Abstract

We present a novel compressive spectral imaging technique that attains spatially resolved ultraspectral resolution. The technique employs a multiscale sampling technique based on the Hadamard basis for the single pixel hyperspectral imager. The proposed multiscale sampling method offers high-quality images at a low compression ratio while also facilitating a preview image at a lower resolution by using the fast Hadamard transform.

© 2019 Optical Society of America

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References

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2019 (1)

Y. Oiknine, I. August, V. Farber, D. Gedalin, and A. Stern, “Compressive sensing hyperspectral imaging by spectral multiplexing with liquid crystal,” J. Imaging 5, 3 (2019).
[Crossref]

2018 (5)

X. Wang, Y. Zhang, X. Ma, T. Xu, and G. R. Arce, “Compressive spectral imaging system based on liquid crystal tunable filter,” Opt. Express 26, 25226–25243 (2018).
[Crossref]

Y. Oiknine, I. August, D. G. Blumberg, and A. Stern, “NIR hyperspectral compressive imager based on a modified Fabry-Perot resonator,” J. Opt. 20, 044011 (2018).
[Crossref]

Y. Oiknine, I. August, and A. Stern, “Multi-aperture snapshot compressive hyperspectral camera,” Opt. Lett. 43, 5042–5045 (2018).
[Crossref]

J. Xia, Y. Yang, H. Cao, C. Han, D. Ge, and W. Zhang, “Visible-near infrared spectrum-based classification of apple chilling injury on cloud computing platform,” Comput. Electron. Agric. 145, 27–34 (2018).
[Crossref]

Z. Zhang, S. Jiao, M. Yao, X. Li, and J. Zhong, “Secured single-pixel broadcast imaging,” Opt. Express 26, 14578–14591 (2018).
[Crossref]

2017 (1)

2016 (2)

I. August, Y. Oiknine, M. AbuLeil, I. Abdulhalim, and A. Stern, “Miniature compressive ultra-spectral imaging system utilizing a single liquid crystal phase retarder,” Sci. Rep. 6, 23524 (2016).
[Crossref]

M. A. Golub, A. Averbuch, M. Nathan, V. A. Zheludev, J. Hauser, S. Gurevitch, R. Malinsky, and A. Kagan, “Compressed sensing snapshot spectral imaging by a regular digital camera with an added optical diffuser,” Appl. Opt. 55, 432–443 (2016).
[Crossref]

2014 (2)

X. Lin, G. Wetzstein, Y. Liu, and Q. Dai, “Dual-coded compressive hyperspectral imaging,” Opt. Lett. 39, 2044–2047 (2014).
[Crossref]

G. R. Arce, D. J. Brady, L. Carin, H. Arguello, and D. S. Kittle, “Compressive coded aperture spectral imaging: An introduction,” IEEE Signal Process. Mag. 31, 105–115 (2014).
[Crossref]

2013 (1)

F. Soldevila, E. Irles, V. Durán, P. Clemente, M. Fernández-Alonso, E. Tajahuerce, and J. Lancis, “Single-pixel polarimetric imaging spectrometer by compressive sensing,” Appl. Phys. B 113, 551–558 (2013).
[Crossref]

2012 (1)

F. D. Van der Meer, H. M. A. Van der Werff, F. J. Van Ruitenbeek, C. A. Hecker, W. H. Bakker, M. F. Noomen, M. Van Der Meijde, E. J. M. Carranza, J. B. De Smeth, and T. Woldai, “Multi- and hyperspectral geologic remote sensing: A review,” Int. J. Appl. Earth Obs. Geoinf. 14, 112–128 (2012).
[Crossref]

2011 (1)

S. Becker, J. Bobin, and E. Candès, “NESTA: a fast and accurate first-order method for sparse recovery,” SIAM J. Imaging Sci. 4, 1–39 (2011).
[Crossref]

2010 (1)

P. W. Yuen and M. Richardson, “An introduction to hyperspectral imaging and its application for security, surveillance and target acquisition,” Imaging Sci. J. 58, 241–253 (2010).
[Crossref]

2008 (1)

2007 (3)

M. E. Gehm, R. John, D. J. Brady, R. M. Willett, and T. J. Schulz, “Single-shot compressive spectral imaging with a dual-disperser architecture,” Opt. Express 15, 14013–14027 (2007).
[Crossref]

R. Baraniuk, “Compressive sensing [lecture notes],” IEEE Signal Process. Mag. 24, 118–121 (2007).
[Crossref]

O. Shacham, O. Haik, and Y. Yitzhaky, “Blind restoration of atmospherically degraded images by automatic best step-edge detection,” Pattern Recog. Lett. 28, 2094–2103 (2007).
[Crossref]

2006 (2)

D. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52, 1289–1306 (2006).
[Crossref]

M. E. Martin, M. B. Wabuyele, K. Chen, P. Kasili, M. Panjehpour, M. Phan, B. Overholt, G. Cunningham, D. Wilson, and R. C. DeNovo, “Development of an advanced hyperspectral imaging (HSI) system with applications for cancer detection,” Ann. Biomed. Eng. 34, 1061–1068 (2006).
[Crossref]

2004 (1)

E. K. Hege, D. O’Connell, W. Johnson, S. Basty, and E. L. Dereniak, “Hyperspectral imaging for astronomy and space surveillance,” Proc. SPIE 5159, 380–392 (2004).
[Crossref]

2001 (2)

P. W. Trezona, “Derivation of the 1964 CIE 10° XYZ colour-matching functions and their applicability in photometry,” Color Res. Appl. 26, 67–75 (2001).
[Crossref]

J. K. Romberg, H. Choi, and R. G. Baraniuk, “Bayesian tree-structured image modeling using wavelet-domain hidden Markov models,” IEEE Trans. Image Process. 10, 1056–1068 (2001).
[Crossref]

2000 (1)

S. G. Chang, B. Yu, and M. Vetterli, “Adaptive wavelet thresholding for image denoising and compression,” IEEE Trans. Image Process. 9, 1532–1546 (2000).
[Crossref]

1986 (1)

M. Lee and M. Kaveh, “Fast Hadamard transform based on a simple matrix factorization,” IEEE Trans. Acoust. Speech Signal Process. 34, 1666–1667 (1986).
[Crossref]

1969 (1)

W. K. Pratt, J. Kane, and H. C. Andrews, “Hadamard transform image coding,” Proc. IEEE 57, 58–68 (1969).
[Crossref]

Abdulhalim, I.

