Abstract

Presented in a three-dimensional structure called a hypercube, hyperspectral imaging suffers from a large volume of data and high computational cost for data analysis. To overcome such drawbacks, principal component analysis (PCA) has been widely applied for feature extraction and dimensionality reduction. However, a severe bottleneck is how to compute the PCA covariance matrix efficiently and avoid computational difficulties, especially when the spatial dimension of the hypercube is large. In this paper, structured covariance PCA (SC-PCA) is proposed for fast computation of the covariance matrix. In line with how spectral data is acquired in either the push-broom or tunable filter method, different implementation schemes of SC-PCA are presented. As the proposed SC-PCA can determine the covariance matrix from partial covariance matrices in parallel even without prior deduction of the mean vector, it facilitates real-time data analysis while the hypercube is acquired. This has significantly reduced the scale of required memory and also allows efficient onsite feature extraction and data reduction to benefit subsequent tasks in coding and compression, transmission, and analytics of hyperspectral data.

© 2014 Optical Society of America

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J. Zabalza, J. Ren, Z. Wang, S. Marshall, and J. Wang, “Singular spectrum analysis for effective feature extraction in hyperspectral imaging,” IEEE Geosci. Remote Sens. Lett. 11, 1886–1890 (2014).
[CrossRef]

J. Zabalza, J. Ren, M. Yang, Y. Zhang, J. Wang, S. Marshall, and J. Han, “Novel folded-PCA for improved feature extraction and data reduction with hyperspectral imaging and SAR in remote sensing,” ISPRS J. Photogr. Remote Sens. 93, 112–122 (2014).
[CrossRef]

J. Ren, J. Zabalza, S. Marshall, and J. Zheng, “Effective feature extraction and data reduction with hyperspectral imaging in remote sensing,” IEEE Signal Process. Mag. 31(4), 149–154 (2014).

2013 (3)

C. C. Chang and C. J. Lin, “LIBSVM: a library for support vector machines,” ACM Trans. Intell. Syst. Technol. 2, 1–27 (2013).

T. Kelman, J. Ren, and S. Marshall, “Effective classification of Chinese tea samples in hyperspectral imaging,” Artific. Intell. Res. 2, 87–96 (2013).

C. Zhao, X. Li, J. Ren, and S. Marshall, “Improved sparse representation using adaptive spatial support for effective target detection in hyperspectral imagery,” Int. J. Remote Sens. 34, 8669–8684 (2013).
[CrossRef]

2012 (1)

R. Jošth, J. Antikainen, J. Havel, A. Herout, P. Zemčík, and M. Hauta-Kasari, “Real-time PCA calculation for spectral imaging (using SIMD and GP-GPU),” J. Real Time Image Proc. 7, 1–9 (2012).

2011 (1)

F. Ndi, F. Adar, and S. H. Atzeni, “Spectral imaging,” Readout 38, 68–73 (2011).

2010 (2)

R. Dianat and S. Kasaei, “Dimension reduction of optical remote sensing images via minimum change rate deviation method,” IEEE Trans. Geosci. Remote Sens. 48, 198–206 (2010).
[CrossRef]

M. Rojas, I. Dópido, A. Plaza, and P. Gamba, “Comparison of support vector machine-based processing chains for hyperspectral image classification,” Proc. SPIE 7810, 78100B (2010).
[CrossRef]

2008 (1)

2007 (1)

2006 (2)

2004 (1)

F. Melgani and L. Bruzzone, “Classification of hyperspectral remote sensing images with support vector machines,” IEEE Trans. Geosci. Remote Sens. 42, 1778–1790 (2004).
[CrossRef]

2003 (1)

J. S. Pearlman, P. S. Barry, C. C. Segal, J. Shepanski, D. Beiso, and S. L. Carman, “Hyperion, a space-based imaging spectrometer,” IEEE Trans. Geosci. Remote Sens. 41, 1160–1173, (2003).
[CrossRef]

1998 (1)

R. O. Green, M. L. Eastwood, C. M. Sarture, T. G. Chrien, M. Aronsson, B. J. Chippendale, J. A. Faust, B. E. Pavri, C. J. Chovit, M. Solis, M. R. Olah, and O. Williams, “Imaging spectroscopy and the airborne visible/infrared imaging spectrometer (AVIRIS),” Remote Sens. Environ. 65, 227–248 (1998).
[CrossRef]

1968 (1)

G. F. Hughes, “On the mean accuracy of statistical pattern recognition,” IEEE Trans. Inf. Theory 14, 55–63 (1968).
[CrossRef]

Abdi, H.

H. Abdi and L. J. Williams, Principal Component Analysis (WIREs Comp Stat, 2010).

Adar, F.

F. Ndi, F. Adar, and S. H. Atzeni, “Spectral imaging,” Readout 38, 68–73 (2011).

Antikainen, J.

