Abstract

Atmospheric correction of visible/infrared spectra traditionally involves either (1) physics-based methods using Radiative Transfer Models (RTMs), or (2) empirical methods using in situ measurements. Here a more general probabilistic formulation unifies the approaches and enables combined solutions. The technique is simple to implement and provides stable results from one or more reference spectra. This makes empirical corrections practical for large or remote environments where it is difficult to acquire coincident field data. First, we use a physics-based solution to define a prior distribution over reflectances and their correction coefficients. We then incorporate reference measurements via Bayesian inference, leading to a Maximum A Posteriori estimate which is generally more accurate than pure physics-based methods yet more stable than pure empirical methods. Gaussian assumptions enable a closed form solution based on Tikhonov regularization. We demonstrate performance in atmospheric simulations and historical data from the “Classic” Airborne Visible Infrared Imaging Spectrometer (AVIRIS-C) acquired during the HyspIRI mission preparatory campaign.

© 2016 Optical Society of America

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References

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    [Crossref] [PubMed]
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  21. Per Christian Hansen, Regularization tools: A MATLAB package for analysis and solution of discrete ill-posed problems, Numerical Algorithms,  6(1):1–35, 1994.
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    [Crossref]
  23. R.N. Clark, G. A Swayze, R. Wise, K E. Livo, T. M Hoefen, R. F. Kokaly, and S. J. Sutley, USGS digital spectral library splib06a (2007).
  24. R. O. Green, M. L. Eastwood, C. M. Sarture, T. G Chrien, M. Aronsson, and B. Chippendale, “Imaging spectroscopy and the airborne visible/infrared imaging spectrometer (AVIRIS),” Remote Sens. Environ. 65(3), 227–248 (1998).
    [Crossref]
  25. B. Mayer and A. Kylling, “Technical note: The libRadtran software package for radiative transfer calculations-description and examples of use,” Atmos. Chem. Phys. 5(7), 1855–1877 (2005).
    [Crossref]
  26. E. P. Shettle, “Models of aerosols, clouds and precipitation for atmospheric propagation studies,” Atmospheric propagation in the UV, visible, IR and mm-region and related system aspects,  14(1), 15–32 (1990).
  27. R. Frouin and B. Pelletier, “Bayesian methodology for inverting satellite ocean-color data,” Remote Sens. Environ. 159, 332–360 (2015).
    [Crossref]

2015 (3)

D. R. Thompson, B. C. Gao, R. O. Green, D. A. Roberts, P. E. Dennison, and S. Lundeen, “Atmospheric correction for global mapping spectroscopy: ATREM advances for the HyspIRI preparatory campaign,” Remote Sens. Environ. 167, 64–77 (2015).
[Crossref]

D. R. Thompson, F. C. Seidel, B. C. Gao, M. M. Gierach, R. O. Green, R. M. Kudela, and P. Mouroulis, “Optimizing irradiance estimates for coastal and inland water imaging spectroscopy,” Geophys. Res. Lett. 42(10), 4116–4123 (2015). 2015GL063287.
[Crossref]

R. Frouin and B. Pelletier, “Bayesian methodology for inverting satellite ocean-color data,” Remote Sens. Environ. 159, 332–360 (2015).
[Crossref]

2013 (1)

B. C. Gao and M. Liu, “A fast smoothing algorithm for post-processing of surface reflectance spectra retrieved from airborne imaging spectrometer data,” Sensors 13(10), 13879–13891 (2013).
[Crossref] [PubMed]

2008 (1)

J. L. Mead, “A priori weighting for parameter estimation,” J. Inverse Ill-posed Problems 16(2), 175–193 (2008).
[Crossref]

2006 (2)

G. Schaepman-Strub, M. E. Schaepman, T. H. Painter, S. Dangel, and J. V. Martonchik, “Reflectance quantities in optical remote sensingdefinitions and case studies,” Remote Sens. Environ. 103(1), 27–42 (2006).
[Crossref]

L. Guanter, R. Richter, and J. Moreno, “Spectral calibration of hyperspectral imagery using atmospheric absorption features,” Appl. Opt. 45(10), 2360–2370 (2006).
[Crossref] [PubMed]

2005 (1)

B. Mayer and A. Kylling, “Technical note: The libRadtran software package for radiative transfer calculations-description and examples of use,” Atmos. Chem. Phys. 5(7), 1855–1877 (2005).
[Crossref]

2001 (1)

M. S. Moran, R. Bryant, K. Thome, W. Ni, Y. Nouvellon, M. P. Gonzalez-Dugo, J. Qi, and T. R. Clarke, “A refined empirical line approach for reflectance factor retrieval from landsat-5 TM and landsat-7 ETM+,” Remote Sens. Environ. 78(1), 71–82 (2001).
[Crossref]

1999 (2)

G. M. Smith and E. J. Milton, “The use of the empirical line method to calibrate remotely sensed data to reflectance,” Int. J. Remote Sens. 20(13), 2653–2662 (1999).
[Crossref]

C. D. Mobley, “Estimation of the remote-sensing reflectance from above-surface measurements,” Appl. Opt. 38(36),7442–7455 (1999).
[Crossref]

1998 (1)

R. O. Green, M. L. Eastwood, C. M. Sarture, T. G Chrien, M. Aronsson, and B. Chippendale, “Imaging spectroscopy and the airborne visible/infrared imaging spectrometer (AVIRIS),” Remote Sens. Environ. 65(3), 227–248 (1998).
[Crossref]