I. August, Y. Oiknine, M. AbuLeil, I. Abdulhalim, and A. Stern, “Miniature compressive ultra-spectral imaging system utilizing a single liquid crystal phase retarder,” Sci. Rep. 6, 23524 (2016).
[Crossref]

AbuLeil, M.

I. August, Y. Oiknine, M. AbuLeil, I. Abdulhalim, and A. Stern, “Miniature compressive ultra-spectral imaging system utilizing a single liquid crystal phase retarder,” Sci. Rep. 6, 23524 (2016).
[Crossref]

Agaian, S. S.

S. S. Agaian, H. G. Sarukhanyan, K. O. Egiazarian, and J. Astola, Hadamard Transforms (SPIE, 2011), pp. 1–13.

Andrews, H. C.

W. K. Pratt, J. Kane, and H. C. Andrews, “Hadamard transform image coding,” Proc. IEEE 57, 58–68 (1969).
[Crossref]

Arce, G. R.

X. Wang, Y. Zhang, X. Ma, T. Xu, and G. R. Arce, “Compressive spectral imaging system based on liquid crystal tunable filter,” Opt. Express 26, 25226–25243 (2018).
[Crossref]

G. R. Arce, D. J. Brady, L. Carin, H. Arguello, and D. S. Kittle, “Compressive coded aperture spectral imaging: An introduction,” IEEE Signal Process. Mag. 31, 105–115 (2014).
[Crossref]

G. R. Arce, H. Rueda, C. V. Correa, A. Ramirez, and H. Arguello, “Snapshot compressive multispectral cameras,” in Wiley Encyclopedia of Electrical and Electronics Engineering (1999), pp. 1–22.

Arguello, H.

G. R. Arce, D. J. Brady, L. Carin, H. Arguello, and D. S. Kittle, “Compressive coded aperture spectral imaging: An introduction,” IEEE Signal Process. Mag. 31, 105–115 (2014).
[Crossref]

G. R. Arce, H. Rueda, C. V. Correa, A. Ramirez, and H. Arguello, “Snapshot compressive multispectral cameras,” in Wiley Encyclopedia of Electrical and Electronics Engineering (1999), pp. 1–22.

Astola, J.

S. S. Agaian, H. G. Sarukhanyan, K. O. Egiazarian, and J. Astola, Hadamard Transforms (SPIE, 2011), pp. 1–13.

August, I.

Y. Oiknine, I. August, V. Farber, D. Gedalin, and A. Stern, “Compressive sensing hyperspectral imaging by spectral multiplexing with liquid crystal,” J. Imaging 5, 3 (2019).
[Crossref]

Y. Oiknine, I. August, D. G. Blumberg, and A. Stern, “NIR hyperspectral compressive imager based on a modified Fabry-Perot resonator,” J. Opt. 20, 044011 (2018).
[Crossref]

Y. Oiknine, I. August, and A. Stern, “Multi-aperture snapshot compressive hyperspectral camera,” Opt. Lett. 43, 5042–5045 (2018).
[Crossref]

I. August, Y. Oiknine, M. AbuLeil, I. Abdulhalim, and A. Stern, “Miniature compressive ultra-spectral imaging system utilizing a single liquid crystal phase retarder,” Sci. Rep. 6, 23524 (2016).
[Crossref]

Averbuch, A.

Bakker, W. H.

F. D. Van der Meer, H. M. A. Van der Werff, F. J. Van Ruitenbeek, C. A. Hecker, W. H. Bakker, M. F. Noomen, M. Van Der Meijde, E. J. M. Carranza, J. B. De Smeth, and T. Woldai, “Multi- and hyperspectral geologic remote sensing: A review,” Int. J. Appl. Earth Obs. Geoinf. 14, 112–128 (2012).
[Crossref]

Baraniuk, R.

R. Baraniuk, “Compressive sensing [lecture notes],” IEEE Signal Process. Mag. 24, 118–121 (2007).
[Crossref]

Baraniuk, R. G.

J. K. Romberg, H. Choi, and R. G. Baraniuk, “Bayesian tree-structured image modeling using wavelet-domain hidden Markov models,” IEEE Trans. Image Process. 10, 1056–1068 (2001).
[Crossref]

Basty, S.

E. K. Hege, D. O’Connell, W. Johnson, S. Basty, and E. L. Dereniak, “Hyperspectral imaging for astronomy and space surveillance,” Proc. SPIE 5159, 380–392 (2004).
[Crossref]

Becker, S.

S. Becker, J. Bobin, and E. Candès, “NESTA: a fast and accurate first-order method for sparse recovery,” SIAM J. Imaging Sci. 4, 1–39 (2011).
[Crossref]

Blumberg, D. G.

Y. Oiknine, I. August, D. G. Blumberg, and A. Stern, “NIR hyperspectral compressive imager based on a modified Fabry-Perot resonator,” J. Opt. 20, 044011 (2018).
[Crossref]

Bobin, J.

S. Becker, J. Bobin, and E. Candès, “NESTA: a fast and accurate first-order method for sparse recovery,” SIAM J. Imaging Sci. 4, 1–39 (2011).
[Crossref]

Brady, D.

Brady, D. J.

G. R. Arce, D. J. Brady, L. Carin, H. Arguello, and D. S. Kittle, “Compressive coded aperture spectral imaging: An introduction,” IEEE Signal Process. Mag. 31, 105–115 (2014).
[Crossref]

M. E. Gehm, R. John, D. J. Brady, R. M. Willett, and T. J. Schulz, “Single-shot compressive spectral imaging with a dual-disperser architecture,” Opt. Express 15, 14013–14027 (2007).
[Crossref]

Burns, P. D.