R. Jošth, J. Antikainen, J. Havel, A. Herout, P. Zemčík, and M. Hauta-Kasari, “Real-time PCA calculation for spectral imaging (using SIMD and GP-GPU),” J. Real Time Image Proc. 7, 1–9 (2012).

Aronsson, M.

R. O. Green, M. L. Eastwood, C. M. Sarture, T. G. Chrien, M. Aronsson, B. J. Chippendale, J. A. Faust, B. E. Pavri, C. J. Chovit, M. Solis, M. R. Olah, and O. Williams, “Imaging spectroscopy and the airborne visible/infrared imaging spectrometer (AVIRIS),” Remote Sens. Environ. 65, 227–248 (1998).
[CrossRef]

Atzeni, S. H.

F. Ndi, F. Adar, and S. H. Atzeni, “Spectral imaging,” Readout 38, 68–73 (2011).

Barry, P. S.

J. S. Pearlman, P. S. Barry, C. C. Segal, J. Shepanski, D. Beiso, and S. L. Carman, “Hyperion, a space-based imaging spectrometer,” IEEE Trans. Geosci. Remote Sens. 41, 1160–1173, (2003).
[CrossRef]

Beiso, D.

J. S. Pearlman, P. S. Barry, C. C. Segal, J. Shepanski, D. Beiso, and S. L. Carman, “Hyperion, a space-based imaging spectrometer,” IEEE Trans. Geosci. Remote Sens. 41, 1160–1173, (2003).
[CrossRef]

Boreman, G. D.

Bruzzone, L.

F. Melgani and L. Bruzzone, “Classification of hyperspectral remote sensing images with support vector machines,” IEEE Trans. Geosci. Remote Sens. 42, 1778–1790 (2004).
[CrossRef]

Carman, S. L.

J. S. Pearlman, P. S. Barry, C. C. Segal, J. Shepanski, D. Beiso, and S. L. Carman, “Hyperion, a space-based imaging spectrometer,” IEEE Trans. Geosci. Remote Sens. 41, 1160–1173, (2003).
[CrossRef]

Chang, C. C.

C. C. Chang and C. J. Lin, “LIBSVM: a library for support vector machines,” ACM Trans. Intell. Syst. Technol. 2, 1–27 (2013).

Chen, B.-Y.

M.-Z. Wang, D.-M. Wang, W.-X. Xu, B.-Y. Chen, and K. Guo, “Parallel computing of covariance matrix and its application on hyperspectral data process,” in Geoscience and Remote Sensing Symposium (IGARSS), July22–27, 2012, pp. 4058–4061.

Chippendale, B. J.

R. O. Green, M. L. Eastwood, C. M. Sarture, T. G. Chrien, M. Aronsson, B. J. Chippendale, J. A. Faust, B. E. Pavri, C. J. Chovit, M. Solis, M. R. Olah, and O. Williams, “Imaging spectroscopy and the airborne visible/infrared imaging spectrometer (AVIRIS),” Remote Sens. Environ. 65, 227–248 (1998).
[CrossRef]

Chovit, C. J.

R. O. Green, M. L. Eastwood, C. M. Sarture, T. G. Chrien, M. Aronsson, B. J. Chippendale, J. A. Faust, B. E. Pavri, C. J. Chovit, M. Solis, M. R. Olah, and O. Williams, “Imaging spectroscopy and the airborne visible/infrared imaging spectrometer (AVIRIS),” Remote Sens. Environ. 65, 227–248 (1998).
[CrossRef]

Chrien, T. G.

R. O. Green, M. L. Eastwood, C. M. Sarture, T. G. Chrien, M. Aronsson, B. J. Chippendale, J. A. Faust, B. E. Pavri, C. J. Chovit, M. Solis, M. R. Olah, and O. Williams, “Imaging spectroscopy and the airborne visible/infrared imaging spectrometer (AVIRIS),” Remote Sens. Environ. 65, 227–248 (1998).
[CrossRef]

Craig, S. E.

Dianat, R.

R. Dianat and S. Kasaei, “Dimension reduction of optical remote sensing images via minimum change rate deviation method,” IEEE Trans. Geosci. Remote Sens. 48, 198–206 (2010).
[CrossRef]

Dópido, I.

M. Rojas, I. Dópido, A. Plaza, and P. Gamba, “Comparison of support vector machine-based processing chains for hyperspectral image classification,” Proc. SPIE 7810, 78100B (2010).
[CrossRef]

Du Bosq, T. W.

Eastwood, M. L.

R. O. Green, M. L. Eastwood, C. M. Sarture, T. G. Chrien, M. Aronsson, B. J. Chippendale, J. A. Faust, B. E. Pavri, C. J. Chovit, M. Solis, M. R. Olah, and O. Williams, “Imaging spectroscopy and the airborne visible/infrared imaging spectrometer (AVIRIS),” Remote Sens. Environ. 65, 227–248 (1998).
[CrossRef]

Faust, J. A.

