Utility of the Wavelet Transform for LAI Estimation Using Hyperspectral Data

We employed the discrete wavelet transform to refl ectance spectra obtained from hyperspectral data to improve estimation of LAI in temperate forests. We estimated LAI for 32 plots across a range of forest types in Wisconsin using hemispherical photography. Plot spectra were extracted from AVIRIS data and transformed into wavelet features using the Haar wavelet. Separately, subsets of spectral bands and the Haar features selected by a genetic algorithm were used as independent variables in linear regressions. Models using wavelet coeffi cients explained the most variance for both broadleaf plots (R2 = 0.90 for wavelet features versus R2 = 0.80 for spectral bands) and all plots independent of forest type (R2 = 0.79 for wavelet features vs. R2 = 0.58 for spectral bands). The forest-type specifi c models were better than the models using all plots combined. Overall, wavelet features appear superior to band refl ectances alone for estimating temperate forest LAI using hyperspectral data. Introduction Leaf area index (LAI) of vegetation canopies controls and moderates different climatic and ecological functions (Gong et al., 1995; Huemmrich et al., 2005; Leblanc and Chen, 2001). In forests, LAI determines light interception and thereby CO2 fi xation, canopy photosynthesis, and stand productivity (Turner et al., 2003). It affects hydrological processes and litter production and thus the dynamics of soil water and nutrient cycling (Oren et al., 1998). As such, most ecosystem process models that simulate carbon and hydrologic cycles require LAI as an input variable (Gower, 2001). LAI is one of the principal factors controlling canopy refl ectance (Asner, 1998). However, LAI alone cannot fully describe the effects of canopy structure on refl ectance as canopies with similar LAI often have signifi cantly different near infrared (NIR) refl ectance (Ollinger, 2011). As such, a large body of research has investigated the use of airborne and satellite remote sensing data for its accurate estimation (Fassnacht et al., 1997; Gong et al., Asim Banskota is with School of Forest Resources and Environmental Science, Michigan Tech, Houghton, Michigan, and formerly with Department of Forest Resources and Environmental Conservation, Virginia Polytechnic Institute and State University, Blacksburg, Virginia ([email protected]). Randolph H. Wynne, Nilam Kayastha, and Valerie A. Thomas are with Department of Forest Resources and Environmental Conservation, Virginia Polytechnic Institute and State University, Blacksburg, Virginia. Shawn P. Serbin and Philip A. Townsend are with Department of Forest and Wildlife Ecology, University of WisconsinMadison, Madison, Wisconsin. Photogrammetric Engineering & Remote Sensing Vol. 79, No. 7, July 2013, pp. 653–662. 0099-1112/13/7907–653/$3.00/0 © 2013 American Society for Photogrammetry and Remote Sensing 1995; Huemmrich et al., 2005; Ilames et al., 2008; Jensen et al., 2012). The most widely used approach is to establish an empirical relationship between LAI measured in situ and spectral vegetation indices (SVIs) calculated from spectral refl ectance in two or three bands (Haboudane et al., 2004). However, most empirical approaches are limited in application because the relationship between LAI and SVIs saturates at dense canopy conditions characterized by high LAI (Broge and Leblanc, 2000). The other shortcoming is that SVIs are sensitive to many different factors apart from variation in LAI, such as variation in leaf optical properties and background spectral refl ectance (Goward et al., 1994). Hyperspectral sensors enable measurement of surface refl ectance in narrow spectral bands, providing a capability to analyze canopy by absorption features and over a near continuous spectrum ( Asner, 1998; Pu et al., 2008; Thenkabail et al., 2002). Both the absorption features and overall shape of the refl ectance curve have been found to be sensitive to variability in LAI (Asner, 1998). Darvishzadeh et al. (2008) and Lee et al. (2004) found that the relationship between measured and estimated LAI can be better explained by multiple regression using a combination of narrow bands from imaging spectroscopy (hyperspectral) data than univariate methods using narrow band SVIs. However, one of the major caveats of using hyperspectral imagery is the greater noise and correlation among spectral bands. Statistical models can suffer from multi-collinearity (Geladi and Kowalski, 1986) and overfi tting (Coops et al., 2003) when a large number of redundant bands are used as predictive variables. Hence, effective use of hyperspectral data for empirical estimation of LAI requires reduction of dimensionality. Such data reduction also leads to the loss of useful features offered by spectroscopic data, such as information about the overall shape of a refl ectance continuum, as well as gradual and abrupt slope changes between neighboring bands. The wavelet transform, a signal processing technique, has become increasingly important to numerous vegetation-related applications of hyperspectral remote sensing (Banskota et al., 2011; Blackburn, 2007; Blackburn and Ferwerda, 2008; Bruce et al., 2001; He et al., 2012; Pu and Gong, 2004; Ranchin et al., 2001; Wang, 2010; Zhang et al., 2006). The wavelet transform reduces the dimensionality of hyperspectral data by projecting them into a new feature space in which just a few wavelet coeffi cients represent most of the information in the original data. Wavelet representation of hyperspectral data also conveys additional information such as the location and nature of