P. D. Burns, “Slanted-edge MTF for digital camera and scanner analysis,” in Is and Ts Pics Conference (2000), pp. 135–138.

Candès, E.

S. Becker, J. Bobin, and E. Candès, “NESTA: a fast and accurate first-order method for sparse recovery,” SIAM J. Imaging Sci. 4, 1–39 (2011).
[Crossref]

Cao, H.

J. Xia, Y. Yang, H. Cao, C. Han, D. Ge, and W. Zhang, “Visible-near infrared spectrum-based classification of apple chilling injury on cloud computing platform,” Comput. Electron. Agric. 145, 27–34 (2018).
[Crossref]

Carin, L.

G. R. Arce, D. J. Brady, L. Carin, H. Arguello, and D. S. Kittle, “Compressive coded aperture spectral imaging: An introduction,” IEEE Signal Process. Mag. 31, 105–115 (2014).
[Crossref]

Carranza, E. J. M.

F. D. Van der Meer, H. M. A. Van der Werff, F. J. Van Ruitenbeek, C. A. Hecker, W. H. Bakker, M. F. Noomen, M. Van Der Meijde, E. J. M. Carranza, J. B. De Smeth, and T. Woldai, “Multi- and hyperspectral geologic remote sensing: A review,” Int. J. Appl. Earth Obs. Geoinf. 14, 112–128 (2012).
[Crossref]

Chang, S. G.

S. G. Chang, B. Yu, and M. Vetterli, “Adaptive wavelet thresholding for image denoising and compression,” IEEE Trans. Image Process. 9, 1532–1546 (2000).
[Crossref]

Chen, K.

M. E. Martin, M. B. Wabuyele, K. Chen, P. Kasili, M. Panjehpour, M. Phan, B. Overholt, G. Cunningham, D. Wilson, and R. C. DeNovo, “Development of an advanced hyperspectral imaging (HSI) system with applications for cancer detection,” Ann. Biomed. Eng. 34, 1061–1068 (2006).
[Crossref]

Chen, Y.

R. Lu and Y. Chen, “Hyperspectral imaging for safety inspection of food and agricultural products,” in Pathogen Detection and Remediation for Safe Eating (1999), pp. 121–134.

Choi, H.

J. K. Romberg, H. Choi, and R. G. Baraniuk, “Bayesian tree-structured image modeling using wavelet-domain hidden Markov models,” IEEE Trans. Image Process. 10, 1056–1068 (2001).
[Crossref]

Clemente, P.

F. Soldevila, E. Irles, V. Durán, P. Clemente, M. Fernández-Alonso, E. Tajahuerce, and J. Lancis, “Single-pixel polarimetric imaging spectrometer by compressive sensing,” Appl. Phys. B 113, 551–558 (2013).
[Crossref]

Correa, C. V.

G. R. Arce, H. Rueda, C. V. Correa, A. Ramirez, and H. Arguello, “Snapshot compressive multispectral cameras,” in Wiley Encyclopedia of Electrical and Electronics Engineering (1999), pp. 1–22.

Cunningham, G.

M. E. Martin, M. B. Wabuyele, K. Chen, P. Kasili, M. Panjehpour, M. Phan, B. Overholt, G. Cunningham, D. Wilson, and R. C. DeNovo, “Development of an advanced hyperspectral imaging (HSI) system with applications for cancer detection,” Ann. Biomed. Eng. 34, 1061–1068 (2006).
[Crossref]

Dai, Q.

De Smeth, J. B.

F. D. Van der Meer, H. M. A. Van der Werff, F. J. Van Ruitenbeek, C. A. Hecker, W. H. Bakker, M. F. Noomen, M. Van Der Meijde, E. J. M. Carranza, J. B. De Smeth, and T. Woldai, “Multi- and hyperspectral geologic remote sensing: A review,” Int. J. Appl. Earth Obs. Geoinf. 14, 112–128 (2012).
[Crossref]

DeNovo, R. C.

M. E. Martin, M. B. Wabuyele, K. Chen, P. Kasili, M. Panjehpour, M. Phan, B. Overholt, G. Cunningham, D. Wilson, and R. C. DeNovo, “Development of an advanced hyperspectral imaging (HSI) system with applications for cancer detection,” Ann. Biomed. Eng. 34, 1061–1068 (2006).
[Crossref]

Dereniak, E. L.

E. K. Hege, D. O’Connell, W. Johnson, S. Basty, and E. L. Dereniak, “Hyperspectral imaging for astronomy and space surveillance,” Proc. SPIE 5159, 380–392 (2004).
[Crossref]

Donoho, D.

D. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52, 1289–1306 (2006).
[Crossref]

Durán, V.

F. Soldevila, E. Irles, V. Durán, P. Clemente, M. Fernández-Alonso, E. Tajahuerce, and J. Lancis, “Single-pixel polarimetric imaging spectrometer by compressive sensing,” Appl. Phys. B 113, 551–558 (2013).
[Crossref]

Egiazarian, K. O.

S. S. Agaian, H. G. Sarukhanyan, K. O. Egiazarian, and J. Astola, Hadamard Transforms (SPIE, 2011), pp. 1–13.

Eldar, Y. C.

Y. C. Eldar and G. Kutyniok, Compressed Sensing: Theory and Applications (Cambridge University, 2013).

Estribeau, M.

M. Estribeau and P. Magnan, “Fast MTF measurement of CMOS imagers using ISO 12333 slanted-edge methodology,” in Detectors and Associated Signal Processing (2004), pp. 243–253.

Farber, V.

Y. Oiknine, I. August, V. Farber, D. Gedalin, and A. Stern, “Compressive sensing hyperspectral imaging by spectral multiplexing with liquid crystal,” J. Imaging 5, 3 (2019).
[Crossref]

Fernández-Alonso, M.

