Abstract
Recently, sparsity and morphological diversity have emerged as a new and effective source of diversity for Blind Source Separation giving rise to novel methods such as Generalized Morphological Component Analysis. The latter takes advantage of the very sparse representation of structured data in large overcomplete dictionaries, to separate sources based on their morphology. Building on GMCA, the purpose of this contribution is to describe a new algorithm for hyperspectral data processing. It assumes the collected data exhibits sparse spectral signatures in addition to sparse spatial morphologies, in specified dictionaries of spectral and spatial waveforms. Numerical experiments are reported which demonstrate the validity of the proposed extension.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Blumensath, T., Davies, M.: Iterative thresholding for sparse approximations. Journal of Fourier Analysis and Applications (submitted, 2007)
Bobin, J., Starck, J.-L., Fadili, J., Moudden, Y., Donoho, D.L.: Morphological Component Analysis: An Adaptive Thresholding Strategy. IEEE Trans. On Image Processing 16(11), 2675 (2007)
Bobin, J., Starck, J.-L., Fadili, M.J., Moudden, Y.: Sparsity and morphological diversity in blind source separation. IEEE Transactions on Image Processing 16(11), 2662 (2007)
Bobin, J., Starck, J.-L., Moudden, Y., Fadili, J.: Blind Source Separation: the Sparsity Revolution. Advances in Imaging and Electron Physics (2008)
Chaux, C., Combettes, P.L., Pesquet, J.-C., Wajs, V.R.: A variational formulation for frame based inverse problems. inverse problems 23, 1495–1518 (2007)
Combettes, P.L., Wajs, V.R.: Signal recovery by proximal forward-backward splitting. SIAM Journal on Multiscale Modeling and Simulation 4(4), 1168–1200 (2005)
Donoho, D.L., Elad, M.: Optimally sparse representation in general (non-orthogonal) dictionaries via ℓ1 minimization. Proc. Nat. Aca. Sci. 100, 2197–2202 (2003)
Hyvarinen, A., Karthikesh, R.: Imposing sparsity on the mixing matrix in independent component analysis. Neurocomputing 49, 151–162 (2002)
Moussaoui, S., Hauksdottir, H., Schmidt, F., Jutten, C., Chanussot, J., Brie, D., Douté, S., Benediktsson, J.A.: On the decomposition of Mars hyperspectral data by ICA and Bayesian positive source separation. Neurocomputing (in press, 2008)
Rubinstein, R., Zibulevsky, M., Elad, M.: Sparsity, take 2: Accelerating sparse-coding techniques using sparse dictionaries (submitted, 2008)
Starck, J.-L., Candès, E.J., Donoho, D.L.: The curvelet transform for image denoising. IEEE Transactions on Image Processing 11(6), 670–684 (2002)
Stone, J.V., Porrill, J., Porter, N.R., Wilkinson, I.W.: Spatiotemporal Independent Component Analysis of Event-Related fMRI Data Using Skewed Probability Density Functions. NeuroImage 15(2), 407–421 (2002)
Tseng, P.: Convergence of a block coordinate descent method for nondifferentiable minimizations. J. of Optim. Theory and Appl. 109(3), 457–494 (2001)
Zhang, Z., Zha, H., Simon, H.: Low-rank approximations with sparse factors I: Basic algorithms and error analysis. SIAM Journal on Matrix Analysis and Applications 23(3), 706–727 (2002)
Zibulevsky, M., Pearlmutter, B.A.: Blind source separation by sparse decomposition in a signal dictionary. Neural Computation 13, 863–882 (2001)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Moudden, Y., Bobin, J., Starck, JL., Fadili, J. (2009). Blind Source Separation with Spatio-Spectral Sparsity Constraints – Application to Hyperspectral Data Analysis. In: Adali, T., Jutten, C., Romano, J.M.T., Barros, A.K. (eds) Independent Component Analysis and Signal Separation. ICA 2009. Lecture Notes in Computer Science, vol 5441. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00599-2_66
Download citation
DOI: https://doi.org/10.1007/978-3-642-00599-2_66
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-00598-5
Online ISBN: 978-3-642-00599-2
eBook Packages: Computer ScienceComputer Science (R0)