R. O. Green, M. L. Eastwood, C. M. Sarture, T. G. Chrien, M. Aronsson, B. J. Chippendale, J. A. Faust, B. E. Pavri, C. J. Chovit, M. Solis, M. R. Olah, and O. Williams, “Imaging spectroscopy and the airborne visible/infrared imaging spectrometer (AVIRIS),” Remote Sens. Environ. 65, 227–248 (1998).
[CrossRef]

Gamba, P.

M. Rojas, I. Dópido, A. Plaza, and P. Gamba, “Comparison of support vector machine-based processing chains for hyperspectral image classification,” Proc. SPIE 7810, 78100B (2010).
[CrossRef]

Gilchrist, J.

K. Gill, J. Ren, S. Marshall, S. Karthick, and J. Gilchrist, “Quality-assured fingerprint image enhancement and extraction using hyperspectral imaging,” in 4th International Conference on Imaging for Crime Detection and Prevention, London (2011).

Gill, K.

K. Gill, J. Ren, S. Marshall, S. Karthick, and J. Gilchrist, “Quality-assured fingerprint image enhancement and extraction using hyperspectral imaging,” in 4th International Conference on Imaging for Crime Detection and Prevention, London (2011).

Green, R. O.

R. O. Green, M. L. Eastwood, C. M. Sarture, T. G. Chrien, M. Aronsson, B. J. Chippendale, J. A. Faust, B. E. Pavri, C. J. Chovit, M. Solis, M. R. Olah, and O. Williams, “Imaging spectroscopy and the airborne visible/infrared imaging spectrometer (AVIRIS),” Remote Sens. Environ. 65, 227–248 (1998).
[CrossRef]

Guo, K.

M.-Z. Wang, D.-M. Wang, W.-X. Xu, B.-Y. Chen, and K. Guo, “Parallel computing of covariance matrix and its application on hyperspectral data process,” in Geoscience and Remote Sensing Symposium (IGARSS), July22–27, 2012, pp. 4058–4061.

Habermeyer, M.

S. Holzwarth, A. Müller, M. Habermeyer, R. Richter, A. Hausold, S. Thiemann, and P. Strohl, “HySens-DAIS 7915/ROSIS imaging spectrometers at DLR,” in Proceedings of the 3rd Earsel Workshop on Imaging Spectroscopy, Herrsching, Germany, May13–16, 2003, pp. 3–14.

Han, J.

J. Zabalza, J. Ren, M. Yang, Y. Zhang, J. Wang, S. Marshall, and J. Han, “Novel folded-PCA for improved feature extraction and data reduction with hyperspectral imaging and SAR in remote sensing,” ISPRS J. Photogr. Remote Sens. 93, 112–122 (2014).
[CrossRef]

Hausold, A.

S. Holzwarth, A. Müller, M. Habermeyer, R. Richter, A. Hausold, S. Thiemann, and P. Strohl, “HySens-DAIS 7915/ROSIS imaging spectrometers at DLR,” in Proceedings of the 3rd Earsel Workshop on Imaging Spectroscopy, Herrsching, Germany, May13–16, 2003, pp. 3–14.

Hauta-Kasari, M.

R. Jošth, J. Antikainen, J. Havel, A. Herout, P. Zemčík, and M. Hauta-Kasari, “Real-time PCA calculation for spectral imaging (using SIMD and GP-GPU),” J. Real Time Image Proc. 7, 1–9 (2012).

Havel, J.

R. Jošth, J. Antikainen, J. Havel, A. Herout, P. Zemčík, and M. Hauta-Kasari, “Real-time PCA calculation for spectral imaging (using SIMD and GP-GPU),” J. Real Time Image Proc. 7, 1–9 (2012).

Herout, A.

R. Jošth, J. Antikainen, J. Havel, A. Herout, P. Zemčík, and M. Hauta-Kasari, “Real-time PCA calculation for spectral imaging (using SIMD and GP-GPU),” J. Real Time Image Proc. 7, 1–9 (2012).

Holzwarth, S.

S. Holzwarth, A. Müller, M. Habermeyer, R. Richter, A. Hausold, S. Thiemann, and P. Strohl, “HySens-DAIS 7915/ROSIS imaging spectrometers at DLR,” in Proceedings of the 3rd Earsel Workshop on Imaging Spectroscopy, Herrsching, Germany, May13–16, 2003, pp. 3–14.

Hughes, G. F.

G. F. Hughes, “On the mean accuracy of statistical pattern recognition,” IEEE Trans. Inf. Theory 14, 55–63 (1968).
[CrossRef]

Intaravanne, Y.

Jošth, R.

R. Jošth, J. Antikainen, J. Havel, A. Herout, P. Zemčík, and M. Hauta-Kasari, “Real-time PCA calculation for spectral imaging (using SIMD and GP-GPU),” J. Real Time Image Proc. 7, 1–9 (2012).

