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Stochastic reconstruction of spatial data using LLE and MPS

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Abstract

Spatial data are widely used in many scientific and engineering fields, such as remote sensing, environment monitoring, weather forecast and mineral exploitation. However, direct measurements of such spatial data sometimes are difficult to achieve due to the expensive cost of equipment or current limited technology, so stochastic reconstruction or simulation of spatial data are necessary based on the principles of statistics. As a typical statistical modeling method, multiple-point statistics (MPS) has been successfully used for stochastic reconstruction by reproducing the features from training images (TIs) to the reconstructed regions. However, because these features mostly have intrinsic nonlinear relations, the traditional MPS methods using linear dimensionality reduction are not suitable to deal with the nonlinear situation. In this paper a new method using locally linear embedding (LLE) and MPS is proposed to resolve this issue. As a classical nonlinear method of dimensionality reduction in manifold learning, LLE is combined with MPS to reduce redundant data of TIs so that the subsequent reconstruction can be faster and more accurate. The tests are performed in both 2D and 3D reconstructions, showing that the reconstructions can reproduce the structural features of TIs and the proposed method has its advantages in reconstruction speed and quality over typical methods using linear dimensionality reduction.

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Acknowledgments

We really appreciate the reviewers for the valuable comments and suggestions on our manuscript. This work is supported by National Program on Key Basic Research Project of China (973 Program, No. 2011CB707305), the National Science and Technology Major Project (No. 2011ZX05009-006), CAS Strategic Priority Research Program (XDB10030402), Talented People Introduction Foundation of Shanghai University of Electric Power (No. K2012-004, K2013-019, K2014-020), and the Excellent University Young Teachers Training Program of Shanghai Municipal Education Commission (ZZsdl13015).

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Authors and Affiliations

  1. College of Computer Science and Technology, Shanghai University of Electric Power, 2588 Changyang Road, Shanghai, 200090, China

    Ting Zhang, Bo Li & Anqin Zhang

  2. College of Engineering, Shanghai Second Polytechnic University, 2360 Jinhai Road, Shanghai, 201209, China

    Yi Du

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  1. Ting Zhang
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  2. Yi Du
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Correspondence to Yi Du.

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Zhang, T., Du, Y., Li, B. et al. Stochastic reconstruction of spatial data using LLE and MPS. Stoch Environ Res Risk Assess 31, 243–256 (2017). https://doi.org/10.1007/s00477-015-1197-z

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  • DOI: https://doi.org/10.1007/s00477-015-1197-z

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