Skip to main content
SpringerLink
Log in

Reconstructions from Compressive Random Projections of Hyperspectral Imagery

  • Chapter
  • First Online:
Book cover Optical Remote Sensing

Part of the book series: Augmented Vision and Reality ((Augment Vis Real,volume 3))

Abstract

High-dimensional data such as hyperspectral imagery is traditionally acquired in full dimensionality before being reduced in dimension prior to processing. Conventional dimensionality reduction on-board remote devices is often prohibitive due to limited computational resources; on the other hand, integrating random projections directly into signal acquisition offers an alternative to explicit dimensionality reduction without incurring sender-side computational cost. Receiver-side reconstruction of hyperspectral data from such random projections in the form of compressive-projection principal component analysis (CPPCA) as well as compressed sensing (CS) is investigated. Specifically considered are single-task CS algorithms which reconstruct each hyperspectral pixel vector of a dataset independently as well as multi-task CS in which the multiple, possibly correlated hyperspectral pixel vectors are reconstructed simultaneously. These CS strategies are compared to CPPCA reconstruction which also exploits cross-vector correlations. Experimental results on popular AVIRIS datasets reveal that CPPCA outperforms various CS algorithms in terms of both squared-error as well as spectral-angle quality measures while requiring only a fraction of the computational cost.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Dataset subsampling is commonly used to expedite covariance-matrix calculation in traditional applications of PCA, e.g., [19, 20]; we suggest modulo partitioning such as \({\bf X}^{(j)} = \left\{{\bf x}_m \in {\bf X} |(m-1) \hbox{ mod } J = j-1 \right\}\) .

  2. 2.

    http://www.lx.it.pt/mtf/GPSR/

  3. 3.

    http://www.people.ee.duke.edu/lihan/cs/

References

  1. Jolliffe, I.T.: Principal Component Analysis. Springer-Verlag, New York (1986)

    Google Scholar 

  2. Prasad, S., Bruce, L.M.: Limitations of principal component analysis for hyperspectral target recognition. IEEE Geosci. Remote Sens. Lett. 5(4), 625–629 (2008)

    Article  Google Scholar 

  3. Wang, J., Chang, C.-I.: Independent component analysis-based dimensionality reduction with applications in hyperspectral image analysis. IEEE Trans. Geosci. Remote Sens. 44(6), 1586–1600 (2006)

    Article  Google Scholar 

  4. Lennon, L., Mercier, G., Mouchot, M.C., Hubert-Moy, L.: Independent component analysis as a tool for the dimensionality reduction and the representation of hyperspectral images. In: Proceedings of the International Geoscience and Remote Sensing Symposium, vol. 6, Sydney, Australia, July 2001, pp. 2893–2895

    Google Scholar 

  5. Roweis, S.T., Saul, L.K.: Nonlinear dimensionality reduction by locally linear embedding. Science 290(5500), 2323–2326 (2000)

    Article  Google Scholar 

  6. Mohan, A., Sapiro, G., Bosch, E.: Spatially coherent nonlinear dimensionality reduction and segmentation of hyperspectral images. IEEE Geosci. Remote Sens. Lett. 4(2), 206–210 (2007)

    Article  Google Scholar 

  7. Candès, E., Romberg, J., Tao, T.: Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Trans. Inf. Theory 52(2), 489–509 (2006)

    Article  Google Scholar 

  8. Candès, E., Tao, T.: Near-optimal signal recovery from random projections: universal encoding strategies?. IEEE Trans. Inf. Theory 52(12), 5406–5425 (2006)

    Article  Google Scholar 

  9. Donoho, D.L.: Compressed sensing. IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006)

    Article  MathSciNet  Google Scholar 

  10. Candès, E.J., Wakin, M.B.: An introduction to compressive sampling. IEEE Signal Process. Mag. 25(2), 21–30 (2008)

    Article  Google Scholar 

  11. Fowler, J.E.: Compressive-projection principal component analysis for the compression of hyperspectral signatures. In: Storer, J.A., Marcellin, M.W. (eds.), Proceedings of the IEEE Data Compression Conference, Snowbird, UT, March 2008, pp. 83–92

    Google Scholar 

  12. Fowler, J.E.: Compressive-projection principal component analysis and the first eigenvector. In: Storer, J.A., Marcellin, M.W. (eds.), Proceedings of the IEEE Data Compression Conference, Snowbird, UT, March 2009, pp. 223–232

    Google Scholar 

  13. Fowler, J.E.: Compressive-projection principal component analysis. IEEE Trans. Image Process. 18(10), 2230–2242 (2009)

    Article  Google Scholar 

  14. Willett, R.M., Gehm, M.E., Brady, D.J.: Multiscale reconstruction for computational spectral imaging. In: Bouman, C.A., Miller, E.L., Pollak, I. (eds.), Computational Imaging V, Proceedings of SPIE 6498, San Jose, CA, January 2007, p. 64980L