Karthick, S.

K. Gill, J. Ren, S. Marshall, S. Karthick, and J. Gilchrist, “Quality-assured fingerprint image enhancement and extraction using hyperspectral imaging,” in 4th International Conference on Imaging for Crime Detection and Prevention, London (2011).

Kasaei, S.

R. Dianat and S. Kasaei, “Dimension reduction of optical remote sensing images via minimum change rate deviation method,” IEEE Trans. Geosci. Remote Sens. 48, 198–206 (2010).
[CrossRef]

Kelman, T.

T. Kelman, J. Ren, and S. Marshall, “Effective classification of Chinese tea samples in hyperspectral imaging,” Artific. Intell. Res. 2, 87–96 (2013).

Kirkpatrick, G. J.

Lee, Z.

Li, Q.-L.

Li, X.

C. Zhao, X. Li, J. Ren, and S. Marshall, “Improved sparse representation using adaptive spatial support for effective target detection in hyperspectral imagery,” Int. J. Remote Sens. 34, 8669–8684 (2013).
[CrossRef]

Lin, C. J.

C. C. Chang and C. J. Lin, “LIBSVM: a library for support vector machines,” ACM Trans. Intell. Syst. Technol. 2, 1–27 (2013).

Liu, Z.

Lohrenz, S. E.

Lopez-Alonso, J. M.

Mahoney, K. L.

Marshall, S.

J. Zabalza, J. Ren, Z. Wang, S. Marshall, and J. Wang, “Singular spectrum analysis for effective feature extraction in hyperspectral imaging,” IEEE Geosci. Remote Sens. Lett. 11, 1886–1890 (2014).
[CrossRef]

J. Ren, J. Zabalza, S. Marshall, and J. Zheng, “Effective feature extraction and data reduction with hyperspectral imaging in remote sensing,” IEEE Signal Process. Mag. 31(4), 149–154 (2014).

J. Zabalza, J. Ren, M. Yang, Y. Zhang, J. Wang, S. Marshall, and J. Han, “Novel folded-PCA for improved feature extraction and data reduction with hyperspectral imaging and SAR in remote sensing,” ISPRS J. Photogr. Remote Sens. 93, 112–122 (2014).
[CrossRef]

C. Zhao, X. Li, J. Ren, and S. Marshall, “Improved sparse representation using adaptive spatial support for effective target detection in hyperspectral imagery,” Int. J. Remote Sens. 34, 8669–8684 (2013).
[CrossRef]

T. Kelman, J. Ren, and S. Marshall, “Effective classification of Chinese tea samples in hyperspectral imaging,” Artific. Intell. Res. 2, 87–96 (2013).

K. Gill, J. Ren, S. Marshall, S. Karthick, and J. Gilchrist, “Quality-assured fingerprint image enhancement and extraction using hyperspectral imaging,” in 4th International Conference on Imaging for Crime Detection and Prevention, London (2011).

Melgani, F.

F. Melgani and L. Bruzzone, “Classification of hyperspectral remote sensing images with support vector machines,” IEEE Trans. Geosci. Remote Sens. 42, 1778–1790 (2004).
[CrossRef]

Müller, A.

S. Holzwarth, A. Müller, M. Habermeyer, R. Richter, A. Hausold, S. Thiemann, and P. Strohl, “HySens-DAIS 7915/ROSIS imaging spectrometers at DLR,” in Proceedings of the 3rd Earsel Workshop on Imaging Spectroscopy, Herrsching, Germany, May13–16, 2003, pp. 3–14.

Ndi, F.

F. Ndi, F. Adar, and S. H. Atzeni, “Spectral imaging,” Readout 38, 68–73 (2011).

Olah, M. R.

R. O. Green, M. L. Eastwood, C. M. Sarture, T. G. Chrien, M. Aronsson, B. J. Chippendale, J. A. Faust, B. E. Pavri, C. J. Chovit, M. Solis, M. R. Olah, and O. Williams, “Imaging spectroscopy and the airborne visible/infrared imaging spectrometer (AVIRIS),” Remote Sens. Environ. 65, 227–248 (1998).
[CrossRef]

Pavri, B. E.

R. O. Green, M. L. Eastwood, C. M. Sarture, T. G. Chrien, M. Aronsson, B. J. Chippendale, J. A. Faust, B. E. Pavri, C. J. Chovit, M. Solis, M. R. Olah, and O. Williams, “Imaging spectroscopy and the airborne visible/infrared imaging spectrometer (AVIRIS),” Remote Sens. Environ. 65, 227–248 (1998).
[CrossRef]

Pearlman, J. S.

J. S. Pearlman, P. S. Barry, C. C. Segal, J. Shepanski, D. Beiso, and S. L. Carman, “Hyperion, a space-based imaging spectrometer,” IEEE Trans. Geosci. Remote Sens. 41, 1160–1173, (2003).
[CrossRef]

Plaza, A.

