Abundance Estimation of Spectrally Similar Minerals by Using Derivative Spectra in Simulated Annealing

This paper presents a method for estimating the partial abundance of spectrally similar minerals in complex mixtures. The method requires formulation of a linear function of individual spectra of individual minerals. The first and second derivatives of each of the different sets of mixed spectra and the individual spectra are determined. The error is minimized by means of simulated annealing. Experiments were made on several different mixtures of selected endmember, which could plausibly occur in real situations. The variance of the differences between the first derivatives of the observed spectrum and the first derivatives of the endmember spectra gives the most precise estimates for the partial abundance of each endmember. We conclude that the use of first-order derivatives provides a valuable contribution to unmixing procedures provided that the signal-to-noise ratio is at least 50 : 1

[1]  David A. Landgrebe,et al.  Hyperspectral data analysis and supervised feature reduction via projection pursuit , 1999, IEEE Trans. Geosci. Remote. Sens..

[2]  Paul E. Johnson,et al.  Quantitative determination of mineral types and abundances from reflectance spectra using principal components analysis , 1985 .

[3]  P. Switzer,et al.  A transformation for ordering multispectral data in terms of image quality with implications for noise removal , 1988 .

[4]  Peter Bajcsy,et al.  Methodology for hyperspectral band and classification model selection , 2003, IEEE Workshop on Advances in Techniques for Analysis of Remotely Sensed Data, 2003.

[5]  J. Boardman.  Automating spectral unmixing of AVIRIS data using convex geometry concepts , 1993 .

[6]  Dor Ben-Amotz,et al.  Second-Derivative Variance Minimization Method for Automated Spectral Subtraction , 2004, Applied spectroscopy.

[7]  John R. Schott,et al.  Evaluation of Two Applications of Spectral Mixing Models to Image Fusion , 2000 .

[8]  Yosio Edemir Shimabukuro,et al.  The least-squares mixing models to generate fraction images derived from remote sensing multispectral data , 1991, IEEE Trans. Geosci. Remote. Sens..

[9]  J. Boardman,et al.  Mapping target signatures via partial unmixing of AVIRIS data: in Summaries , 1995 .

[10]  J. Settle,et al.  Mapping Vegetation, Soils, and Geology in Semiarid Shrublands Using Spectral Matching and Mixture Modeling of SWIR AVIRIS Imagery , 1999 .

[11]  P. Groves,et al.  Methodology For Hyperspectral Band Selection , 2004 .

[12]  W. Farrand.  Mapping the distribution of mine tailings in the Coeur d'Alene River Valley, Idaho, through the use of a constrained energy minimization technique , 1997 .

[13]  Ehl Emile Aarts,et al.  Simulated annealing and Boltzmann machines , 2003 .

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

[15]  J. Boardman.  Inversion Of Imaging Spectrometry Data Using Singular Value Decomposition , 1989, 12th Canadian Symposium on Remote Sensing Geoscience and Remote Sensing Symposium,.

[16]  E. Ben-Dor,et al.  Visible and near-infrared (0.4–1.1 μm) analysis of arid and semiarid soils , 1994 .

[17]  J. K. Crowley,et al.  Spectral reflectance properties (0.4–2.5 μm) of secondary Fe-oxide, Fe-hydroxide, and Fe-sulphate-hydrate minerals associated with sulphide-bearing mine wastes , 2003, Geochemistry: Exploration, Environment, Analysis.

[18]  Douglas G. Goodin,et al.  Analysis of suspended solids in water using remotely sensed high resolution derivative spectra , 1993 .

[19]  S. J. Sutley,et al.  Using Imaging Spectroscopy To Map Acidic Mine Waste , 2000 .

[20]  F. J. García-Haro,et al.  Linear spectral mixture modelling to estimate vegetation amount from optical spectral data , 1996 .

[21]  Stéphane Audry,et al.  The impact of sulphide oxidation on dissolved metal (Cd, Zn, Cu, Cr, Co, Ni, U) inputs into the Lot–Garonne fluvial system (France) , 2005 .

[22]  N. Linford,et al.  Estimating the approximate firing temperature of burnt archaeological sediments through an unmixing algorithm applied to hysteresis data , 2004 .

[23]  Brian S. Penn,et al.  Using simulated annealing to obtain optimal linear end-member mixtures of hyperspectral data , 2002 .

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

[25]  Barbara L. Sherriff,et al.  The attenuation of Ni, Zn and Cu, by secondary Fe phases of different crystallinity from surface and ground water of two sulfide mine tailings in Manitoba, Canada , 2005 .

[26]  D. Blowes,et al.  Release, transport and attenuation of metals from an old tailings impoundment , 2005 .

[27]  Maurice D. Craig,et al.  Minimum-volume transforms for remotely sensed data , 1994, IEEE Trans. Geosci. Remote. Sens..

[28]  G. Metternicht,et al.  Estimating Erosion Surface Features by Linear Mixture Modeling , 1998 .

[29]  R. N. Fraser,et al.  Hyperspectral remote sensing of turbidity and chlorophyll a among Nebraska Sand Hills lakes , 1998 .

[30]  G. Ferrier,et al.  Application of Imaging Spectrometer Data in Identifying Environmental Pollution Caused by Mining at Rodaquilar, Spain , 1999 .