Self-dictionary sparse regression for hyperspectral unmixing: Greedy pursuit and pure pixel search are related

Xiao Fu, Wing Kin Ma, Tsung Han Chan, José M. Bioucas-Dias

Research output: Contribution to journalArticlepeer-review

59 Scopus citations


This paper considers a recently emerged hyperspectral unmixing formulation based on sparse regression of a self-dictionary multiple measurement vector (SD-MMV) model, wherein the measured hyperspectral pixels are used as the dictionary. Operating under the pure pixel assumption, this SD-MMV formalism is special in that it allows simultaneous identification of the endmember spectral signatures and the number of endmembers. Previous SD-MMV studies mainly focus on convex relaxations. In this study, we explore the alternative of greedy pursuit, which generally provides efficient and simple algorithms. In particular, we design a greedy SD-MMV algorithm using simultaneous orthogonal matching pursuit. Intriguingly, the proposed greedy algorithm is shown to be closely related to some existing pure pixel search algorithms, especially, the successive projection algorithm (SPA). Thus, a link between SD-MMV and pure pixel search is revealed. We then perform exact recovery analyses, and prove that the proposed greedy algorithm is robust to noise-including its identification of the (unknown) number of endmembers-under a sufficiently low noise level. The identification performance of the proposed greedy algorithm is demonstrated through both synthetic and real-data experiments.

Original languageEnglish (US)
Article number2410763
Pages (from-to)1128-1141
Number of pages14
JournalIEEE Journal on Selected Topics in Signal Processing
Issue number6
StatePublished - Sep 1 2015

Bibliographical note

Publisher Copyright:
© 2007-2012 IEEE.


  • Greedy pursuit
  • hyperspectral unmixing
  • number of endmembers estimation
  • self-dictionary sparse regression


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