A Dictionary-Based Generalization of Robust PCA With Applications to Target Localization in Hyperspectral Imaging

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 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 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.Index Terms-Hyperspectral imaging, Robust-PCA, dictionary sparse, target localization, and remote sensing.

Tensor Robust CUR for Compression and Denoising of Hyperspectral Data

“…Robust PCA (RPCA) algorithms have been used in many remote sensing applications [37], [42]- [45]. Rambhatla et al [43] proposed a dictionary-based RPCA algorithm for target localization in hyperspectral imaging. Liu et al [44] developed a log-based RPCA algorithm to remove noise in hyperspectral images.…”

An iterative coordinate descent algorithm to compute sparse low-rank approximations

“…For interpretability and consistency issues [2], researchers have introduced the sparse principal component analysis (sPCA): PCA with the additional constraint that the singular vectors to compute are sparse, i.e., U p is now sparse and orthonormal. This approach has seen many signal processing applications such as image decomposition and texture segmentation [3], shape encoding in images [4], compressed hyperspectral imaging [5], target localization in hyperspectral imaging [6], and moving object detection in videos [7].…”