F. Soldevila, E. Irles, V. Durán, P. Clemente, M. Fernández-Alonso, E. Tajahuerce, and J. Lancis, “Single-pixel polarimetric imaging spectrometer by compressive sensing,” Appl. Phys. B 113, 551–558 (2013).
[Crossref]

Foucart, S.

S. Foucart and H. Rauhut, “Uncertainty principles and lower bounds,” in A Mathematical Introduction to Compressive Sensing (Birkhäuser, 2013), p. 383.

Ge, D.

J. Xia, Y. Yang, H. Cao, C. Han, D. Ge, and W. Zhang, “Visible-near infrared spectrum-based classification of apple chilling injury on cloud computing platform,” Comput. Electron. Agric. 145, 27–34 (2018).
[Crossref]

Gedalin, D.

Y. Oiknine, I. August, V. Farber, D. Gedalin, and A. Stern, “Compressive sensing hyperspectral imaging by spectral multiplexing with liquid crystal,” J. Imaging 5, 3 (2019).
[Crossref]

Gehm, M. E.

Golub, M. A.

Gurevitch, S.

Haik, O.

O. Shacham, O. Haik, and Y. Yitzhaky, “Blind restoration of atmospherically degraded images by automatic best step-edge detection,” Pattern Recog. Lett. 28, 2094–2103 (2007).
[Crossref]

Han, C.

J. Xia, Y. Yang, H. Cao, C. Han, D. Ge, and W. Zhang, “Visible-near infrared spectrum-based classification of apple chilling injury on cloud computing platform,” Comput. Electron. Agric. 145, 27–34 (2018).
[Crossref]

Hauser, J.

Hecker, C. A.

F. D. Van der Meer, H. M. A. Van der Werff, F. J. Van Ruitenbeek, C. A. Hecker, W. H. Bakker, M. F. Noomen, M. Van Der Meijde, E. J. M. Carranza, J. B. De Smeth, and T. Woldai, “Multi- and hyperspectral geologic remote sensing: A review,” Int. J. Appl. Earth Obs. Geoinf. 14, 112–128 (2012).
[Crossref]

Hege, E. K.

E. K. Hege, D. O’Connell, W. Johnson, S. Basty, and E. L. Dereniak, “Hyperspectral imaging for astronomy and space surveillance,” Proc. SPIE 5159, 380–392 (2004).
[Crossref]

Irles, E.

F. Soldevila, E. Irles, V. Durán, P. Clemente, M. Fernández-Alonso, E. Tajahuerce, and J. Lancis, “Single-pixel polarimetric imaging spectrometer by compressive sensing,” Appl. Phys. B 113, 551–558 (2013).
[Crossref]

Jain, A. K.

A. K. Jain, Fundamentals of Digital Image Processing (Prentice Hall, 1989), pp. 30–31.

Jiao, S.

John, R.

Johnson, W.

E. K. Hege, D. O’Connell, W. Johnson, S. Basty, and E. L. Dereniak, “Hyperspectral imaging for astronomy and space surveillance,” Proc. SPIE 5159, 380–392 (2004).
[Crossref]

Kagan, A.

Kane, J.

W. K. Pratt, J. Kane, and H. C. Andrews, “Hadamard transform image coding,” Proc. IEEE 57, 58–68 (1969).
[Crossref]

Kasili, P.

M. E. Martin, M. B. Wabuyele, K. Chen, P. Kasili, M. Panjehpour, M. Phan, B. Overholt, G. Cunningham, D. Wilson, and R. C. DeNovo, “Development of an advanced hyperspectral imaging (HSI) system with applications for cancer detection,” Ann. Biomed. Eng. 34, 1061–1068 (2006).
[Crossref]

Kaveh, M.

M. Lee and M. Kaveh, “Fast Hadamard transform based on a simple matrix factorization,” IEEE Trans. Acoust. Speech Signal Process. 34, 1666–1667 (1986).
[Crossref]

Kelly, K.

T. Sun and K. Kelly, “Compressive sensing hyperspectral imager,” in Computational Optical Sensing and Imaging (2009), paper CTuA5.

Kittle, D. S.

G. R. Arce, D. J. Brady, L. Carin, H. Arguello, and D. S. Kittle, “Compressive coded aperture spectral imaging: An introduction,” IEEE Signal Process. Mag. 31, 105–115 (2014).
[Crossref]

Kohm, K.

K. Kohm, “Modulation transfer function measurement method and results for the orbview-3 high resolution imaging satellite,” in Proceedings of ISPRS (2004), pp. 12–23.

Kravets, V.

V. Kravets and A. Stern, “Variable density multiscale compressive sampling with Hadamard matrix,” submitted for publication.

Kutyniok, G.

Y. C. Eldar and G. Kutyniok, Compressed Sensing: Theory and Applications (Cambridge University, 2013).

Lancis, J.

F. Soldevila, E. Irles, V. Durán, P. Clemente, M. Fernández-Alonso, E. Tajahuerce, and J. Lancis, “Single-pixel polarimetric imaging spectrometer by compressive sensing,” Appl. Phys. B 113, 551–558 (2013).
[Crossref]

Lee, M.

M. Lee and M. Kaveh, “Fast Hadamard transform based on a simple matrix factorization,” IEEE Trans. Acoust. Speech Signal Process. 34, 1666–1667 (1986).
[Crossref]

Li, X.

Lin, X.

Liu, Y.

Lu, R.

R. Lu and Y. Chen, “Hyperspectral imaging for safety inspection of food and agricultural products,” in Pathogen Detection and Remediation for Safe Eating (1999), pp. 121–134.

Ma, X.

Magnan, P.

M. Estribeau and P. Magnan, “Fast MTF measurement of CMOS imagers using ISO 12333 slanted-edge methodology,” in Detectors and Associated Signal Processing (2004), pp. 243–253.

Malinsky, R.