1997 (1)

E. F. Vermote, D. Tanré, J. L Deuze, M. Herman, and J. J Morcette, “Second simulation of the satellite signal in the solar spectrum, 6s: An overview,” IEEE Trans. Geosci. and Remote Sens. 35(3), 675–686 (1997).
[Crossref]

1995 (1)

P. M. Teillet and G. Fedosejevs, “On the dark target approach to atmospheric correction of remotely sensed data,” Canadian J. Remote Sens. 21(4), 374–387 (1995).
[Crossref]

1994 (1)

Per Christian Hansen, Regularization tools: A MATLAB package for analysis and solution of discrete ill-posed problems, Numerical Algorithms,  6(1):1–35, 1994.
[Crossref]

1993 (1)

B. C. Gao, K. B. Heidebrecht, and A. F. Goetz, “Derivation of scaled surface reflectances from AVIRIS data,” Remote Sens. Environ. 44(2), 165–178 (1993).
[Crossref]

1990 (3)

D. Tanré, C. Deroo, P. Duhaut, M. Herman, J. J. Morcrette, J. Perbos, and P. Y. Deschamps, “Technical note description of a computer code to simulate the satellite signal in the solar spectrum: the 5s code,” Int. J. Remote Sens. 11(4), 659–668 (1990).
[Crossref]

B. C. Gao and A. F. Goetz, “Column atmospheric water vapor and vegetation liquid water retrievals from airborne imaging spectrometer data,” J. Geophys. Res.: Atmos. 95(D4), 3549–3564 (1990).
[Crossref]

E. P. Shettle, “Models of aerosols, clouds and precipitation for atmospheric propagation studies,” Atmospheric propagation in the UV, visible, IR and mm-region and related system aspects,  14(1), 15–32 (1990).

1989 (1)

P. M. Teillet, “Surface reflectance retrieval using atmospheric correction algorithms,” IGARSS Geoscience and Remote Sensing Symposium 2, 864–867 (1989).

1988 (1)

Abreu, L. W.

F. X. Kneizys, E. P. Shettle, L. W. Abreu, J. H. Chetwynd, and G. P. Anderson, “Users guide to LOWTRAN 7,” No. AFGL-TR-88-0177, Air Force Geophysics Lab, Hanscom AFB MA, (1988).

Acharya, P.K.

P.K. Acharya, A. Berk, and G. P. Anderson, “Modtran 5.3.2 user’s manual,” Spectral Sciences, Inc, Burlington, MA (2013).

Adler-Golden, S. M.

M. W. Matthew, S. M. Adler-Golden, A. Berk, G. Felde, G. P. Anderson, D. Gorodetzky, S. Paswaters, and M. Shippert, “Atmospheric correction of spectral imagery: evaluation of the FLAASH algorithm with AVIRIS data,” Appl. Imag. Patt. Recog. Workshop, 157–163 (2002).

Anderson, G. P.

M. W. Matthew, S. M. Adler-Golden, A. Berk, G. Felde, G. P. Anderson, D. Gorodetzky, S. Paswaters, and M. Shippert, “Atmospheric correction of spectral imagery: evaluation of the FLAASH algorithm with AVIRIS data,” Appl. Imag. Patt. Recog. Workshop, 157–163 (2002).

P.K. Acharya, A. Berk, and G. P. Anderson, “Modtran 5.3.2 user’s manual,” Spectral Sciences, Inc, Burlington, MA (2013).

F. X. Kneizys, E. P. Shettle, L. W. Abreu, J. H. Chetwynd, and G. P. Anderson, “Users guide to LOWTRAN 7,” No. AFGL-TR-88-0177, Air Force Geophysics Lab, Hanscom AFB MA, (1988).

Aronsson, M.

R. O. Green, M. L. Eastwood, C. M. Sarture, T. G Chrien, M. Aronsson, and B. Chippendale, “Imaging spectroscopy and the airborne visible/infrared imaging spectrometer (AVIRIS),” Remote Sens. Environ. 65(3), 227–248 (1998).
[Crossref]

Berk, A.

P.K. Acharya, A. Berk, and G. P. Anderson, “Modtran 5.3.2 user’s manual,” Spectral Sciences, Inc, Burlington, MA (2013).

M. W. Matthew, S. M. Adler-Golden, A. Berk, G. Felde, G. P. Anderson, D. Gorodetzky, S. Paswaters, and M. Shippert, “Atmospheric correction of spectral imagery: evaluation of the FLAASH algorithm with AVIRIS data,” Appl. Imag. Patt. Recog. Workshop, 157–163 (2002).

Boardman, J. W.

J. W. Boardman, “Post-ATREM polishing of AVIRIS apparent reflectance data using EFFORT: a lesson in accuracy versus precision,” JPL Airborne Earth Sci. Workshop1(53) (1998).

Bryant, R.

M. S. Moran, R. Bryant, K. Thome, W. Ni, Y. Nouvellon, M. P. Gonzalez-Dugo, J. Qi, and T. R. Clarke, “A refined empirical line approach for reflectance factor retrieval from landsat-5 TM and landsat-7 ETM+,” Remote Sens. Environ. 78(1), 71–82 (2001).
[Crossref]

Chetwynd, J. H.