M. Rojas, I. Dópido, A. Plaza, and P. Gamba, “Comparison of support vector machine-based processing chains for hyperspectral image classification,” Proc. SPIE 7810, 78100B (2010).
[CrossRef]

Ren, J.

J. Zabalza, J. Ren, Z. Wang, S. Marshall, and J. Wang, “Singular spectrum analysis for effective feature extraction in hyperspectral imaging,” IEEE Geosci. Remote Sens. Lett. 11, 1886–1890 (2014).
[CrossRef]

J. Zabalza, J. Ren, M. Yang, Y. Zhang, J. Wang, S. Marshall, and J. Han, “Novel folded-PCA for improved feature extraction and data reduction with hyperspectral imaging and SAR in remote sensing,” ISPRS J. Photogr. Remote Sens. 93, 112–122 (2014).
[CrossRef]

J. Ren, J. Zabalza, S. Marshall, and J. Zheng, “Effective feature extraction and data reduction with hyperspectral imaging in remote sensing,” IEEE Signal Process. Mag. 31(4), 149–154 (2014).

T. Kelman, J. Ren, and S. Marshall, “Effective classification of Chinese tea samples in hyperspectral imaging,” Artific. Intell. Res. 2, 87–96 (2013).

C. Zhao, X. Li, J. Ren, and S. Marshall, “Improved sparse representation using adaptive spatial support for effective target detection in hyperspectral imagery,” Int. J. Remote Sens. 34, 8669–8684 (2013).
[CrossRef]

K. Gill, J. Ren, S. Marshall, S. Karthick, and J. Gilchrist, “Quality-assured fingerprint image enhancement and extraction using hyperspectral imaging,” in 4th International Conference on Imaging for Crime Detection and Prevention, London (2011).

Richter, R.

S. Holzwarth, A. Müller, M. Habermeyer, R. Richter, A. Hausold, S. Thiemann, and P. Strohl, “HySens-DAIS 7915/ROSIS imaging spectrometers at DLR,” in Proceedings of the 3rd Earsel Workshop on Imaging Spectroscopy, Herrsching, Germany, May13–16, 2003, pp. 3–14.

Rojas, M.

M. Rojas, I. Dópido, A. Plaza, and P. Gamba, “Comparison of support vector machine-based processing chains for hyperspectral image classification,” Proc. SPIE 7810, 78100B (2010).
[CrossRef]

Sarture, C. M.

R. O. Green, M. L. Eastwood, C. M. Sarture, T. G. Chrien, M. Aronsson, B. J. Chippendale, J. A. Faust, B. E. Pavri, C. J. Chovit, M. Solis, M. R. Olah, and O. Williams, “Imaging spectroscopy and the airborne visible/infrared imaging spectrometer (AVIRIS),” Remote Sens. Environ. 65, 227–248 (1998).
[CrossRef]

Schofield, O. M.

Segal, C. C.

J. S. Pearlman, P. S. Barry, C. C. Segal, J. Shepanski, D. Beiso, and S. L. Carman, “Hyperion, a space-based imaging spectrometer,” IEEE Trans. Geosci. Remote Sens. 41, 1160–1173, (2003).
[CrossRef]

Shepanski, J.

J. S. Pearlman, P. S. Barry, C. C. Segal, J. Shepanski, D. Beiso, and S. L. Carman, “Hyperion, a space-based imaging spectrometer,” IEEE Trans. Geosci. Remote Sens. 41, 1160–1173, (2003).
[CrossRef]

Solis, M.

R. O. Green, M. L. Eastwood, C. M. Sarture, T. G. Chrien, M. Aronsson, B. J. Chippendale, J. A. Faust, B. E. Pavri, C. J. Chovit, M. Solis, M. R. Olah, and O. Williams, “Imaging spectroscopy and the airborne visible/infrared imaging spectrometer (AVIRIS),” Remote Sens. Environ. 65, 227–248 (1998).
[CrossRef]

Steward, R. G.

Strohl, P.

S. Holzwarth, A. Müller, M. Habermeyer, R. Richter, A. Hausold, S. Thiemann, and P. Strohl, “HySens-DAIS 7915/ROSIS imaging spectrometers at DLR,” in Proceedings of the 3rd Earsel Workshop on Imaging Spectroscopy, Herrsching, Germany, May13–16, 2003, pp. 3–14.

Sumriddetchkajorn, S.

Thiemann, S.

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F. Vagni, “Survey of hyperspectral and multispectral imaging technologies,” , 2007.

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M.-Z. Wang, D.-M. Wang, W.-X. Xu, B.-Y. Chen, and K. Guo, “Parallel computing of covariance matrix and its application on hyperspectral data process,” in Geoscience and Remote Sensing Symposium (IGARSS), July22–27, 2012, pp. 4058–4061.