Martin, M. E.

M. E. Martin, M. B. Wabuyele, K. Chen, P. Kasili, M. Panjehpour, M. Phan, B. Overholt, G. Cunningham, D. Wilson, and R. C. DeNovo, “Development of an advanced hyperspectral imaging (HSI) system with applications for cancer detection,” Ann. Biomed. Eng. 34, 1061–1068 (2006).
[Crossref]

Nathan, M.

Noomen, M. F.

F. D. Van der Meer, H. M. A. Van der Werff, F. J. Van Ruitenbeek, C. A. Hecker, W. H. Bakker, M. F. Noomen, M. Van Der Meijde, E. J. M. Carranza, J. B. De Smeth, and T. Woldai, “Multi- and hyperspectral geologic remote sensing: A review,” Int. J. Appl. Earth Obs. Geoinf. 14, 112–128 (2012).
[Crossref]

O’Connell, D.

E. K. Hege, D. O’Connell, W. Johnson, S. Basty, and E. L. Dereniak, “Hyperspectral imaging for astronomy and space surveillance,” Proc. SPIE 5159, 380–392 (2004).
[Crossref]

Oiknine, Y.

Y. Oiknine, I. August, V. Farber, D. Gedalin, and A. Stern, “Compressive sensing hyperspectral imaging by spectral multiplexing with liquid crystal,” J. Imaging 5, 3 (2019).
[Crossref]

Y. Oiknine, I. August, and A. Stern, “Multi-aperture snapshot compressive hyperspectral camera,” Opt. Lett. 43, 5042–5045 (2018).
[Crossref]

Y. Oiknine, I. August, D. G. Blumberg, and A. Stern, “NIR hyperspectral compressive imager based on a modified Fabry-Perot resonator,” J. Opt. 20, 044011 (2018).
[Crossref]

I. August, Y. Oiknine, M. AbuLeil, I. Abdulhalim, and A. Stern, “Miniature compressive ultra-spectral imaging system utilizing a single liquid crystal phase retarder,” Sci. Rep. 6, 23524 (2016).
[Crossref]

Overholt, B.

M. E. Martin, M. B. Wabuyele, K. Chen, P. Kasili, M. Panjehpour, M. Phan, B. Overholt, G. Cunningham, D. Wilson, and R. C. DeNovo, “Development of an advanced hyperspectral imaging (HSI) system with applications for cancer detection,” Ann. Biomed. Eng. 34, 1061–1068 (2006).
[Crossref]

Panjehpour, M.

M. E. Martin, M. B. Wabuyele, K. Chen, P. Kasili, M. Panjehpour, M. Phan, B. Overholt, G. Cunningham, D. Wilson, and R. C. DeNovo, “Development of an advanced hyperspectral imaging (HSI) system with applications for cancer detection,” Ann. Biomed. Eng. 34, 1061–1068 (2006).
[Crossref]

Phan, M.

M. E. Martin, M. B. Wabuyele, K. Chen, P. Kasili, M. Panjehpour, M. Phan, B. Overholt, G. Cunningham, D. Wilson, and R. C. DeNovo, “Development of an advanced hyperspectral imaging (HSI) system with applications for cancer detection,” Ann. Biomed. Eng. 34, 1061–1068 (2006).
[Crossref]

Pratt, W. K.

W. K. Pratt, J. Kane, and H. C. Andrews, “Hadamard transform image coding,” Proc. IEEE 57, 58–68 (1969).
[Crossref]

Ramirez, A.

G. R. Arce, H. Rueda, C. V. Correa, A. Ramirez, and H. Arguello, “Snapshot compressive multispectral cameras,” in Wiley Encyclopedia of Electrical and Electronics Engineering (1999), pp. 1–22.

Rauhut, H.

S. Foucart and H. Rauhut, “Uncertainty principles and lower bounds,” in A Mathematical Introduction to Compressive Sensing (Birkhäuser, 2013), p. 383.

Richardson, M.

P. W. Yuen and M. Richardson, “An introduction to hyperspectral imaging and its application for security, surveillance and target acquisition,” Imaging Sci. J. 58, 241–253 (2010).
[Crossref]

Romberg, J. K.

J. K. Romberg, H. Choi, and R. G. Baraniuk, “Bayesian tree-structured image modeling using wavelet-domain hidden Markov models,” IEEE Trans. Image Process. 10, 1056–1068 (2001).
[Crossref]

Rueda, H.

G. R. Arce, H. Rueda, C. V. Correa, A. Ramirez, and H. Arguello, “Snapshot compressive multispectral cameras,” in Wiley Encyclopedia of Electrical and Electronics Engineering (1999), pp. 1–22.

Sarukhanyan, H. G.

S. S. Agaian, H. G. Sarukhanyan, K. O. Egiazarian, and J. Astola, Hadamard Transforms (SPIE, 2011), pp. 1–13.

Schulz, T. J.

Shacham, O.

O. Shacham, O. Haik, and Y. Yitzhaky, “Blind restoration of atmospherically degraded images by automatic best step-edge detection,” Pattern Recog. Lett. 28, 2094–2103 (2007).
[Crossref]

Soldevila, F.

F. Soldevila, E. Irles, V. Durán, P. Clemente, M. Fernández-Alonso, E. Tajahuerce, and J. Lancis, “Single-pixel polarimetric imaging spectrometer by compressive sensing,” Appl. Phys. B 113, 551–558 (2013).
[Crossref]

Stern, A.

