A Bayesian approach to estimating linear mixtures with unknown covariance structure
AbstractIn this paper, we study a new Bayesian approach for the analysis of linearly mixed structures. In particular, we consider the case of hyperspectral images, which have to be decomposed into a collection of distinct spectra, called endmembers, and a set of associated proportions for every pixel in the scene. This problem, often referred to as spectral unmixing, is usually considered on the basis of the linear mixing model (LMM). In unsupervised approaches, the endmember signatures have to be calculated by an endmember extraction algorithm, which generally relies on the supposition that there are pure (unmixed) pixels contained in the image. In practice, this assumption may not hold for highly mixed data and consequently the extracted endmember spectra differ from the true ones. A way out of this dilemma is to consider the problem under the normal compositional model (NCM). Contrary to the LMM, the NCM treats the endmembers as random Gaussian vectors and not as deterministic quantities. Existing Bayesian approaches for estimating the proportions under the NCM are restricted to the case that the covariance matrix of the Gaussian endmembers is a multiple of the identity matrix. The self-evident conclusion is that this model is not suitable when the variance differs from one spectral channel to the other, which is a common phenomenon in practice. In this paper, we first propose a Bayesian strategy for the estimation of the mixing proportions under the assumption of varying variances in the spectral bands. Then we generalize this model to handle the case of a completely unknown covariance structure. For both algorithms, we present Gibbs sampling strategies and compare their performance with other, state of the art, unmixing routines on synthetic as well as on real hyperspectral fluorescence spectroscopy data.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoArticle provided by Taylor and Francis Journals in its journal Journal of Applied Statistics.
Volume (Year): 38 (2011)
Issue (Month): 9 (September)
Contact details of provider:
Web page: http://taylorandfrancis.metapress.com/link.asp?target=journal&id=100411
You can help add them by filling out this form.
CitEc Project, subscribe to its RSS feed for this item.
- Kazianka, Hannes, 2012. "Objective Bayesian analysis for the normal compositional model," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1528-1544.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Michael McNulty).
If references are entirely missing, you can add them using this form.