Linear spectral unmixing via matrix factorization: Identifiability criteria for sparse abundances

Chia Hsiang Lin, José M. Bioucas Dias

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Citations (Scopus)

Abstract

In hyperspectral unmixing and in many other areas (e.g., chemometrics, topic modeling, archetypal analysis) simplex-structured matrix factorization (SSMF) plays an essential role as suggested by years of research efforts devoted to this theme. Specifically, SSMF factorizes a data matrix into two matrix factors with one factor (i.e., the abundances) constrained to have its columns lying in the unit simplex. SSMF criteria include the well-known Craig's seminal minimum-volume enclosing simplex (MVES), originally proposed for blind hyperspectral unmixing, and the recently introduced maximum-volume inscribed ellipsoid (MVIE). The identifiability analysis of those criteria is essential to understand their fundamental behavior and also to devise effective SSMF algorithms tailored to the specificities of the different application scenarios. Our analysis is motivated by a simple fact taking place in most remotely sensed hyperspectral mixtures: in most pixels, only a subset of the materials is present. This is to say that the abundances exhibit a form of sparsity and thus lie in the boundary of the data simplex. We then derive some elegant sufficient condition, showing that as long as data points are locally well spread, perfect SSMF identifiability of both criteria can be guaranteed.

Original languageEnglish
Title of host publication2018 IEEE International Geoscience and Remote Sensing Symposium, IGARSS 2018 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages6155-6158
Number of pages4
ISBN (Electronic)9781538671504
DOIs
Publication statusPublished - 2018 Oct 31
Event38th Annual IEEE International Geoscience and Remote Sensing Symposium, IGARSS 2018 - Valencia, Spain
Duration: 2018 Jul 222018 Jul 27

Publication series

NameInternational Geoscience and Remote Sensing Symposium (IGARSS)
Volume2018-July

Conference

Conference38th Annual IEEE International Geoscience and Remote Sensing Symposium, IGARSS 2018
CountrySpain
CityValencia
Period18-07-2218-07-27

    Fingerprint

All Science Journal Classification (ASJC) codes

  • Computer Science Applications
  • Earth and Planetary Sciences(all)

Cite this

Lin, C. H., & Bioucas Dias, J. M. (2018). Linear spectral unmixing via matrix factorization: Identifiability criteria for sparse abundances. In 2018 IEEE International Geoscience and Remote Sensing Symposium, IGARSS 2018 - Proceedings (pp. 6155-6158). [8518462] (International Geoscience and Remote Sensing Symposium (IGARSS); Vol. 2018-July). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/IGARSS.2018.8518462