Y. Oiknine, I. August, V. Farber, D. Gedalin, and A. Stern, “Compressive sensing hyperspectral imaging by spectral multiplexing with liquid crystal,” J. Imaging 5, 3 (2019).
[Crossref]

Y. Oiknine, I. August, D. G. Blumberg, and A. Stern, “NIR hyperspectral compressive imager based on a modified Fabry-Perot resonator,” J. Opt. 20, 044011 (2018).
[Crossref]

Y. Oiknine, I. August, and A. Stern, “Multi-aperture snapshot compressive hyperspectral camera,” Opt. Lett. 43, 5042–5045 (2018).
[Crossref]

I. August, Y. Oiknine, M. AbuLeil, I. Abdulhalim, and A. Stern, “Miniature compressive ultra-spectral imaging system utilizing a single liquid crystal phase retarder,” Sci. Rep. 6, 23524 (2016).
[Crossref]

A. Stern, Optical Compressive Imaging (CRC Press/Taylor & Francis, 2017).

V. Kravets and A. Stern, “Variable density multiscale compressive sampling with Hadamard matrix,” submitted for publication.

Sun, T.

T. Sun and K. Kelly, “Compressive sensing hyperspectral imager,” in Computational Optical Sensing and Imaging (2009), paper CTuA5.

Tajahuerce, E.

F. Soldevila, E. Irles, V. Durán, P. Clemente, M. Fernández-Alonso, E. Tajahuerce, and J. Lancis, “Single-pixel polarimetric imaging spectrometer by compressive sensing,” Appl. Phys. B 113, 551–558 (2013).
[Crossref]

Trezona, P. W.

P. W. Trezona, “Derivation of the 1964 CIE 10° XYZ colour-matching functions and their applicability in photometry,” Color Res. Appl. 26, 67–75 (2001).
[Crossref]

Van der Meer, F. D.

F. D. Van der Meer, H. M. A. Van der Werff, F. J. Van Ruitenbeek, C. A. Hecker, W. H. Bakker, M. F. Noomen, M. Van Der Meijde, E. J. M. Carranza, J. B. De Smeth, and T. Woldai, “Multi- and hyperspectral geologic remote sensing: A review,” Int. J. Appl. Earth Obs. Geoinf. 14, 112–128 (2012).
[Crossref]

Van Der Meijde, M.

F. D. Van der Meer, H. M. A. Van der Werff, F. J. Van Ruitenbeek, C. A. Hecker, W. H. Bakker, M. F. Noomen, M. Van Der Meijde, E. J. M. Carranza, J. B. De Smeth, and T. Woldai, “Multi- and hyperspectral geologic remote sensing: A review,” Int. J. Appl. Earth Obs. Geoinf. 14, 112–128 (2012).
[Crossref]

Van der Werff, H. M. A.

F. D. Van der Meer, H. M. A. Van der Werff, F. J. Van Ruitenbeek, C. A. Hecker, W. H. Bakker, M. F. Noomen, M. Van Der Meijde, E. J. M. Carranza, J. B. De Smeth, and T. Woldai, “Multi- and hyperspectral geologic remote sensing: A review,” Int. J. Appl. Earth Obs. Geoinf. 14, 112–128 (2012).
[Crossref]

Van Ruitenbeek, F. J.

F. D. Van der Meer, H. M. A. Van der Werff, F. J. Van Ruitenbeek, C. A. Hecker, W. H. Bakker, M. F. Noomen, M. Van Der Meijde, E. J. M. Carranza, J. B. De Smeth, and T. Woldai, “Multi- and hyperspectral geologic remote sensing: A review,” Int. J. Appl. Earth Obs. Geoinf. 14, 112–128 (2012).
[Crossref]

Vetterli, M.

S. G. Chang, B. Yu, and M. Vetterli, “Adaptive wavelet thresholding for image denoising and compression,” IEEE Trans. Image Process. 9, 1532–1546 (2000).
[Crossref]

Wabuyele, M. B.

M. E. Martin, M. B. Wabuyele, K. Chen, P. Kasili, M. Panjehpour, M. Phan, B. Overholt, G. Cunningham, D. Wilson, and R. C. DeNovo, “Development of an advanced hyperspectral imaging (HSI) system with applications for cancer detection,” Ann. Biomed. Eng. 34, 1061–1068 (2006).
[Crossref]

Wagadarikar, A.

Wang, X.

Wetzstein, G.

Willett, R.

Willett, R. M.

Wilson, D.

M. E. Martin, M. B. Wabuyele, K. Chen, P. Kasili, M. Panjehpour, M. Phan, B. Overholt, G. Cunningham, D. Wilson, and R. C. DeNovo, “Development of an advanced hyperspectral imaging (HSI) system with applications for cancer detection,” Ann. Biomed. Eng. 34, 1061–1068 (2006).
[Crossref]

Woldai, T.

F. D. Van der Meer, H. M. A. Van der Werff, F. J. Van Ruitenbeek, C. A. Hecker, W. H. Bakker, M. F. Noomen, M. Van Der Meijde, E. J. M. Carranza, J. B. De Smeth, and T. Woldai, “Multi- and hyperspectral geologic remote sensing: A review,” Int. J. Appl. Earth Obs. Geoinf. 14, 112–128 (2012).
[Crossref]

Xia, J.

J. Xia, Y. Yang, H. Cao, C. Han, D. Ge, and W. Zhang, “Visible-near infrared spectrum-based classification of apple chilling injury on cloud computing platform,” Comput. Electron. Agric. 145, 27–34 (2018).
[Crossref]

Xu, T.

Yang, Y.

J. Xia, Y. Yang, H. Cao, C. Han, D. Ge, and W. Zhang, “Visible-near infrared spectrum-based classification of apple chilling injury on cloud computing platform,” Comput. Electron. Agric. 145, 27–34 (2018).
[Crossref]

Yao, M.

Yitzhaky, Y.

O. Shacham, O. Haik, and Y. Yitzhaky, “Blind restoration of atmospherically degraded images by automatic best step-edge detection,” Pattern Recog. Lett. 28, 2094–2103 (2007).
[Crossref]

Yu, B.

S. G. Chang, B. Yu, and M. Vetterli, “Adaptive wavelet thresholding for image denoising and compression,” IEEE Trans. Image Process. 9, 1532–1546 (2000).
[Crossref]

Yuen, P. W.