Wang, J.

J. Zabalza, J. Ren, Z. Wang, S. Marshall, and J. Wang, “Singular spectrum analysis for effective feature extraction in hyperspectral imaging,” IEEE Geosci. Remote Sens. Lett. 11, 1886–1890 (2014).
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J. Zabalza, J. Ren, M. Yang, Y. Zhang, J. Wang, S. Marshall, and J. Han, “Novel folded-PCA for improved feature extraction and data reduction with hyperspectral imaging and SAR in remote sensing,” ISPRS J. Photogr. Remote Sens. 93, 112–122 (2014).
[CrossRef]

Wang, M.-Z.

M.-Z. Wang, D.-M. Wang, W.-X. Xu, B.-Y. Chen, and K. Guo, “Parallel computing of covariance matrix and its application on hyperspectral data process,” in Geoscience and Remote Sensing Symposium (IGARSS), July22–27, 2012, pp. 4058–4061.

Wang, Z.

J. Zabalza, J. Ren, Z. Wang, S. Marshall, and J. Wang, “Singular spectrum analysis for effective feature extraction in hyperspectral imaging,” IEEE Geosci. Remote Sens. Lett. 11, 1886–1890 (2014).
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Williams, O.

R. O. Green, M. L. Eastwood, C. M. Sarture, T. G. Chrien, M. Aronsson, B. J. Chippendale, J. A. Faust, B. E. Pavri, C. J. Chovit, M. Solis, M. R. Olah, and O. Williams, “Imaging spectroscopy and the airborne visible/infrared imaging spectrometer (AVIRIS),” Remote Sens. Environ. 65, 227–248 (1998).
[CrossRef]

Xu, W.-X.

M.-Z. Wang, D.-M. Wang, W.-X. Xu, B.-Y. Chen, and K. Guo, “Parallel computing of covariance matrix and its application on hyperspectral data process,” in Geoscience and Remote Sensing Symposium (IGARSS), July22–27, 2012, pp. 4058–4061.

Yan, J.

Yang, M.

J. Zabalza, J. Ren, M. Yang, Y. Zhang, J. Wang, S. Marshall, and J. Han, “Novel folded-PCA for improved feature extraction and data reduction with hyperspectral imaging and SAR in remote sensing,” ISPRS J. Photogr. Remote Sens. 93, 112–122 (2014).
[CrossRef]

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J. Ren, J. Zabalza, S. Marshall, and J. Zheng, “Effective feature extraction and data reduction with hyperspectral imaging in remote sensing,” IEEE Signal Process. Mag. 31(4), 149–154 (2014).

J. Zabalza, J. Ren, M. Yang, Y. Zhang, J. Wang, S. Marshall, and J. Han, “Novel folded-PCA for improved feature extraction and data reduction with hyperspectral imaging and SAR in remote sensing,” ISPRS J. Photogr. Remote Sens. 93, 112–122 (2014).
[CrossRef]

J. Zabalza, J. Ren, Z. Wang, S. Marshall, and J. Wang, “Singular spectrum analysis for effective feature extraction in hyperspectral imaging,” IEEE Geosci. Remote Sens. Lett. 11, 1886–1890 (2014).
[CrossRef]

Zemcík, P.

R. Jošth, J. Antikainen, J. Havel, A. Herout, P. Zemčík, and M. Hauta-Kasari, “Real-time PCA calculation for spectral imaging (using SIMD and GP-GPU),” J. Real Time Image Proc. 7, 1–9 (2012).

Zhang, D.

Zhang, Y.

J. Zabalza, J. Ren, M. Yang, Y. Zhang, J. Wang, S. Marshall, and J. Han, “Novel folded-PCA for improved feature extraction and data reduction with hyperspectral imaging and SAR in remote sensing,” ISPRS J. Photogr. Remote Sens. 93, 112–122 (2014).
[CrossRef]

Zhao, C.

C. Zhao, X. Li, J. Ren, and S. Marshall, “Improved sparse representation using adaptive spatial support for effective target detection in hyperspectral imagery,” Int. J. Remote Sens. 34, 8669–8684 (2013).
[CrossRef]

Zheng, J.

J. Ren, J. Zabalza, S. Marshall, and J. Zheng, “Effective feature extraction and data reduction with hyperspectral imaging in remote sensing,” IEEE Signal Process. Mag. 31(4), 149–154 (2014).

ACM Trans. Intell. Syst. Technol. (1)

C. C. Chang and C. J. Lin, “LIBSVM: a library for support vector machines,” ACM Trans. Intell. Syst. Technol. 2, 1–27 (2013).

Appl. Opt. (4)

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T. Kelman, J. Ren, and S. Marshall, “Effective classification of Chinese tea samples in hyperspectral imaging,” Artific. Intell. Res. 2, 87–96 (2013).

