Two-Step Constrained Nonlinear Spectral Mixture Analysis Method for Mitigating the Collinearity Effect

Spectral mixture analysis (SMA) is widely used to quantify the fraction of each component (endmember) of mixed pixels that contain spectral signals from more than one land surface type. Generally, nonlinear SMA (NSMA) outperforms linear SMA (LSMA) in the vegetation (tree, shrub, crop, and grass) and soil mixture case because NSMA considers the significant multiple scattering that exists for these mixtures. However, compared to LSMA, the bilinear NSMA method, which is a typical physical-based NSMA method, is undermined by its susceptibility to the collinearity effect. In this paper, a two-step constrained NSMA method (referred to as TsC-NSMA) is proposed to mitigate the collinearity effect in the bilinear NSMA method. The theoretical maximum likelihood range is mathematically derived for each endmember fraction, and the ranges are used as additional constraints for the bilinear NSMA method to optimize the unmixing results. Three different data sets, including simulated spectral data, an in situ ground plot spectral measurement, and a Landsat8 Operational Land Imager image, were used to assess the performance of the TsC-NSMA method. The results indicated that TsC-NSMA achieved the highest estimation accuracy for all mixed scenarios which either contain severe endmember collinearity or high noise levels, thereby suggesting its ability to mitigate the collinearity effect in the bilinear NSMA method with the potential to improve the estimation of endmember fractions in practical applications.

[1]  Xiuping Jia,et al.  Collinearity and orthogonality of endmembers in linear spectral unmixing , 2012, Int. J. Appl. Earth Obs. Geoinformation.

[2]  Jyotsna Ravi,et al.  Feasibility of neural network approach in spectral mixture analysis of reflectance spectra , 2008 .

[3]  R. Tibshirani.  Regression Shrinkage and Selection via the Lasso , 1996 .

[4]  Xuexia Chen,et al.  Spectral mixture analyses of hyperspectral data acquired using a tethered balloon , 2006 .

[5]  Eric D. Kolaczyk,et al.  Gaussian mixture discriminant analysis and sub-pixel land cover characterization in remote sensing , 2003 .

[6]  P. Atkinson,et al.  Mapping sub-pixel proportional land cover with AVHRR imagery , 1997 .

[7]  Jean-Yves Tourneret,et al.  Nonlinear unmixing of hyperspectral images using a generalized bilinear model , 2011 .

[8]  Kohei Arai,et al.  Forest parameter estimation by means of Monte-Carlo simulations with experimental considerations , 2009 .

[9]  S. M. Jong,et al.  Improving the results of spectral unmixing of Landsat thematic mapper imagery by enhancing the orthogonality of end-members , 2000 .

[10]  G. Monette,et al.  Generalized Collinearity Diagnostics , 1992 .

[11]  J. Townshend,et al.  Continuous fields of vegetation characteristics at the global scale at 1‐km resolution , 1999 .

[12]  Fenglei Fan,et al.  Enhancing endmember selection in multiple endmember spectral mixture analysis (MESMA) for urban impervious surface area mapping using spectral angle and spectral distance parameters , 2014, Int. J. Appl. Earth Obs. Geoinformation.

[13]  John F. Mustard,et al.  Compositional gradients across mare-highland contacts: Importance and geological implication of lateral transport , 2000 .

[14]  Laurent Tits,et al.  Quantifying Nonlinear Spectral Mixing in Vegetated Areas: Computer Simulation Model Validation and First Results , 2014, IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing.

[15]  Weiguo Liu,et al.  ART-MMAP: a neural network approach to subpixel classification , 2004, IEEE Transactions on Geoscience and Remote Sensing.

[16]  John R. Miller,et al.  Comparative study between a new nonlinear model and common linear model for analysing laboratory simulated‐forest hyperspectral data , 2009 .

[17]  José M. Bioucas-Dias,et al.  Nonlinear mixture model for hyperspectral unmixing , 2009, Remote Sensing.

