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

Yoann Altmann, Marcelo Pereyra, José Bioucas-Dias

Research output: Contribution to journalArticle

Abstract

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 literature.
Original languageEnglish
Pages (from-to)5800-5811
Number of pages12
JournalIEEE Transactions on Image Processing
Volume24
Issue number12
Early online date7 Oct 2015
DOIs
Publication statusPublished - Dec 2015

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pixel
Markov chain
methodology
material
experiment
parameter

Keywords

  • Collaborative sparse regression
  • Spectral unmixing
  • Bayesian estimation
  • Markov chain Monte Carlo methods

Cite this

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title = "Collaborative sparse regression using spatially correlated supports - Application to hyperspectral unmixing",
abstract = "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 priorispatially 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 pixelscannot 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 orabsent 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, thusrelieving 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 literature.",
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Collaborative sparse regression using spatially correlated supports - Application to hyperspectral unmixing. / Altmann, Yoann; Pereyra, Marcelo; Bioucas-Dias, José .

In: IEEE Transactions on Image Processing, Vol. 24, No. 12, 12.2015, p. 5800-5811 .

Research output: Contribution to journalArticle

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