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Handbook of Geomathematics pp 785–812Cite as

Quantitative Remote Sensing Inversion in Earth Science: Theory and NumericalTreatment

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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; (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.

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Acknowledgments

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, 40974075 and Knowledge Innovation Programs of Chinese Academy of Sciences KZCX2-YW-QN107.

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Authors and Affiliations

  1. Key Laboratory of Petroleum Geophysics, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, People’s Republic of China

    Yanfei Wang

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  1. Yanfei Wang
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Editors and Affiliations

  1. Geomathematics Group, Technische Universität Kaiserslautern, 3049, 67653, Kaiserslautern, Germany

    Willi Freeden

  2. Department of Mathematics, University of Central Florida, Orlando, FL, 32816, USA

    M. Zuhair Nashed

  3. Computational Mathematics, Technische Universität Braunschweig, Pockelsstraße 14, 38106, Braunschweig, Germany

    Thomas Sonar

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Wang, Y. (2010). Quantitative Remote Sensing Inversion in Earth Science: Theory and NumericalTreatment. In: Freeden, W., Nashed, M.Z., Sonar, T. (eds) Handbook of Geomathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01546-5_26

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