F. X. Kneizys, E. P. Shettle, L. W. Abreu, J. H. Chetwynd, and G. P. Anderson, “Users guide to LOWTRAN 7,” No. AFGL-TR-88-0177, Air Force Geophysics Lab, Hanscom AFB MA, (1988).

Chippendale, B.

R. O. Green, M. L. Eastwood, C. M. Sarture, T. G Chrien, M. Aronsson, and B. Chippendale, “Imaging spectroscopy and the airborne visible/infrared imaging spectrometer (AVIRIS),” Remote Sens. Environ. 65(3), 227–248 (1998).
[Crossref]

Chrien, T. G

R. O. Green, M. L. Eastwood, C. M. Sarture, T. G Chrien, M. Aronsson, and B. Chippendale, “Imaging spectroscopy and the airborne visible/infrared imaging spectrometer (AVIRIS),” Remote Sens. Environ. 65(3), 227–248 (1998).
[Crossref]

Clark, R.N.

R.N. Clark, G. A Swayze, R. Wise, K E. Livo, T. M Hoefen, R. F. Kokaly, and S. J. Sutley, USGS digital spectral library splib06a (2007).

Clarke, T. R.

M. S. Moran, R. Bryant, K. Thome, W. Ni, Y. Nouvellon, M. P. Gonzalez-Dugo, J. Qi, and T. R. Clarke, “A refined empirical line approach for reflectance factor retrieval from landsat-5 TM and landsat-7 ETM+,” Remote Sens. Environ. 78(1), 71–82 (2001).
[Crossref]

Dangel, S.

G. Schaepman-Strub, M. E. Schaepman, T. H. Painter, S. Dangel, and J. V. Martonchik, “Reflectance quantities in optical remote sensingdefinitions and case studies,” Remote Sens. Environ. 103(1), 27–42 (2006).
[Crossref]

Dennison, P. E.

D. R. Thompson, B. C. Gao, R. O. Green, D. A. Roberts, P. E. Dennison, and S. Lundeen, “Atmospheric correction for global mapping spectroscopy: ATREM advances for the HyspIRI preparatory campaign,” Remote Sens. Environ. 167, 64–77 (2015).
[Crossref]

Deroo, C.

D. Tanré, C. Deroo, P. Duhaut, M. Herman, J. J. Morcrette, J. Perbos, and P. Y. Deschamps, “Technical note description of a computer code to simulate the satellite signal in the solar spectrum: the 5s code,” Int. J. Remote Sens. 11(4), 659–668 (1990).
[Crossref]

Deschamps, P. Y.

D. Tanré, C. Deroo, P. Duhaut, M. Herman, J. J. Morcrette, J. Perbos, and P. Y. Deschamps, “Technical note description of a computer code to simulate the satellite signal in the solar spectrum: the 5s code,” Int. J. Remote Sens. 11(4), 659–668 (1990).
[Crossref]

Deuze, J. L

E. F. Vermote, D. Tanré, J. L Deuze, M. Herman, and J. J Morcette, “Second simulation of the satellite signal in the solar spectrum, 6s: An overview,” IEEE Trans. Geosci. and Remote Sens. 35(3), 675–686 (1997).
[Crossref]

Duhaut, P.

D. Tanré, C. Deroo, P. Duhaut, M. Herman, J. J. Morcrette, J. Perbos, and P. Y. Deschamps, “Technical note description of a computer code to simulate the satellite signal in the solar spectrum: the 5s code,” Int. J. Remote Sens. 11(4), 659–668 (1990).
[Crossref]

Eastwood, M. L.

R. O. Green, M. L. Eastwood, C. M. Sarture, T. G Chrien, M. Aronsson, and B. Chippendale, “Imaging spectroscopy and the airborne visible/infrared imaging spectrometer (AVIRIS),” Remote Sens. Environ. 65(3), 227–248 (1998).
[Crossref]

Fedosejevs, G.

P. M. Teillet and G. Fedosejevs, “On the dark target approach to atmospheric correction of remotely sensed data,” Canadian J. Remote Sens. 21(4), 374–387 (1995).
[Crossref]

Felde, G.

M. W. Matthew, S. M. Adler-Golden, A. Berk, G. Felde, G. P. Anderson, D. Gorodetzky, S. Paswaters, and M. Shippert, “Atmospheric correction of spectral imagery: evaluation of the FLAASH algorithm with AVIRIS data,” Appl. Imag. Patt. Recog. Workshop, 157–163 (2002).

Frouin, R.

R. Frouin and B. Pelletier, “Bayesian methodology for inverting satellite ocean-color data,” Remote Sens. Environ. 159, 332–360 (2015).
[Crossref]

Gao, B. C.

D. R. Thompson, B. C. Gao, R. O. Green, D. A. Roberts, P. E. Dennison, and S. Lundeen, “Atmospheric correction for global mapping spectroscopy: ATREM advances for the HyspIRI preparatory campaign,” Remote Sens. Environ. 167, 64–77 (2015).
[Crossref]

D. R. Thompson, F. C. Seidel, B. C. Gao, M. M. Gierach, R. O. Green, R. M. Kudela, and P. Mouroulis, “Optimizing irradiance estimates for coastal and inland water imaging spectroscopy,” Geophys. Res. Lett. 42(10), 4116–4123 (2015). 2015GL063287.
[Crossref]

B. C. Gao and M. Liu, “A fast smoothing algorithm for post-processing of surface reflectance spectra retrieved from airborne imaging spectrometer data,” Sensors 13(10), 13879–13891 (2013).
[Crossref] [PubMed]

B. C. Gao, K. B. Heidebrecht, and A. F. Goetz, “Derivation of scaled surface reflectances from AVIRIS data,” Remote Sens. Environ. 44(2), 165–178 (1993).
[Crossref]

B. C. Gao and A. F. Goetz, “Column atmospheric water vapor and vegetation liquid water retrievals from airborne imaging spectrometer data,” J. Geophys. Res.: Atmos. 95(D4), 3549–3564 (1990).
[Crossref]

Gierach, M. M.