[18]  R. O’Brien,et al.  A Caution Regarding Rules of Thumb for Variance Inflation Factors , 2007 .

[19]  Mu Zhu,et al.  Stochastic Stepwise Ensembles for Variable Selection , 2010, 1003.5930.

[20]  R. Singer,et al.  Mars - Large scale mixing of bright and dark surface materials and implications for analysis of spectral reflectance , 1979 .

[21]  J. C. Price.  How unique are spectral signatures , 1994 .

[22]  Jin Chen,et al.  A Quantitative Analysis of Virtual Endmembers' Increased Impact on the Collinearity Effect in Spectral Unmixing , 2011, IEEE Transactions on Geoscience and Remote Sensing.

[23]  M. Revan Özkale,et al.  Combining Unbiased Ridge and Principal Component Regression Estimators , 2009 .

[24]  Jin Chen,et al.  Assessment of Multiple Scattering in the Reflectance of Semiarid Shrublands , 2015, IEEE Transactions on Geoscience and Remote Sensing.

[25]  John B. Adams,et al.  Quantitative subpixel spectral detection of targets in multispectral images. [terrestrial and planetary surfaces] , 1992 .

[26]  W. Verstraeten,et al.  Nonlinear Hyperspectral Mixture Analysis for tree cover estimates in orchards , 2009 .

[27]  T. Fearn.  Ridge Regression , 2013 .

[28]  Xiaorun Li,et al.  Nonlinear Spectral Mixture Analysis by Determining Per-Pixel Endmember Sets , 2014, IEEE Geoscience and Remote Sensing Letters.

[29]  Kohei Arai,et al.  Nonlinear mixture model of mixed pixels in remote sensing satellite images based on Monte Carlo simulation , 2008 .

[30]  Chein-I Chang,et al.  Fully constrained least squares linear spectral mixture analysis method for material quantification in hyperspectral imagery , 2001, IEEE Trans. Geosci. Remote. Sens..

[31]  S. Weisberg,et al.  Applied Linear Regression (2nd ed.). , 1986 .

[32]  Jin Chen,et al.  Generalization of Subpixel Analysis for Hyperspectral Data With Flexibility in Spectral Similarity Measures , 2009, IEEE Transactions on Geoscience and Remote Sensing.

[33]  Yuan Zhou,et al.  Estimation of Fractional Vegetation Cover in Semiarid Areas by Integrating Endmember Reflectance Purification Into Nonlinear Spectral Mixture Analysis , 2015, IEEE Geoscience and Remote Sensing Letters.

[34]  P. Mausel,et al.  Application of spectral mixture analysis to Amazonian land-use and land-cover classification , 2004 .

[35]  Qian Du,et al.  Nonlinear Spectral Mixture Analysis for Hyperspectral Imagery in an Unknown Environment , 2010, IEEE Geoscience and Remote Sensing Letters.

[36]  A. E. Hoerl,et al.  Ridge regression: biased estimation for nonorthogonal problems , 2000 .

[37]  Gregory S. Okin,et al.  Mapping North African landforms using continental scale unmixing of MODIS imagery , 2005 .

[38]  Alfonso Fernández-Manso,et al.  Spectral unmixing , 2012 .

[39]  J. Friedman,et al.  A Statistical View of Some Chemometrics Regression Tools , 1993 .

[40]  T. W. Ray,et al.  Nonlinear Spectral Mixing in Desert Vegetation , 1996 .

[41]  Giles M. Foody,et al.  Approaches for the production and evaluation of fuzzy land cover classifications from remotely-sensed data , 1996 .

[42]  D. Roberts,et al.  Sub-pixel mapping of urban land cover using multiple endmember spectral mixture analysis: Manaus, Brazil , 2007 .

[43]  Paul D. Gader,et al.  A Review of Nonlinear Hyperspectral Unmixing Methods , 2014, IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing.