Collaborative sparse regression using spatially correlated supports - Application to hyperspectral unmixing

Yoann Altmann, Marcelo Pereyra, Jose Bioucas-Dias

Research output: Contribution to journalArticle (Academic Journal)peer-review

34 Citations (Scopus)
324 Downloads (Pure)


This paper presents a new Bayesian collaborative sparse regression method for
linear unmixing of hyperspectral images. Our contribution is twofold; first, we
propose a new Bayesian model for structured sparse regression in which the
supports of the sparse abundance vectors are a priori spatially correlated
across pixels (i.e., materials are spatially organised rather than randomly
distributed at a pixel level). This prior information is encoded in the model
through a truncated multivariate Ising Markov random field, which also takes
into consideration the facts that pixels cannot be empty (i.e, there is at
least one material present in each pixel), and that different materials may
exhibit different degrees of spatial regularity. Secondly, we propose an
advanced Markov chain Monte Carlo algorithm to estimate the posterior
probabilities that materials are present or absent in each pixel, and,
conditionally to the maximum marginal a posteriori configuration of the
support, compute the MMSE estimates of the abundance vectors. A remarkable
property of this algorithm is that it self-adjusts the values of the parameters
of the Markov random field, thus relieving practitioners from setting
regularisation parameters by cross-validation. The performance of the proposed
methodology is finally demonstrated through a series of experiments with
synthetic and real data and comparisons with other algorithms from the
Original languageEnglish
Pages (from-to)5800-5811
Number of pages12
JournalIEEE Transactions on Image Processing
Issue number12
Publication statusPublished - 7 Oct 2015


  • Collaborative sparse regression
  • spectral unmixing
  • Bayesian estimation
  • Markov random fields
  • Markov chain Monte Carlo methods


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  • 8092 EPSRC D063485

    Nason, G. P.

    1/08/16 → …

    Project: Research

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