D. R. Thompson, F. C. Seidel, B. C. Gao, M. M. Gierach, R. O. Green, R. M. Kudela, and P. Mouroulis, “Optimizing irradiance estimates for coastal and inland water imaging spectroscopy,” Geophys. Res. Lett. 42(10), 4116–4123 (2015). 2015GL063287.
[Crossref]

Goetz, A. F.

B. C. Gao, K. B. Heidebrecht, and A. F. Goetz, “Derivation of scaled surface reflectances from AVIRIS data,” Remote Sens. Environ. 44(2), 165–178 (1993).
[Crossref]

B. C. Gao and A. F. Goetz, “Column atmospheric water vapor and vegetation liquid water retrievals from airborne imaging spectrometer data,” J. Geophys. Res.: Atmos. 95(D4), 3549–3564 (1990).
[Crossref]

Gonzalez-Dugo, M. P.

M. S. Moran, R. Bryant, K. Thome, W. Ni, Y. Nouvellon, M. P. Gonzalez-Dugo, J. Qi, and T. R. Clarke, “A refined empirical line approach for reflectance factor retrieval from landsat-5 TM and landsat-7 ETM+,” Remote Sens. Environ. 78(1), 71–82 (2001).
[Crossref]

Gorodetzky, D.

M. W. Matthew, S. M. Adler-Golden, A. Berk, G. Felde, G. P. Anderson, D. Gorodetzky, S. Paswaters, and M. Shippert, “Atmospheric correction of spectral imagery: evaluation of the FLAASH algorithm with AVIRIS data,” Appl. Imag. Patt. Recog. Workshop, 157–163 (2002).

Green, R. O.

D. R. Thompson, B. C. Gao, R. O. Green, D. A. Roberts, P. E. Dennison, and S. Lundeen, “Atmospheric correction for global mapping spectroscopy: ATREM advances for the HyspIRI preparatory campaign,” Remote Sens. Environ. 167, 64–77 (2015).
[Crossref]

D. R. Thompson, F. C. Seidel, B. C. Gao, M. M. Gierach, R. O. Green, R. M. Kudela, and P. Mouroulis, “Optimizing irradiance estimates for coastal and inland water imaging spectroscopy,” Geophys. Res. Lett. 42(10), 4116–4123 (2015). 2015GL063287.
[Crossref]

R. O. Green, M. L. Eastwood, C. M. Sarture, T. G Chrien, M. Aronsson, and B. Chippendale, “Imaging spectroscopy and the airborne visible/infrared imaging spectrometer (AVIRIS),” Remote Sens. Environ. 65(3), 227–248 (1998).
[Crossref]

Guanter, L.

Heidebrecht, K. B.

B. C. Gao, K. B. Heidebrecht, and A. F. Goetz, “Derivation of scaled surface reflectances from AVIRIS data,” Remote Sens. Environ. 44(2), 165–178 (1993).
[Crossref]

Herman, M.

E. F. Vermote, D. Tanré, J. L Deuze, M. Herman, and J. J Morcette, “Second simulation of the satellite signal in the solar spectrum, 6s: An overview,” IEEE Trans. Geosci. and Remote Sens. 35(3), 675–686 (1997).
[Crossref]

D. Tanré, C. Deroo, P. Duhaut, M. Herman, J. J. Morcrette, J. Perbos, and P. Y. Deschamps, “Technical note description of a computer code to simulate the satellite signal in the solar spectrum: the 5s code,” Int. J. Remote Sens. 11(4), 659–668 (1990).
[Crossref]

Hoefen, T. M

R.N. Clark, G. A Swayze, R. Wise, K E. Livo, T. M Hoefen, R. F. Kokaly, and S. J. Sutley, USGS digital spectral library splib06a (2007).

Jayaweera, K.

Kneizys, F. X.

F. X. Kneizys, E. P. Shettle, L. W. Abreu, J. H. Chetwynd, and G. P. Anderson, “Users guide to LOWTRAN 7,” No. AFGL-TR-88-0177, Air Force Geophysics Lab, Hanscom AFB MA, (1988).

Kokaly, R. F.

R.N. Clark, G. A Swayze, R. Wise, K E. Livo, T. M Hoefen, R. F. Kokaly, and S. J. Sutley, USGS digital spectral library splib06a (2007).

Kudela, R. M.

D. R. Thompson, F. C. Seidel, B. C. Gao, M. M. Gierach, R. O. Green, R. M. Kudela, and P. Mouroulis, “Optimizing irradiance estimates for coastal and inland water imaging spectroscopy,” Geophys. Res. Lett. 42(10), 4116–4123 (2015). 2015GL063287.
[Crossref]

Kylling, A.

B. Mayer and A. Kylling, “Technical note: The libRadtran software package for radiative transfer calculations-description and examples of use,” Atmos. Chem. Phys. 5(7), 1855–1877 (2005).
[Crossref]

Liu, M.

B. C. Gao and M. Liu, “A fast smoothing algorithm for post-processing of surface reflectance spectra retrieved from airborne imaging spectrometer data,” Sensors 13(10), 13879–13891 (2013).
[Crossref] [PubMed]

Livo, K E.

R.N. Clark, G. A Swayze, R. Wise, K E. Livo, T. M Hoefen, R. F. Kokaly, and S. J. Sutley, USGS digital spectral library splib06a (2007).

Lundeen, S.

D. R. Thompson, B. C. Gao, R. O. Green, D. A. Roberts, P. E. Dennison, and S. Lundeen, “Atmospheric correction for global mapping spectroscopy: ATREM advances for the HyspIRI preparatory campaign,” Remote Sens. Environ. 167, 64–77 (2015).
[Crossref]

Martonchik, J. V.

G. Schaepman-Strub, M. E. Schaepman, T. H. Painter, S. Dangel, and J. V. Martonchik, “Reflectance quantities in optical remote sensingdefinitions and case studies,” Remote Sens. Environ. 103(1), 27–42 (2006).
[Crossref]

Matthew, M. W.

M. W. Matthew, S. M. Adler-Golden, A. Berk, G. Felde, G. P. Anderson, D. Gorodetzky, S. Paswaters, and M. Shippert, “Atmospheric correction of spectral imagery: evaluation of the FLAASH algorithm with AVIRIS data,” Appl. Imag. Patt. Recog. Workshop, 157–163 (2002).

Mayer, B.

B. Mayer and A. Kylling, “Technical note: The libRadtran software package for radiative transfer calculations-description and examples of use,” Atmos. Chem. Phys. 5(7), 1855–1877 (2005).
[Crossref]

Mead, J. L.

J. L. Mead, “A priori weighting for parameter estimation,” J. Inverse Ill-posed Problems 16(2), 175–193 (2008).
[Crossref]

Milton, E. J.

G. M. Smith and E. J. Milton, “The use of the empirical line method to calibrate remotely sensed data to reflectance,” Int. J. Remote Sens. 20(13), 2653–2662 (1999).
[Crossref]

Mobley, C. D.

Moran, M. S.

M. S. Moran, R. Bryant, K. Thome, W. Ni, Y. Nouvellon, M. P. Gonzalez-Dugo, J. Qi, and T. R. Clarke, “A refined empirical line approach for reflectance factor retrieval from landsat-5 TM and landsat-7 ETM+,” Remote Sens. Environ. 78(1), 71–82 (2001).
[Crossref]

Morcette, J. J

E. F. Vermote, D. Tanré, J. L Deuze, M. Herman, and J. J Morcette, “Second simulation of the satellite signal in the solar spectrum, 6s: An overview,” IEEE Trans. Geosci. and Remote Sens. 35(3), 675–686 (1997).
[Crossref]

Morcrette, J. J.

D. Tanré, C. Deroo, P. Duhaut, M. Herman, J. J. Morcrette, J. Perbos, and P. Y. Deschamps, “Technical note description of a computer code to simulate the satellite signal in the solar spectrum: the 5s code,” Int. J. Remote Sens. 11(4), 659–668 (1990).
[Crossref]

Moreno, J.

Mouroulis, P.

D. R. Thompson, F. C. Seidel, B. C. Gao, M. M. Gierach, R. O. Green, R. M. Kudela, and P. Mouroulis, “Optimizing irradiance estimates for coastal and inland water imaging spectroscopy,” Geophys. Res. Lett. 42(10), 4116–4123 (2015). 2015GL063287.
[Crossref]

Ni, W.

M. S. Moran, R. Bryant, K. Thome, W. Ni, Y. Nouvellon, M. P. Gonzalez-Dugo, J. Qi, and T. R. Clarke, “A refined empirical line approach for reflectance factor retrieval from landsat-5 TM and landsat-7 ETM+,” Remote Sens. Environ. 78(1), 71–82 (2001).
[Crossref]

Nouvellon, Y.

M. S. Moran, R. Bryant, K. Thome, W. Ni, Y. Nouvellon, M. P. Gonzalez-Dugo, J. Qi, and T. R. Clarke, “A refined empirical line approach for reflectance factor retrieval from landsat-5 TM and landsat-7 ETM+,” Remote Sens. Environ. 78(1), 71–82 (2001).
[Crossref]

Painter, T. H.

G. Schaepman-Strub, M. E. Schaepman, T. H. Painter, S. Dangel, and J. V. Martonchik, “Reflectance quantities in optical remote sensingdefinitions and case studies,” Remote Sens. Environ. 103(1), 27–42 (2006).
[Crossref]

Paswaters, S.

M. W. Matthew, S. M. Adler-Golden, A. Berk, G. Felde, G. P. Anderson, D. Gorodetzky, S. Paswaters, and M. Shippert, “Atmospheric correction of spectral imagery: evaluation of the FLAASH algorithm with AVIRIS data,” Appl. Imag. Patt. Recog. Workshop, 157–163 (2002).

Pelletier, B.

R. Frouin and B. Pelletier, “Bayesian methodology for inverting satellite ocean-color data,” Remote Sens. Environ. 159, 332–360 (2015).
[Crossref]

Perbos, J.