P. W. Yuen and M. Richardson, “An introduction to hyperspectral imaging and its application for security, surveillance and target acquisition,” Imaging Sci. J. 58, 241–253 (2010).
[Crossref]

Zhang, W.

J. Xia, Y. Yang, H. Cao, C. Han, D. Ge, and W. Zhang, “Visible-near infrared spectrum-based classification of apple chilling injury on cloud computing platform,” Comput. Electron. Agric. 145, 27–34 (2018).
[Crossref]

Zhang, Y.

Zhang, Z.

Zheludev, V. A.

Zheng, G.

Zhong, J.

Ann. Biomed. Eng. (1)

M. E. Martin, M. B. Wabuyele, K. Chen, P. Kasili, M. Panjehpour, M. Phan, B. Overholt, G. Cunningham, D. Wilson, and R. C. DeNovo, “Development of an advanced hyperspectral imaging (HSI) system with applications for cancer detection,” Ann. Biomed. Eng. 34, 1061–1068 (2006).
[Crossref]

Appl. Opt. (2)

Appl. Phys. B (1)

F. Soldevila, E. Irles, V. Durán, P. Clemente, M. Fernández-Alonso, E. Tajahuerce, and J. Lancis, “Single-pixel polarimetric imaging spectrometer by compressive sensing,” Appl. Phys. B 113, 551–558 (2013).
[Crossref]

Color Res. Appl. (1)

P. W. Trezona, “Derivation of the 1964 CIE 10° XYZ colour-matching functions and their applicability in photometry,” Color Res. Appl. 26, 67–75 (2001).
[Crossref]

Comput. Electron. Agric. (1)

J. Xia, Y. Yang, H. Cao, C. Han, D. Ge, and W. Zhang, “Visible-near infrared spectrum-based classification of apple chilling injury on cloud computing platform,” Comput. Electron. Agric. 145, 27–34 (2018).
[Crossref]

IEEE Signal Process. Mag. (2)

R. Baraniuk, “Compressive sensing [lecture notes],” IEEE Signal Process. Mag. 24, 118–121 (2007).
[Crossref]

G. R. Arce, D. J. Brady, L. Carin, H. Arguello, and D. S. Kittle, “Compressive coded aperture spectral imaging: An introduction,” IEEE Signal Process. Mag. 31, 105–115 (2014).
[Crossref]

IEEE Trans. Acoust. Speech Signal Process. (1)

M. Lee and M. Kaveh, “Fast Hadamard transform based on a simple matrix factorization,” IEEE Trans. Acoust. Speech Signal Process. 34, 1666–1667 (1986).
[Crossref]

IEEE Trans. Image Process. (2)

S. G. Chang, B. Yu, and M. Vetterli, “Adaptive wavelet thresholding for image denoising and compression,” IEEE Trans. Image Process. 9, 1532–1546 (2000).
[Crossref]

J. K. Romberg, H. Choi, and R. G. Baraniuk, “Bayesian tree-structured image modeling using wavelet-domain hidden Markov models,” IEEE Trans. Image Process. 10, 1056–1068 (2001).
[Crossref]

IEEE Trans. Inf. Theory (1)

D. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52, 1289–1306 (2006).
[Crossref]

Imaging Sci. J. (1)

P. W. Yuen and M. Richardson, “An introduction to hyperspectral imaging and its application for security, surveillance and target acquisition,” Imaging Sci. J. 58, 241–253 (2010).
[Crossref]

Int. J. Appl. Earth Obs. Geoinf. (1)

F. D. Van der Meer, H. M. A. Van der Werff, F. J. Van Ruitenbeek, C. A. Hecker, W. H. Bakker, M. F. Noomen, M. Van Der Meijde, E. J. M. Carranza, J. B. De Smeth, and T. Woldai, “Multi- and hyperspectral geologic remote sensing: A review,” Int. J. Appl. Earth Obs. Geoinf. 14, 112–128 (2012).
[Crossref]

J. Imaging (1)

Y. Oiknine, I. August, V. Farber, D. Gedalin, and A. Stern, “Compressive sensing hyperspectral imaging by spectral multiplexing with liquid crystal,” J. Imaging 5, 3 (2019).
[Crossref]

J. Opt. (1)

Y. Oiknine, I. August, D. G. Blumberg, and A. Stern, “NIR hyperspectral compressive imager based on a modified Fabry-Perot resonator,” J. Opt. 20, 044011 (2018).
[Crossref]

Opt. Express (4)

Opt. Lett. (2)

Pattern Recog. Lett. (1)

O. Shacham, O. Haik, and Y. Yitzhaky, “Blind restoration of atmospherically degraded images by automatic best step-edge detection,” Pattern Recog. Lett. 28, 2094–2103 (2007).
[Crossref]

Proc. IEEE (1)

W. K. Pratt, J. Kane, and H. C. Andrews, “Hadamard transform image coding,” Proc. IEEE 57, 58–68 (1969).
[Crossref]

Proc. SPIE (1)

E. K. Hege, D. O’Connell, W. Johnson, S. Basty, and E. L. Dereniak, “Hyperspectral imaging for astronomy and space surveillance,” Proc. SPIE 5159, 380–392 (2004).
[Crossref]

Sci. Rep. (1)

I. August, Y. Oiknine, M. AbuLeil, I. Abdulhalim, and A. Stern, “Miniature compressive ultra-spectral imaging system utilizing a single liquid crystal phase retarder,” Sci. Rep. 6, 23524 (2016).
[Crossref]

SIAM J. Imaging Sci. (1)

S. Becker, J. Bobin, and E. Candès, “NESTA: a fast and accurate first-order method for sparse recovery,” SIAM J. Imaging Sci. 4, 1–39 (2011).
[Crossref]

Other (12)

V. Kravets and A. Stern, “Variable density multiscale compressive sampling with Hadamard matrix,” submitted for publication.

A. K. Jain, Fundamentals of Digital Image Processing (Prentice Hall, 1989), pp. 30–31.

K. Kohm, “Modulation transfer function measurement method and results for the orbview-3 high resolution imaging satellite,” in Proceedings of ISPRS (2004), pp. 12–23.

