are often correlated, matched filtering based approaches may not be appropriate in this case. In this work, we present a technique to localize targets of interest based on their spectral signatures. We also present the corresponding recovery guarantees, leveraging our recent theoretical results. To this end, we model a HS image as a superposition of a low-rank component and a dictionary sparse component, wherein the dictionary consists of the $\textit{a priori}$ known characteristic spectral responses of the target we wish to localize. Finally, we analyze the performance of the proposed approach via experimental validation on real HS data for a classification task, and compare it with related techniques.