D. Tanré, C. Deroo, P. Duhaut, M. Herman, J. J. Morcrette, J. Perbos, and P. Y. Deschamps, “Technical note description of a computer code to simulate the satellite signal in the solar spectrum: the 5s code,” Int. J. Remote Sens. 11(4), 659–668 (1990).
[Crossref]

Qi, J.

M. S. Moran, R. Bryant, K. Thome, W. Ni, Y. Nouvellon, M. P. Gonzalez-Dugo, J. Qi, and T. R. Clarke, “A refined empirical line approach for reflectance factor retrieval from landsat-5 TM and landsat-7 ETM+,” Remote Sens. Environ. 78(1), 71–82 (2001).
[Crossref]

Richter, R.

L. Guanter, R. Richter, and J. Moreno, “Spectral calibration of hyperspectral imagery using atmospheric absorption features,” Appl. Opt. 45(10), 2360–2370 (2006).
[Crossref] [PubMed]

R. Richter and D. Schlapfer, “Atmospheric/topographic correction for satellite imagery,” DLR report DLR-IB, 565–601 (2005).

Roberts, D. A.

D. R. Thompson, B. C. Gao, R. O. Green, D. A. Roberts, P. E. Dennison, and S. Lundeen, “Atmospheric correction for global mapping spectroscopy: ATREM advances for the HyspIRI preparatory campaign,” Remote Sens. Environ. 167, 64–77 (2015).
[Crossref]

Sarture, C. M.

R. O. Green, M. L. Eastwood, C. M. Sarture, T. G Chrien, M. Aronsson, and B. Chippendale, “Imaging spectroscopy and the airborne visible/infrared imaging spectrometer (AVIRIS),” Remote Sens. Environ. 65(3), 227–248 (1998).
[Crossref]

Schaepman, M. E.

G. Schaepman-Strub, M. E. Schaepman, T. H. Painter, S. Dangel, and J. V. Martonchik, “Reflectance quantities in optical remote sensingdefinitions and case studies,” Remote Sens. Environ. 103(1), 27–42 (2006).
[Crossref]

Schaepman-Strub, G.

G. Schaepman-Strub, M. E. Schaepman, T. H. Painter, S. Dangel, and J. V. Martonchik, “Reflectance quantities in optical remote sensingdefinitions and case studies,” Remote Sens. Environ. 103(1), 27–42 (2006).
[Crossref]

Schlapfer, D.

R. Richter and D. Schlapfer, “Atmospheric/topographic correction for satellite imagery,” DLR report DLR-IB, 565–601 (2005).

Seidel, F. C.

D. R. Thompson, F. C. Seidel, B. C. Gao, M. M. Gierach, R. O. Green, R. M. Kudela, and P. Mouroulis, “Optimizing irradiance estimates for coastal and inland water imaging spectroscopy,” Geophys. Res. Lett. 42(10), 4116–4123 (2015). 2015GL063287.
[Crossref]

Shettle, E. P.

E. P. Shettle, “Models of aerosols, clouds and precipitation for atmospheric propagation studies,” Atmospheric propagation in the UV, visible, IR and mm-region and related system aspects,  14(1), 15–32 (1990).

F. X. Kneizys, E. P. Shettle, L. W. Abreu, J. H. Chetwynd, and G. P. Anderson, “Users guide to LOWTRAN 7,” No. AFGL-TR-88-0177, Air Force Geophysics Lab, Hanscom AFB MA, (1988).

Shippert, M.

M. W. Matthew, S. M. Adler-Golden, A. Berk, G. Felde, G. P. Anderson, D. Gorodetzky, S. Paswaters, and M. Shippert, “Atmospheric correction of spectral imagery: evaluation of the FLAASH algorithm with AVIRIS data,” Appl. Imag. Patt. Recog. Workshop, 157–163 (2002).

Smith, G. M.

G. M. Smith and E. J. Milton, “The use of the empirical line method to calibrate remotely sensed data to reflectance,” Int. J. Remote Sens. 20(13), 2653–2662 (1999).
[Crossref]

Stamnes, K.

Sutley, S. J.

R.N. Clark, G. A Swayze, R. Wise, K E. Livo, T. M Hoefen, R. F. Kokaly, and S. J. Sutley, USGS digital spectral library splib06a (2007).

Swayze, G. A

R.N. Clark, G. A Swayze, R. Wise, K E. Livo, T. M Hoefen, R. F. Kokaly, and S. J. Sutley, USGS digital spectral library splib06a (2007).

Tanré, D.

E. F. Vermote, D. Tanré, J. L Deuze, M. Herman, and J. J Morcette, “Second simulation of the satellite signal in the solar spectrum, 6s: An overview,” IEEE Trans. Geosci. and Remote Sens. 35(3), 675–686 (1997).
[Crossref]

D. Tanré, C. Deroo, P. Duhaut, M. Herman, J. J. Morcrette, J. Perbos, and P. Y. Deschamps, “Technical note description of a computer code to simulate the satellite signal in the solar spectrum: the 5s code,” Int. J. Remote Sens. 11(4), 659–668 (1990).
[Crossref]

Teillet, P. M.

P. M. Teillet and G. Fedosejevs, “On the dark target approach to atmospheric correction of remotely sensed data,” Canadian J. Remote Sens. 21(4), 374–387 (1995).
[Crossref]

P. M. Teillet, “Surface reflectance retrieval using atmospheric correction algorithms,” IGARSS Geoscience and Remote Sensing Symposium 2, 864–867 (1989).