P. D. Burns, “Slanted-edge MTF for digital camera and scanner analysis,” in Is and Ts Pics Conference (2000), pp. 135–138.

M. Estribeau and P. Magnan, “Fast MTF measurement of CMOS imagers using ISO 12333 slanted-edge methodology,” in Detectors and Associated Signal Processing (2004), pp. 243–253.

S. S. Agaian, H. G. Sarukhanyan, K. O. Egiazarian, and J. Astola, Hadamard Transforms (SPIE, 2011), pp. 1–13.

G. R. Arce, H. Rueda, C. V. Correa, A. Ramirez, and H. Arguello, “Snapshot compressive multispectral cameras,” in Wiley Encyclopedia of Electrical and Electronics Engineering (1999), pp. 1–22.

R. Lu and Y. Chen, “Hyperspectral imaging for safety inspection of food and agricultural products,” in Pathogen Detection and Remediation for Safe Eating (1999), pp. 121–134.

S. Foucart and H. Rauhut, “Uncertainty principles and lower bounds,” in A Mathematical Introduction to Compressive Sensing (Birkhäuser, 2013), p. 383.

Y. C. Eldar and G. Kutyniok, Compressed Sensing: Theory and Applications (Cambridge University, 2013).

A. Stern, Optical Compressive Imaging (CRC Press/Taylor & Francis, 2017).

T. Sun and K. Kelly, “Compressive sensing hyperspectral imager,” in Computational Optical Sensing and Imaging (2009), paper CTuA5.

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Figures (12)

Fig. 1.
Fig. 1. Example of a Paley ordered 16-by-16 Hadamard matrix, R4. The white areas represent “1” and the black ones represent “1”. Notice that the upper-half matrix captures the coarse scale, while the lower half captures the fine scales.
Fig. 2.
Fig. 2. (a) Original image. (b) Detailed coefficient subbands of the Haar wavelet at different scales. (c) Appropriate parts of the 2D multiscale Hadamard transform of the image.
Fig. 3.
Fig. 3. Flowchart for choosing the best variable density sampling rate per each wavelet subband of the sample image data set.
Fig. 4.
Fig. 4. Optimal (in terms of PSNR) coefficient density of Hadamard samples at 8-by-8, 16-by-16, 32-by-32, and 64-by-64 subbands for (a) CR=10:1, (b) CR=10:1.5, (c) CR=10:2, and (d) CR=10:3, respectively. Blue solid line represents the mean number of samples among the hyperspectral test images and the error-bar represents the standard deviation.
Fig. 5.
Fig. 5. Imaging setup. The halogen lamp light source is projected on the DMD. The structured light according to the DMD pattern is then projected through the imaging lens onto the scene. The light from the scene is then collected by the spectrometer.
Fig. 6.
Fig. 6. Overall system MTF (dashed) compared with the projection optics’ MTF (solid lines) measured at 450, 550, 650, and 700 nm.
Fig. 7.
Fig. 7. (a) Montage of 42 out of the 2048 reconstructed images. The subset images were chosen in the range of 445–715 nm at a spatial resolution of 256×256. (b) Color image obtained by projecting the spectral image on the RGB color space using the 1964 CIE color-matching functions. (c) Reference image captured with an RGB camera.
Fig. 8.
Fig. 8. Upper row: Color images obtained by using (a) the proposed multiscale sampling scheme (PSNR=33.8dB, SSIM=0.90), (b) the conventional compressive sampling scheme, where the Hadamard coefficients are chosen uniformly at random (PSNR=18.3dB, SSIM=0.37), and (c) the zig-zag scanning method [38,39] (PSNR=31.6dB, SSIM=0.89). Bottom row: Map of the sample points in the 2D Paley ordered Hadamard transform [Fig. 2(c)], taken (d) according to the Haar subbands with the proposed variable density sampling, (e) uniformly at random, and (f) according to the zig-zag scanning method. The color images (a), (b), and (c) are obtained by projecting the spectral image on the RGB color space using the 1964 CIE color-matching functions. The PSNR values are provided in the caption.
Fig. 9.
Fig. 9. (a) Montage of 42 out of the 2048 possible hyperspectral images. The subset images were chosen in the range of 445–715 nm with a spatial resolution of 64×64. (b) Preview 64×64 color image obtained by projecting the spectral image on the RGB color space using the 1964 CIE color-matching functions.
Fig. 10.
Fig. 10. (a) Montage of 42 out of the 2048 possible hyperspectral images. The subset images were chosen in the range of 445–715 nm with a spatial resolution of 128×128. (b) Color image obtained by projecting the spectral image on the RGB color space using the 1964 CIE color-matching functions. (c) Reference image captured with an RGB camera.
Fig. 11.
Fig. 11. (a) Normalized reflected spectrum signature, chosen in the range from 400 to 700 nm of a rotten area of the apple. The reconstructed spectrum from the compressive (10:1) measurements is compared with the direct measurements. (b) Image of the localized projection on the rotten area of the apple.
Fig. 12.
Fig. 12. (a) Image segmentation of the rotten (red) area of the apple. (b) Normalized reflected spectrum signature, in the range from 400 to 700 nm, of the rotten area of the apple compared with a ripe (not rotten) area.

Tables (1)

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Table 1. Densities of Samples per the Four Finest Haar Detail Coefficients Subbands (from Level 1 to Level 4) that give the Best PSNR Reconstruction Results Relative to the Five Test Images

Equations (5)

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

g=Φf,
Rn=12(Rn1(11)Rn1(11))R0=1,
G=RnFRnT.
g=H2nf=(RnRn)f,
GLL(l)=Rl1SLL(l)Rl1T,GLH(l)=Rl1SLH(l)Rl1,GHL(l)=Rl1SHL(l)Rl1T,GHH(l)=Rl1SHH(l)Rl1,

Metrics