IEEE Geosci. Remote Sens. Lett. (1)

J. Zabalza, J. Ren, Z. Wang, S. Marshall, and J. Wang, “Singular spectrum analysis for effective feature extraction in hyperspectral imaging,” IEEE Geosci. Remote Sens. Lett. 11, 1886–1890 (2014).
[CrossRef]

IEEE Signal Process. Mag. (1)

J. Ren, J. Zabalza, S. Marshall, and J. Zheng, “Effective feature extraction and data reduction with hyperspectral imaging in remote sensing,” IEEE Signal Process. Mag. 31(4), 149–154 (2014).

IEEE Trans. Geosci. Remote Sens. (3)

R. Dianat and S. Kasaei, “Dimension reduction of optical remote sensing images via minimum change rate deviation method,” IEEE Trans. Geosci. Remote Sens. 48, 198–206 (2010).
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F. Melgani and L. Bruzzone, “Classification of hyperspectral remote sensing images with support vector machines,” IEEE Trans. Geosci. Remote Sens. 42, 1778–1790 (2004).
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J. S. Pearlman, P. S. Barry, C. C. Segal, J. Shepanski, D. Beiso, and S. L. Carman, “Hyperion, a space-based imaging spectrometer,” IEEE Trans. Geosci. Remote Sens. 41, 1160–1173, (2003).
[CrossRef]

IEEE Trans. Inf. Theory (1)

G. F. Hughes, “On the mean accuracy of statistical pattern recognition,” IEEE Trans. Inf. Theory 14, 55–63 (1968).
[CrossRef]

Int. J. Remote Sens. (1)

C. Zhao, X. Li, J. Ren, and S. Marshall, “Improved sparse representation using adaptive spatial support for effective target detection in hyperspectral imagery,” Int. J. Remote Sens. 34, 8669–8684 (2013).
[CrossRef]

ISPRS J. Photogr. Remote Sens. (1)

J. Zabalza, J. Ren, M. Yang, Y. Zhang, J. Wang, S. Marshall, and J. Han, “Novel folded-PCA for improved feature extraction and data reduction with hyperspectral imaging and SAR in remote sensing,” ISPRS J. Photogr. Remote Sens. 93, 112–122 (2014).
[CrossRef]

J. Real Time Image Proc. (1)

R. Jošth, J. Antikainen, J. Havel, A. Herout, P. Zemčík, and M. Hauta-Kasari, “Real-time PCA calculation for spectral imaging (using SIMD and GP-GPU),” J. Real Time Image Proc. 7, 1–9 (2012).

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M. Rojas, I. Dópido, A. Plaza, and P. Gamba, “Comparison of support vector machine-based processing chains for hyperspectral image classification,” Proc. SPIE 7810, 78100B (2010).
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F. Ndi, F. Adar, and S. H. Atzeni, “Spectral imaging,” Readout 38, 68–73 (2011).

Remote Sens. Environ. (1)

R. O. Green, M. L. Eastwood, C. M. Sarture, T. G. Chrien, M. Aronsson, B. J. Chippendale, J. A. Faust, B. E. Pavri, C. J. Chovit, M. Solis, M. R. Olah, and O. Williams, “Imaging spectroscopy and the airborne visible/infrared imaging spectrometer (AVIRIS),” Remote Sens. Environ. 65, 227–248 (1998).
[CrossRef]

Other (6)

S. Holzwarth, A. Müller, M. Habermeyer, R. Richter, A. Hausold, S. Thiemann, and P. Strohl, “HySens-DAIS 7915/ROSIS imaging spectrometers at DLR,” in Proceedings of the 3rd Earsel Workshop on Imaging Spectroscopy, Herrsching, Germany, May13–16, 2003, pp. 3–14.

M.-Z. Wang, D.-M. Wang, W.-X. Xu, B.-Y. Chen, and K. Guo, “Parallel computing of covariance matrix and its application on hyperspectral data process,” in Geoscience and Remote Sensing Symposium (IGARSS), July22–27, 2012, pp. 4058–4061.

“Hyperspectral remote sensing scenes,” 2014, http://www.ehu.es/ccwintco/index.php/Hyperspectral_Remote_Sensing_Scenes .

F. Vagni, “Survey of hyperspectral and multispectral imaging technologies,” , 2007.

H. Abdi and L. J. Williams, Principal Component Analysis (WIREs Comp Stat, 2010).

K. Gill, J. Ren, S. Marshall, S. Karthick, and J. Gilchrist, “Quality-assured fingerprint image enhancement and extraction using hyperspectral imaging,” in 4th International Conference on Imaging for Crime Detection and Prevention, London (2011).

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Figures (10)

Fig. 1.
Fig. 1.

3D hypercube in HSI.

Fig. 2.
Fig. 2.

Optic scheme for (a) scanning methods and (b) tunable filter.

Fig. 3.
Fig. 3.

Different techniques in acquiring a 3D hypercube.

Fig. 4.
Fig. 4.

