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Quantitative Remote Sensing Inversion in Earth Science: Theory and Numerical Treatment

  • Yanfei  Wang
Living reference work entry

Abstract

Quantitative remote sensing is an appropriate way to estimate structural parameters and spectral component signatures of Earth surface cover type. Since the real physical system that couples the atmosphere, water, and the land surface is very complicated and should be a continuous process, sometimes it requires a comprehensive set of parameters to describe such a system, so any practical physical model can only be approximated by a mathematical model which includes only a limited number of the most important parameters that capture the major variation of the real system. The pivot problem for quantitative remote sensing is the inversion. Inverse problems are typically ill-posed. The ill-posed nature is characterized by (C1) the solution may not exist, (C2) the dimension of the solution space may be infinite, and (C3) the solution is not continuous with variations of the observed signals. These issues exist nearly for all inverse problems in geoscience and quantitative remote sensing. For example, when the observation system is band-limited or sampling is poor, i.e., there are too few observations, or directions are poor located, the inversion process would be underdetermined, which leads to the large condition number of the normalized system and the significant noise propagation. Hence (C2) and (C3) would be the highlight difficulties for quantitative remote sensing inversion. This chapter will address the theory and methods from the viewpoint that the quantitative remote sensing inverse problems can be represented by kernel-based operator equations and solved by coupling regularization and optimization methods.

Keywords

Inverse Problem Tikhonov Regularization Size Distribution Function Trust Region Method Aerosol Optical Thickness 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

This research is supported by National “973” Key Basic Research Developments Program of China under grant numbers 2007CB714400, National Natural Science Foundation of China (NSFC) under grant numbers 10871191 and 40974075, and Knowledge Innovation Programs of Chinese Academy of Sciences KZCX2-YW-QN107.

References

  1. Ångström A (1929) On the atmospheric transmission of sun radiation and on dust in the air. Geogr Ann 11:156–166Google Scholar
  2. Barzilai J, Borwein J (1988) Two-point step size gradient methods. IMA J Numer Anal 8:141–148CrossRefzbMATHMathSciNetGoogle Scholar
  3. Bockmann C (2001) Hybrid regularization method for the ill-posed inversion of multiwavelength lidar data in the retrieval of aerosol size distributions. Appl Opt 40:1329–1342CrossRefGoogle Scholar
  4. Bockmann C, Kirsche A (2006) Iterative regularization method for lidar remote sensing. Comput Phys Commun 174:607–615CrossRefGoogle Scholar
  5. Bohren GF, Huffman DR (1983) Absorption and scattering of light by small particles. Wiley, New YorkGoogle Scholar
  6. Brakhage H (1987) On ill-posed problems and the method of conjugate gradients. In: Engl HW, Groetsch CW (eds) Inverse and ill-posed problems. Academic, Boston, pp 165–175CrossRefGoogle Scholar
  7. Camps-Valls G (2008) New machine-learning paradigm provides advantages for remote sensing. SPIE Newsroom. doi:10.1117/2.1200806. 1100Google Scholar
  8. Davies CN (1974) Size distribution of atmospheric aerosol. J Aerosol Sci 5:293–300CrossRefGoogle Scholar
  9. Dennis JE, Schnable RB (1983) Numerical methods for unconstrained optimization and nonlinear equations. Prentice Hall, Englewood CliffszbMATHGoogle Scholar
  10. Fletcher R (2001) On the Barzilai-Borwein method. Numerical Analysis report NA/207Google Scholar
  11. Houghton JT, Meira Filho LG, Callander BA, Harris N, Kattenberg A, Maskell K (1966) Climate change 1995. Published for the Intergovernmental Panel on Climate Change, Cambridge University PressGoogle Scholar
  12. Junge CE (1955) The size distribution and aging of natural aerosols as determined from electrical and optical data on the atmosphere. J Meteorol 12:13–25CrossRefGoogle Scholar
  13. Kelley CT (1999) Iterative methods for optimization. SIAM, PhiladelphiaCrossRefzbMATHGoogle Scholar
  14. King MD, Byrne DM, Herman BM, Reagan JA (1978) Aerosol size distributions obtained by inversion of spectral optical depth measurements. J Aerosol Sci 35:2153–2167Google Scholar
  15. Li X, Wang J, Hu B, Strahler AH (1998) On utilization of a priori knowledge in inversion of remote sensing models. Sci China D 41:580–585CrossRefGoogle Scholar
  16. Li X, Wang J, Strahler AH (1999) Apparent reciprocal failure in BRDF of structured surfaces. Prog Nat Sci 9:747–750Google Scholar
  17. Li X, Gao F, Liu Q, Wang JD, Strahler AH (2000) Validation of a new GO kernel and inversion of land surface albedo by kernel-driven model (1). J Remote Sens 4:1–7zbMATHGoogle Scholar
  18. Li X, Gao F, Wang J, Strahler AH (2001) A priori knowledge accumulation and its application to linear BRDF model inversion. J Geophys Res 106:11925–11935CrossRefGoogle Scholar
  19. Mccartney GJ (1976) Optics of atmosphere. Wiley, New YorkGoogle Scholar
  20. Nguyen T, Cox K (1989) A method for the determination of aerosol particle distributions from light extinction data. In: Abstracts of the American association for aerosol research annual meeting, American Association of Aerosol Research, Cincinnati, pp 330–330Google Scholar
  21. Nocedal J (1980) Updating quasi-Newton matrices with limited storage. Math Comput 95:339–353MathSciNetGoogle Scholar
  22. Phillips DL (1962) A technique for the numerical solution of certain integral equations of the first kind. J Assoc Comput Mach 9:84–97CrossRefzbMATHMathSciNetGoogle Scholar
  23. Pokrovsky O, Roujean JL (2002) Land surface albedo retrieval via kernel-based BRDF modeling: I. Statistical inversion method and model comparison. Remote Sens Environ 84:100–119CrossRefGoogle Scholar
  24. Pokrovsky OM, Roujean JL (2003) Land surface albedo retrieval via kernel-based BRDF modeling: II. An optimal design scheme for the angular sampling. Remote Sens Environ 84:120–142CrossRefGoogle Scholar
  25. Pokrovsky IO, Pokrovsky OM, Roujean JL (2003) Development of an operational procedure to estimate surface albedo from the SEVIRI/MSG observing system by using POLDER BRDF measurements: II. Comparison of several inversion techniques and uncertainty in albedo estimates. Remote Sens Environ 87:215–242CrossRefGoogle Scholar
  26. Privette JL, Eck TF, Deering DW (1997) Estimating spectral albedo and nadir reflectance through inversion of simple bidirectional reflectance distribution models with AVHRR/MODIS-like data. J Geophys Res 102:29529–29542CrossRefGoogle Scholar
  27. Roujean JL, Leroy M, Deschamps PY (1992) A bidirectional reflectance model of the Earth’s surface for the correction of remote sensing data. J Geophys Res 97:20455–20468CrossRefGoogle Scholar
  28. Strahler AH, Li XW, Liang S, Muller J-P, Barnsley MJ, Lewis P (1994) MODIS BRDF/albedo product: algorithm technical basis document. NASA EOS-MODIS Doc. 2.1Google Scholar
  29. Strahler AH, Lucht W, Schaaf CB, Tsang T, Gao F, Li X, Muller JP, Lewis P, Barnsley MJ (1999) MODIS BRDF/albedo product: algorithm theoretical basis document. NASA EOS-MODIS Doc. 5.0Google Scholar
  30. Tikhonov AN, Arsenin VY (1977) Solutions of ill-posed problems. Wiley, New YorkzbMATHGoogle Scholar
  31. Tikhonov AN, Goncharsky AV, Stepanov VV, Yagola AG (1995) Numerical methods for the solution of ill-posed problems. Kluwer, DordrechtCrossRefzbMATHGoogle Scholar
  32. Twomey S (1975) Comparison of constrained linear inversion and an iterative nonlinear algorithm applied to the indirect estimation of particle size distributions. J Comput Phys 18:188–200CrossRefGoogle Scholar
  33. Twomey S (1977) Atmospheric aerosols. Elsevier, AmsterdamGoogle Scholar
  34. Verstraete MM, Pinty B, Myneny RB (1996) Potential and limitations of information extraction on the terrestrial biosphere from satellite remote sensing. Remote Sens Environ 58:201–214CrossRefGoogle Scholar
  35. Voutilainenand A, Kaipio JP (2000) Statistical inversion of aerosol size distribution data. J Aerosol Sci 31:767–768CrossRefGoogle Scholar
  36. Wagner W, Ullrich A, Ducic V, Melzer T, Studnicka N (2006) Gaussian decomposition and calibration of a novel small-footprint full-waveform digitising airborne laser scanner. ISPRS J Photogram Remote Sens 60:100–112CrossRefGoogle Scholar
  37. Wang YF (2007) Computational methods for inverse problems and their applications. Higher Education Press, BeijingGoogle Scholar
  38. Wang YF (2008) An efficient gradient method for maximum entropy regularizing retrieval of atmospheric aerosol particle size distribution function. J Aerosol Sci 39:305–322CrossRefGoogle Scholar
  39. Wang YF, Ma SQ (2007) Projected Barzilai-Borwein methods for large scale nonnegative image restorations. Inverse Probl Sci Eng 15:559–583CrossRefzbMATHMathSciNetGoogle Scholar
  40. Wang YF, Ma SQ (2009) A fast subspace method for image deblurring. Appl Math Comput 215:2359–2377CrossRefzbMATHMathSciNetGoogle Scholar
  41. Wang YF, Xiao TY (2001) Fast realization algorithms for determining regularization parameters in linear inverse problems. Inverse Probl 17:281–291CrossRefzbMATHMathSciNetGoogle Scholar
  42. Wang YF, Yang CC (2008) A regularizing active set method for retrieval of atmospheric aerosol particle size distribution function. J Opt Soc Am A 25:348–356CrossRefGoogle Scholar
  43. Wang YF, Yuan YX (2002) On the regularity of a trust region-CG algorithm for nonlinear ill-posed inverse problems. In: Sunada T, Sy PW, Yang L (eds) Proceedings of the third Asian mathematical conference, Diliman, Philippines, 23–27, Oct 2000. World Scientific, Singapore, pp 562–580CrossRefGoogle Scholar
  44. Wang YF, Yuan YX (2003) A trust region algorithm for solving distributed parameter identification problem. J Comput Math 21:759–772zbMATHMathSciNetGoogle Scholar
  45. Wang YF, Yuan YX (2005) Convergence and regularity of trust region methods for nonlinear ill-posed inverse problems. Inverse Probl 21:821–838CrossRefzbMATHMathSciNetGoogle Scholar
  46. Wang YF, Li XW, Ma SQ, Yang H, Nashed Z, Guan YN (2005) BRDF model inversion of multiangular remote sensing: ill-posedness and interior point solution method. In: Proceedings of the 9th international symposium on physical measurements and signature in remote sensing (ISPMSRS), Beijing, 17–19 Oct 2005, vol XXXVI, pp 328–330Google Scholar
  47. Wang YF, Fan SF, Feng X, Yan GJ, Guan YN (2006a) Regularized inversion method for retrieval of aerosol particle size distribution function in W 1, 2 space. Appl Opt 45:7456–7467CrossRefGoogle Scholar
  48. Wang YF, Wen Z, Nashed Z, Sun Q (2006b) Direct fast method for time-limited signal reconstruction. Appl Opt 45:3111–3126CrossRefGoogle Scholar
  49. Wang YF, Li XW, Nashed Z, Zhao F, Yang H, Guan YN, Zhang H (2007a) Regularized kernel-based BRDF model inversion method for ill-posed land surface parameter retrieval. Remote Sens Environ 111:36–50CrossRefGoogle Scholar
  50. Wang YF, Fan SF, Feng X (2007b) Retrieval of the aerosol particle size distribution function by incorporating a priori information. J Aerosol Sci 38:885–901CrossRefGoogle Scholar
  51. Wang YF, Yang CC, Li XW (2008) A regularizing kernel-based BRDF model inversion method for ill-posed land surface parameter retrieval using smoothness constraint. J Geophys Res 113:D13101CrossRefGoogle Scholar
  52. Wang YF, Zhang JZ, Roncat A, Künzer C, Wagner W (2009a) Regularizing method for the determination of the backscatter cross-section in Lidar data. J Opt Soc Am A 26:1071–1079CrossRefGoogle Scholar
  53. Wang YF, Cao JJ, Yuan YX, Yang CC, Xiu NH (2009b) Regularizing active set method for nonnegatively constrained ill-posed multichannel image restoration problem. Appl Opt 48:1389–1401CrossRefGoogle Scholar
  54. Wang YF, Yang CC, Li XW (2009c) Kernel-based quantitative remote sensing inversion. In: Camps-Valls G, Bruzzone L (eds) Kernel methods for remote sensing data analysis. Wiley, New YorkGoogle Scholar
  55. Wang YF, Ma SQ, Yang H, Wang JD, Li XW (2009d) On the effective inversion by imposing a priori information for retrieval of land surface parameters. Sci China D 39:360–369Google Scholar
  56. Wanner W, Li X, Strahler AH (1995) On the derivation of kernels for kernel-driven models of bidirectional reflectance. J Geophys Res 100:21077–21090CrossRefGoogle Scholar
  57. Xiao TY, Yu SG, Wang YF (2003) Numerical methods for the solution of inverse problems. Science Press, BeijingGoogle Scholar
  58. Ye YY (1997) Interior point algorithms: theory and analysis. Wiley, ChichesterCrossRefzbMATHGoogle Scholar
  59. Yuan YX (1993) Numerical methods for nonlinear programming. Shanghai Science and Technology Publication, ShanghaiGoogle Scholar
  60. Yuan YX (1994) Nonlinear programming: trust region algorithms. In: Xiao ST, Wu F (eds) Proceedings of Chinese SIAM annual meeting, Tsinghua University Press, Beijing, pp 83–97Google Scholar
  61. Yuan YX (2001) A scaled central path for linear programming. J Comput Math 19:35–40zbMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Key Laboratory of Petroleum GeophysicsInstitute of Geology and Geophysics, Chinese Academy of SciencesBeijingPeople’s Republic of China

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