Thome, K.

M. S. Moran, R. Bryant, K. Thome, W. Ni, Y. Nouvellon, M. P. Gonzalez-Dugo, J. Qi, and T. R. Clarke, “A refined empirical line approach for reflectance factor retrieval from landsat-5 TM and landsat-7 ETM+,” Remote Sens. Environ. 78(1), 71–82 (2001).
[Crossref]

Thompson, D. R.

D. R. Thompson, B. C. Gao, R. O. Green, D. A. Roberts, P. E. Dennison, and S. Lundeen, “Atmospheric correction for global mapping spectroscopy: ATREM advances for the HyspIRI preparatory campaign,” Remote Sens. Environ. 167, 64–77 (2015).
[Crossref]

D. R. Thompson, F. C. Seidel, B. C. Gao, M. M. Gierach, R. O. Green, R. M. Kudela, and P. Mouroulis, “Optimizing irradiance estimates for coastal and inland water imaging spectroscopy,” Geophys. Res. Lett. 42(10), 4116–4123 (2015). 2015GL063287.
[Crossref]

Tsay, S.-Chee

Vermote, E. F.

E. F. Vermote, D. Tanré, J. L Deuze, M. Herman, and J. J Morcette, “Second simulation of the satellite signal in the solar spectrum, 6s: An overview,” IEEE Trans. Geosci. and Remote Sens. 35(3), 675–686 (1997).
[Crossref]

Wiscombe, W.

Wise, R.

R.N. Clark, G. A Swayze, R. Wise, K E. Livo, T. M Hoefen, R. F. Kokaly, and S. J. Sutley, USGS digital spectral library splib06a (2007).

Appl. Opt. (3)

Atmos. Chem. Phys. (1)

B. Mayer and A. Kylling, “Technical note: The libRadtran software package for radiative transfer calculations-description and examples of use,” Atmos. Chem. Phys. 5(7), 1855–1877 (2005).
[Crossref]

Atmospheric propagation in the UV, visible, IR and mm-region and related system aspects (1)

E. P. Shettle, “Models of aerosols, clouds and precipitation for atmospheric propagation studies,” Atmospheric propagation in the UV, visible, IR and mm-region and related system aspects,  14(1), 15–32 (1990).

Canadian J. Remote Sens. (1)

P. M. Teillet and G. Fedosejevs, “On the dark target approach to atmospheric correction of remotely sensed data,” Canadian J. Remote Sens. 21(4), 374–387 (1995).
[Crossref]

Geophys. Res. Lett. (1)

D. R. Thompson, F. C. Seidel, B. C. Gao, M. M. Gierach, R. O. Green, R. M. Kudela, and P. Mouroulis, “Optimizing irradiance estimates for coastal and inland water imaging spectroscopy,” Geophys. Res. Lett. 42(10), 4116–4123 (2015). 2015GL063287.
[Crossref]

IEEE Trans. Geosci. and Remote Sens. (1)

E. F. Vermote, D. Tanré, J. L Deuze, M. Herman, and J. J Morcette, “Second simulation of the satellite signal in the solar spectrum, 6s: An overview,” IEEE Trans. Geosci. and Remote Sens. 35(3), 675–686 (1997).
[Crossref]

IGARSS Geoscience and Remote Sensing Symposium (1)

P. M. Teillet, “Surface reflectance retrieval using atmospheric correction algorithms,” IGARSS Geoscience and Remote Sensing Symposium 2, 864–867 (1989).

Int. J. Remote Sens. (2)

D. Tanré, C. Deroo, P. Duhaut, M. Herman, J. J. Morcrette, J. Perbos, and P. Y. Deschamps, “Technical note description of a computer code to simulate the satellite signal in the solar spectrum: the 5s code,” Int. J. Remote Sens. 11(4), 659–668 (1990).
[Crossref]

G. M. Smith and E. J. Milton, “The use of the empirical line method to calibrate remotely sensed data to reflectance,” Int. J. Remote Sens. 20(13), 2653–2662 (1999).
[Crossref]

J. Geophys. Res.: Atmos. (1)

B. C. Gao and A. F. Goetz, “Column atmospheric water vapor and vegetation liquid water retrievals from airborne imaging spectrometer data,” J. Geophys. Res.: Atmos. 95(D4), 3549–3564 (1990).
[Crossref]

J. Inverse Ill-posed Problems (1)

J. L. Mead, “A priori weighting for parameter estimation,” J. Inverse Ill-posed Problems 16(2), 175–193 (2008).
[Crossref]

Numerical Algorithms (1)

Per Christian Hansen, Regularization tools: A MATLAB package for analysis and solution of discrete ill-posed problems, Numerical Algorithms,  6(1):1–35, 1994.
[Crossref]

Remote Sens. Environ. (6)

M. S. Moran, R. Bryant, K. Thome, W. Ni, Y. Nouvellon, M. P. Gonzalez-Dugo, J. Qi, and T. R. Clarke, “A refined empirical line approach for reflectance factor retrieval from landsat-5 TM and landsat-7 ETM+,” Remote Sens. Environ. 78(1), 71–82 (2001).
[Crossref]

R. Frouin and B. Pelletier, “Bayesian methodology for inverting satellite ocean-color data,” Remote Sens. Environ. 159, 332–360 (2015).
[Crossref]

R. O. Green, M. L. Eastwood, C. M. Sarture, T. G Chrien, M. Aronsson, and B. Chippendale, “Imaging spectroscopy and the airborne visible/infrared imaging spectrometer (AVIRIS),” Remote Sens. Environ. 65(3), 227–248 (1998).
[Crossref]

B. C. Gao, K. B. Heidebrecht, and A. F. Goetz, “Derivation of scaled surface reflectances from AVIRIS data,” Remote Sens. Environ. 44(2), 165–178 (1993).
[Crossref]

D. R. Thompson, B. C. Gao, R. O. Green, D. A. Roberts, P. E. Dennison, and S. Lundeen, “Atmospheric correction for global mapping spectroscopy: ATREM advances for the HyspIRI preparatory campaign,” Remote Sens. Environ. 167, 64–77 (2015).
[Crossref]

G. Schaepman-Strub, M. E. Schaepman, T. H. Painter, S. Dangel, and J. V. Martonchik, “Reflectance quantities in optical remote sensingdefinitions and case studies,” Remote Sens. Environ. 103(1), 27–42 (2006).
[Crossref]

Sensors (1)

B. C. Gao and M. Liu, “A fast smoothing algorithm for post-processing of surface reflectance spectra retrieved from airborne imaging spectrometer data,” Sensors 13(10), 13879–13891 (2013).
[Crossref] [PubMed]

Other (6)

J. W. Boardman, “Post-ATREM polishing of AVIRIS apparent reflectance data using EFFORT: a lesson in accuracy versus precision,” JPL Airborne Earth Sci. Workshop1(53) (1998).

R. Richter and D. Schlapfer, “Atmospheric/topographic correction for satellite imagery,” DLR report DLR-IB, 565–601 (2005).

M. W. Matthew, S. M. Adler-Golden, A. Berk, G. Felde, G. P. Anderson, D. Gorodetzky, S. Paswaters, and M. Shippert, “Atmospheric correction of spectral imagery: evaluation of the FLAASH algorithm with AVIRIS data,” Appl. Imag. Patt. Recog. Workshop, 157–163 (2002).

P.K. Acharya, A. Berk, and G. P. Anderson, “Modtran 5.3.2 user’s manual,” Spectral Sciences, Inc, Burlington, MA (2013).

F. X. Kneizys, E. P. Shettle, L. W. Abreu, J. H. Chetwynd, and G. P. Anderson, “Users guide to LOWTRAN 7,” No. AFGL-TR-88-0177, Air Force Geophysics Lab, Hanscom AFB MA, (1988).

R.N. Clark, G. A Swayze, R. Wise, K E. Livo, T. M Hoefen, R. F. Kokaly, and S. J. Sutley, USGS digital spectral library splib06a (2007).

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Figures (6)

Fig. 1
Fig. 1

Performance as a function of the regularization factor δ and number of reference spectra. The empirical solution is favorable as more reference spectra become available.

Fig. 2
Fig. 2

DISORT simulations compare multiple correction methods: the traditional empirical line (EL); the refined empirical line of [20] (REL); spectral polishing (SP); and the Bayesian empirical line correction (BEL). Arrowheads indicate 1-σ error bars and/or performance means that lie outside the chart.

Fig. 3
Fig. 3

The reference spectra in our AVIRIS-C study lie in a large flightlines transecting part of the US state of California.

Fig. 4
Fig. 4

Reference spectra used in the terrestrial AVIRIS-C evaluation. (a) Bright surface (b) Bare rock (c) Bare rock (d) Roof (e) Boat ramp (f) Church parking lot (g) Soccer field (h) USDA parking lot.

Fig. 5
Fig. 5

Example spectrum of a bare rock surface, before and after correction, compared with a held out in situ measurement not used in testing. The correction removes some roughness in the original spectrum while and aligns the slope of the reflectance shape.

Fig. 6
Fig. 6

Performance of multiple methods for AVIRIS-C data: the traditional empirical line (EL); the refined empirical line of [20] (REL); spectral polishing (SP); and the Bayesian empirical line correction (BEL). Convergence rates resemble Fig. 2.

Tables (1)

Tables Icon

Table 1 Mathematical notation

Equations (9)

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ρ 0 = π L F cos ( ψ ) = ρ a + T ρ 1 ρ S
x EL = arg min x ( Ax t 2 ) = ( A T A ) 1 A T t
ρ ^ i = B i μ T = [ 1 , ω i ] [ 0 , 1 ] T
Q = [ η o 2 0 0 η g 2 ] 1 P = [ η m 2 0 0 0 0 η m 2 ] 1
p ( ρ i , x | θ ) p ( ρ i | x , θ ) p ( x | θ ) p ( ρ i | x ) p ( x | θ ) log p ( ρ i , x | θ ) z 1 ( Bx t ) T P ( Bx t ) z 2 ( x μ ) T Q ( x μ )
x BEL = arg min x ( Bx t P 2 + x μ Q 2 )
x BEL = μ + ( B T PB + Q ) 1 B T P ( t B μ )
ϕ s g = N ( 1 , γ s g 2 ) ϕ s o = N ( 0 , γ s o 2 )
L s j = L s j N ( ϕ s g , γ j g 2 ) + N ( ϕ s o , γ j o 2 )

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