# A Dictionary-Based Generalization of Robust PCA Part II: Applications to Hyperspectral Demixing

## TL;DR

This paper introduces a novel convex demixing approach for hyperspectral image analysis, leveraging dictionary-based sparse modeling to localize targets with correlated spectral signatures, supported by theoretical guarantees and experimental validation.

## Contribution

It extends robust PCA methods to hyperspectral demixing by modeling spectral signatures as dictionary sparse components, providing new recovery guarantees and practical algorithms.

## Key findings

- Effective target localization in hyperspectral images.
- Outperforms existing methods in classification accuracy.
- Theoretical recovery guarantees established.

## Abstract

We consider the task of localizing targets of interest in a hyperspectral (HS) image based on their spectral signature(s), by posing the problem as two distinct convex demixing task(s). With 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. However, since $\textit{signatures}$ of different materials are often correlated, matched filtering-based approaches may not be apply here. 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, and develop techniques for two different sparsity structures, resulting from different model assumptions. We also present the corresponding recovery guarantees, leveraging our recent theoretical results from a companion paper. Finally, we analyze the performance of the proposed approach via experimental evaluations on real HS datasets for a classification task, and compare its performance with related techniques.