Data matrix in conventional PCA.

Fig. 5.
Fig. 5.

Comparison between the conventional PCA and the proposed approaches with SC-PCA from the HSI hypercube in determining the covariance matrix.

Fig. 6.
Fig. 6.

One band image at a wavelength of 667 nm (left) and the ground truth maps (right) for the Indian Pines data set.

Fig. 7.
Fig. 7.

One band image at a wavelength of 521 nm (left) and the ground truth maps (right) for the Pavia UA data set.

Fig. 8.
Fig. 8.

One band image at a wavelength of 671 nm (top) and the ground truth maps (bottom) for the Botswana A data set.

Fig. 9.
Fig. 9.

Classification rate (%) using 1–10 components extracted for the three data sets.

Fig. 10.
Fig. 10.

Approximated running time (ms) in the covariance matrix computation for the three data sets after acquisition is completed (red line).

Tables (5)

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Table 1. Symbols, Notations and Major Equations Used in Conventional PCA and the Proposed SC-PCA

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Table 2. Means and Standard Deviations of the Classification Rate (%) for the Three Data Sets with 10 Principal Components

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Table 3. Matrix Sizes and Memory Requirements (kB) in the Covariance Matrix Computation for the Three Data Sets

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Table 4. Number of Multiplications and Additions in the Covariance Matrix Computation for Conventional PCA and the SC-PCA Schemes When Applied on the Whole Hypercube

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Table 5. Number of Multiplications and Additions in the Covariance Matrix Computation for the Proposed SC-PCA Schemes Distributed in the Acquisition Process

Equations (26)

Equations on this page are rendered with MathJax. Learn more.

x¯=1HWn=1HWxn.
pn=xnx¯n[1,HW],
C=E{(xnE{xn})(xnE{xn})T}=E{pnpnT}=PPT,
C(pixel)=n=1HWCn(pixel),Cn(pixel)=pnpnT.
Ph(R)=[phph+Hph+(W1)H]B×W.
C(Row)=h=1HCh(Row),Ch(Row)=Ph(R)[Ph(R)]T,
Pw(C)=[p1+H(w1)p2+H(w1)pH+H(w1)]B×H.
C(Col)=w=1WCw(Col),Cw(Col)=Pw(C)[Pw(C)]T,
Pb(B)=[p1(b)pH(W1)+1(b)pH(b)pHW(b)].
C(Band)(i,j)=vec(Pb=i(B))[vec(Pb=j(B))]T,
pnpnT=xnxnT+Mn(pixel)Mn(pixel)=x¯x¯Txnx¯Tx¯xnT,
pn(i)pn(j)=(xn(i)x¯(i))(xn(j)x¯(j))=xn(i)xn(j)+x¯(i)x¯(j)xn(i)x¯(j)x¯(i)xn(j).
C(pixel)=n=1HWxnxnT+n=1HWMn(pixel).
Ph(R)[Ph(R)]T=Xh(R)[Xh(R)]T+Mh(R)Mh(R)=x¯x¯TXh(R)[x¯x¯]B×WT[x¯x¯]B×W[Xh(R)]T,
C(Row)=h=1HXh(R)[Xh(R)]T+h=1HMh(R).
Pw(C)[Pw(C)]T=Xw(C)[Xw(C)]T+Mw(C)Mw(C)=x¯x¯TXw(C)[x¯x¯]B×HT[x¯x¯]B×H[Xw(C)]T,
C(Col)=w=1WXw(C)[Xw(C)]T+w=1WMw(C).
CM=n=1HWMn(pixel)=h=1HMh(R)=w=1WMw(C)=n=1HW[x¯x¯Txnx¯Tx¯xnT].
CM(i,j)=n=1HWx¯(i)x¯(j)n=1HWxn(i)x¯(j)n=1HWx¯(i)xn(j)=HW(x¯(i)x¯(j))x¯(j)n=1HWxn(i)x¯(i)n=1HWxn(j),
x¯(j)HW1HWn=1HWxn(i)=x¯(j)HWx¯(i)x¯(i)HW1HWn=1HWxn(j)=x¯(i)HWx¯(j).
CM(i,j)=HWx¯(i)x¯(j).
CM(i,j)=1HWn=1HWxn(i)n=1HWxn(j).
C(pixel)=n=1HWxnxnT+CMC(Row)=h=1HXh(R)[Xh(R)]T+CMC(Col)=w=1WXw(C)[Xw(C)]T+CM.
C(i,j)=n=1HWpn(i)pn(j).
Cn(pixel)=pnpnT=[pn(1)pn(1)pn(1)pn(B)pn(B)pn(1)pn(B)pn(B)]B×B.
C(pixel)=n=1HWCn(pixel)=[n=1HWpn(1)pn(1)n=1HWpn(1)pn(B)n=1HWpn(B)pn(1)n=1HWpn(B)pn(B)]B×B.

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