    Google Scholar 

  15. Pitsianis, N.P., Brady, D.J., Portnoy, A., Sun, X., Suleski, T., Fiddy, M.A., Feldman, M.R., TeKolste, R.D.: Compressive imaging sensors. In: Athale, R.A., Zolper, J.C. (eds.), Intelligent Integrated Microsystems, Proceedings of SPIE 6232, Kissimmee, FL, April 2006, p. 62320A

    Google Scholar 

  16. Brady, D.J.: Micro-optics and megapixels. Opt. Photon. News 17(11), 24–29 (2006)

    Article  Google Scholar 

  17. Parlett, B.N.: The Symmetric Eigenvalue Problem. Society for Industrial and Applied Mathematics, Philadelphia (1998)

    MATH  Google Scholar 

  18. Combettes, P.L.: The foundations of set theoretic estimation. Proc. IEEE 81(2), 182–208 (1993)

    Article  Google Scholar 

  19. Penna, B., Tillo, T., Magli, E., Olmo, G.: A new low complexity KLT for lossy hyperspectral data compression. In: Proceedings of the International Geoscience and Remote Sensing Symposium, vol. 7, Denver, CO, August 2006, pp. 3525–3528

    Google Scholar 

  20. Du, Q., Fowler, J.E.: Low-complexity principal component analysis for hyperspectral image compression. Int. J. High Perform. Comput. Appl. 22(4), 438–448 (2008)

    Article  Google Scholar 

  21. Chen, S.S., Donoho, D.L., Saunders, M.A.: Atomic decomposition by basis pursuit. SIAM J. Sci. Comput. 20(1), 33–61 (1998)

    Article  MathSciNet  Google Scholar 

  22. Candès, E., Romberg, J., Tao, T.: Stable signal recovery from incomplete and inaccurate measurements. Commun. Pure Appl. Math. 59(8), 1207–1223 (2006)

    Article  MATH  Google Scholar 

  23. Candès, E., Romberg, J.: ℓ1-magic: Recovery of Sparse Signals via Convex Programming. California Institute of Technology, Pasadena (2005)

    Google Scholar 

  24. Figueiredo, M.A.T., Nowak, R.D., Wright, S.J.: Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems. IEEE J. Sel. Areas Commun. 1(4), 586–597 (2007)

    Google Scholar 

  25. Do, T.T., Gan, L., Nguyen, N., Tran, T.D.: Sparsity adaptive matching pursuit algorithm for practical compressed sensing. In: Proceedings of the 42th Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, California, October 2008, pp. 581–587

    Google Scholar 

  26. Ji, S., Dunson, D., Carin, L.: Multitask compressive sensing. IEEE Trans. Signal Process. 57(1), 92–106 (2009)

    Article  MathSciNet  Google Scholar 

  27. Fornasier, M., Rauhut, H.: Recovery algorithms for vector-valued data with joint sparsity constraints. SIAM J. Numer. Anal. 46(2), 577–613 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  28. Mishali, M., Eldar, Y.C.: Reduce and boost: recovering arbitrary sets of jointly sparse vectors. IEEE Trans. Signal Process. 56(10), 4692–4702 (2008)

    Article  MathSciNet  Google Scholar 

  29. Wipf, D.P., Rao, B.D.: An empirical Bayesian strategy for solving the simultaneous sparse approximation problem. IEEE Trans. Signal Process. 55(7), 3704–3716 (2007)

    Article  MathSciNet  Google Scholar 

  30. Tropp, J.A., Gilbert, A.C., Strauss, M.J.: Algorithms for simultaneous sparse approximation. Part I: greedy pursuit. Signal Process. 86(3), 572–588 (2006)

    Article  MATH  Google Scholar 

  31. Tropp, J.A.: Algorithms for simultaneous sparse approximation. Part II: convex relaxation. Signal Process. 86(3), 589–602 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  32. Ji, S., Xue, Y., Carin, L.: Bayesian compressive sensing. IEEE Trans. Signal Process. 56(6), 2346–2356 (2008)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electrical and Computer Engineering, Geosystems Research Institute, Mississippi State University, Mississippi State, MS, 39762, USA

    James E. Fowler & Qian Du

Authors
  1. James E. Fowler
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Qian Du
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to James E. Fowler .

Editor information

Editors and Affiliations

  1. Geosystems Research Inst., Dept. Electrical & Computer Engineering, Mississippi State University, Mississippi State, 39762, Mississippi, USA

    Saurabh Prasad

  2. Geosystems Research Inst., Dept. Electrical & Computer Engineering, Mississippi State University, Mississippi State, 39762, Mississippi, USA

    Lori M. Bruce

  3. Institut Polytechnique de Grenoble, av. Félix Viallet 46, Grenoble CX 1, 38000, France

    Jocelyn Chanussot

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Fowler, J.E., Du, Q. (2011). Reconstructions from Compressive Random Projections of Hyperspectral Imagery. In: Prasad, S., Bruce, L., Chanussot, J. (eds) Optical Remote Sensing. Augmented Vision and Reality, vol 3. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14212-3_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-14212-3_3

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14211-6

  • Online ISBN: 978-3-642-14212-3

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation