{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,8]],"date-time":"2025-11-08T22:39:25Z","timestamp":1762641565630,"version":"build-2065373602"},"reference-count":59,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2013,5,24]],"date-time":"2013-05-24T00:00:00Z","timestamp":1369353600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>The need for an efficient and standard technique for optimal spectral sampling of hyperspectral data during the inversion of canopy reflectance models has been the subject of many studies. The objective of this study was to investigate the utility of the discrete wavelet transform (DWT) for extracting useful features from hyperspectral data with which forest LAI can be estimated through inversion of a three dimensional radiative transfer model, the Discrete Anisotropy Radiative Transfer (DART) model. DART, coupled with the leaf optical properties model PROSPECT, was inverted with AVIRIS data using a look-up-table (LUT)-based inversion approach. We used AVIRIS data and in situ LAI measurements from two different hardwood forested sites in Wisconsin, USA. Prior to inversion, model-simulated and AVIRIS hyperspectral data were transformed into discrete wavelet coefficients using Haar wavelets. The LUT inversion was performed with three different datasets, the original reflectance bands, the full set of wavelet extracted features, and two wavelet subsets containing 99.99% and 99.0% of the cumulative energy of the original signal. The energy subset containing 99.99% of the cumulative signal energy provided better estimates of LAI (RMSE = 0.46, R2 = 0.77) than the original spectral bands (RMSE = 0.60, R2 = 0.47). The results indicate that the discrete wavelet transform can increase the accuracy of LAI estimates by improving the LUT-based inversion of DART (and, potentially, by implication, other terrestrial radiative transfer models) using hyperspectral data. The improvement in accuracy of LAI estimates is potentially due to different properties of wavelet analysis such as multi-scale representation, dimensionality reduction, and noise removal.<\/jats:p>","DOI":"10.3390\/rs5062639","type":"journal-article","created":{"date-parts":[[2013,5,24]],"date-time":"2013-05-24T13:02:03Z","timestamp":1369400523000},"page":"2639-2659","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":37,"title":["Investigating the Utility of Wavelet Transforms for Inverting a 3-D Radiative Transfer Model Using Hyperspectral Data to Retrieve Forest LAI"],"prefix":"10.3390","volume":"5","author":[{"given":"Asim","family":"Banskota","sequence":"first","affiliation":[{"name":"Geospatial and Environmental Analysis Program, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3649-835X","authenticated-orcid":false,"given":"Randolph","family":"Wynne","sequence":"additional","affiliation":[{"name":"Department of Forest Resources and Environmental Conservation,  Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2189-6013","authenticated-orcid":false,"given":"Valerie","family":"Thomas","sequence":"additional","affiliation":[{"name":"Department of Forest Resources and Environmental Conservation,  Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA"}]},{"given":"Shawn","family":"Serbin","sequence":"additional","affiliation":[{"name":"Department of Forest and Wildlife Ecology, University of Wisconsin-Madison, Madison,  WI 53706, USA"}]},{"given":"Nilam","family":"Kayastha","sequence":"additional","affiliation":[{"name":"Geospatial and Environmental Analysis Program, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA"}]},{"given":"Jean","family":"Gastellu-Etchegorry","sequence":"additional","affiliation":[{"name":"Centre d'\u00e9tudes spatiales de la biosph\u00e8re (CESBIO), 18 Avenue Edouard Belin,  F-31055 Toulouse Cedex, France"}]},{"given":"Philip","family":"Townsend","sequence":"additional","affiliation":[{"name":"Department of Forest and Wildlife Ecology, University of Wisconsin-Madison, Madison,  WI 53706, USA"}]}],"member":"1968","published-online":{"date-parts":[[2013,5,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"4381","DOI":"10.1080\/01431160500113393","article-title":"Time-series validation of MODIS land biophysical products in a Kalahari woodland, Africa","volume":"26","author":"Huemmrich","year":"2005","journal-title":"Int. J. Remote Sens"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"278","DOI":"10.3390\/rs2010278","article-title":"Spatial enhancement of MODIS-based images of leaf area index: Application to the boreal forest region of Northern Alberta, Canada","volume":"2","author":"Hassan","year":"2010","journal-title":"Remote Sens"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1380","DOI":"10.3390\/rs1041380","article-title":"Leaf Area Index (LAI) estimation of boreal forest using wide optics airborne winter photos","volume":"1","author":"Manninen","year":"2009","journal-title":"Remote Sens"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"234","DOI":"10.1016\/S0034-4257(98)00014-5","article-title":"Biophysical and biochemical sources of variability in canopy reflectance","volume":"64","author":"Asner","year":"1998","journal-title":"Remote Sens. Environ"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1139","DOI":"10.3390\/rs1041139","article-title":"Enhanced automated canopy characterization from hyperspectral data by a novel two step radiative transfer model inversion approach","volume":"1","author":"Dorigo","year":"2009","journal-title":"Remote Sens"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1389","DOI":"10.14358\/PERS.74.11.1389","article-title":"Leaf area index (LAI) change detection analysis on Loblolly pine (Pinus taeda) following complete understory removal","volume":"74","author":"Ilames","year":"2008","journal-title":"Photogramm. Eng. Remote Sensing"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"3766","DOI":"10.3390\/rs4123766","article-title":"Calibration of a Species-specific spectral vegetation index for Leaf Area Index (LAI) monitoring: Example with modis reflectance time-series on eucalyptus plantations","volume":"4","author":"Marsden","year":"2012","journal-title":"Remote Sens"},{"key":"ref_8","first-page":"1107","article-title":"Coniferous forest leaf-area index estimation along the Oregon transect using compact airborne spectrographic imager data","volume":"61","author":"Gong","year":"1995","journal-title":"Photogramm. Eng. Remote Sensing"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1758","DOI":"10.3390\/rs4061758","article-title":"Combined use of airborne lidar and DBInSAR data to estimate LAI in temperate mixed forests","volume":"4","author":"Peduzzi","year":"2012","journal-title":"Remote Sens"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1177\/030913339401800204","article-title":"Imaging spectrometry","volume":"18","author":"Curran","year":"1994","journal-title":"Progr. Phys. Geogr"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1080\/02757250009532396","article-title":"Inversion methods for physically based models","volume":"18","author":"Kimes","year":"2000","journal-title":"Remote Sens. Rev"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1016\/S0034-4257(96)00069-7","article-title":"Potential and limitations of information extraction on the terrestrial biosphere from satellite remote sensing","volume":"58","author":"Verstraete","year":"1996","journal-title":"Remote Sens. Environ"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2592","DOI":"10.1016\/j.rse.2007.12.003","article-title":"Inversion of a radiative transfer model for estimating vegetation LAI and chlorophyll in heterogeneous grassland","volume":"112","author":"Darvishzadeh","year":"2008","journal-title":"Remote Sens. Environ"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1341","DOI":"10.1016\/j.agrformet.2008.03.011","article-title":"Assessing the effects of the clumping phenomenon on BRDF of a maize crop based on 3D numerical scenes using DART model","volume":"148","author":"Duthoit","year":"2008","journal-title":"Agric. For. Meteorol"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1016\/0034-4257(95)00253-7","article-title":"Modeling radiative transfer in heterogeneous 3-D vegetation canopies","volume":"58","author":"Demarez","year":"1996","journal-title":"Remote Sens. Environ"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1016\/S0034-4257(03)00146-9","article-title":"An interpolation procedure for generalizing a look-up table inversion method","volume":"87","author":"Gascon","year":"2003","journal-title":"Remote Sens. Environ"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1016\/0168-1923(91)90069-3","article-title":"Modeling radiative transfer and photosynthesis in three dimensional vegetation canopies","volume":"55","author":"Myneni","year":"1991","journal-title":"Agric. For. Meteorol"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"302","DOI":"10.1109\/36.134080","article-title":"Remote-sensing of solar-radiation absorbed and reflected by vegetated land surfaces","volume":"30","author":"Myneni","year":"1992","journal-title":"IEEE Trans. Geosci. Remote Sens"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"5601","DOI":"10.1080\/01431160412331291305","article-title":"Retrieval of forest biophysical variables by inverting a 3-D radiative transfer model and using high and very high resolution imagery","volume":"25","author":"Gascon","year":"2004","journal-title":"Int. J. Remote Sens"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1080\/0143116031000115166","article-title":"DART: A 3D model for simulating satellite images and studying surface radiation budget","volume":"25","author":"Martin","year":"2004","journal-title":"Int. J. Remote Sens"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1029\/2003JD004252","article-title":"Radiation transfer model intercomparison (RAMI) exercise: Results from the second phase","volume":"109","author":"Pinty","year":"2004","journal-title":"J. Geophys. Res.-Atmos"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2639","DOI":"10.1080\/014311698214433","article-title":"Attributes of neural networks for extracting continuous vegetation variables from optical and radar measurements","volume":"19","author":"Kimes","year":"1998","journal-title":"Int. J. Remote Sens"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1016\/j.rse.2005.10.006","article-title":"Inversion of a forest reflectance model to estimate structural canopy variables from hyperspectral remote sensing data","volume":"100","author":"Schlerf","year":"2006","journal-title":"Remote Sens. Environ"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"32257","DOI":"10.1029\/98JD02462","article-title":"Synergistic algorithm for estimating vegetation canopy leaf area index and fraction of absorbed photosynthetically active radiation from MODIS and MISR data","volume":"103","author":"Knyazikhin","year":"1998","journal-title":"J. Geophys. Res"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"501","DOI":"10.1177\/0309133307084626","article-title":"Recent developments in estimating land surface biogeophysical variables from optical remote sensing","volume":"31","author":"Liang","year":"2007","journal-title":"Progr. Phys. Geogr"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"3576","DOI":"10.1364\/AO.44.003576","article-title":"Interpretation of hyperspectral remote-sensing imagery by spectrum matching and look-up tables","volume":"44","author":"Mobley","year":"2005","journal-title":"Appl. Opt"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1080\/02757250009532417","article-title":"On the potential of CHRIS\/PROBA for estimating vegetation canopy properties from space","volume":"19","author":"Barnsley","year":"2000","journal-title":"Remote Sens. Rev"},{"key":"ref_28","unstructured":"Goel, N.S. (1988, January 18\u201322). A Perspective on Vegetation Canopy Reflectance Models. Aussois, France."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"S123","DOI":"10.1016\/j.rse.2009.03.001","article-title":"Earth system science related imaging spectroscopy\u2014An assessment","volume":"113","author":"Schaepman","year":"2009","journal-title":"Remote Sens. Environ"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"555","DOI":"10.1051\/agro:2002039","article-title":"Reliability of the estimation of vegetation characteristics by inversion of three canopy reflectance models on airborne POLDER data","volume":"22","author":"Bacour","year":"2002","journal-title":"Agronomie"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1016\/j.rse.2004.06.005","article-title":"Inversion of a radiative transfer model with hyperspectral observations for LAI mapping in poplar plantations","volume":"92","author":"Meroni","year":"2004","journal-title":"Remote Sens. Environ"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1051\/agro:2000105","article-title":"Investigation of a model inversion technique to estimate canopy biophysical variables from spectral and directional reflectance data","volume":"20","author":"Weiss","year":"2000","journal-title":"Agronomie"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"3551","DOI":"10.1080\/01431161003698302","article-title":"Improving within-genus tree species discrimination using the discrete wavelet transform applied to airborne hyperspectral data","volume":"32","author":"Banskota","year":"2011","journal-title":"Int. J. Remote Sens"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"2831","DOI":"10.1080\/01431160600928625","article-title":"Wavelet decomposition of hyperspectral data: A novel approach to quantifying pigment concentrations in vegetation","volume":"28","author":"Blackburn","year":"2007","journal-title":"Int. J. Remote Sens"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"205","DOI":"10.2307\/2261007","article-title":"Characterizing canopy gap structure in forests using wavelet analysis","volume":"80","author":"Bradshaw","year":"1992","journal-title":"J. Ecol"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"2217","DOI":"10.1109\/36.957284","article-title":"Automated detection of subpixel hyperspectral targets with continuous and discrete wavelet transforms","volume":"39","author":"Bruce","year":"2001","journal-title":"IEEE Trans. Geosci. Remote Sens"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1197","DOI":"10.3390\/rs2051197","article-title":"Applying multifractal analysis to remotely sensed data for assessing PYVV infection in potato (Solanum tuberosum L.) crops","volume":"2","author":"Piro","year":"2010","journal-title":"Remote Sens"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"863","DOI":"10.1109\/TGRS.2003.810712","article-title":"Automatic reduction of hyperspectral imagery using wavelet spectral analysis","volume":"41","author":"Kaewpijit","year":"2003","journal-title":"IEEE Trans. Geosci. Remote Sens"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1016\/j.rse.2006.06.010","article-title":"Intra- and inter-class spectral variability of tropical tree species at La Selva, Costa Rica: Implications for species identification using HYDICE imagery","volume":"105","author":"Zhang","year":"2006","journal-title":"Remote Sens. Environ"},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Banskota, A., Wynne, R.H., Serbin, S.P., Kayastha, N., Thomas, V.A., and Townsend, P.A. (2013). Utility of the Wavelet transform for LAI estimation using hyperspectral data. Photogramm. Eng. Remote Sensing, accepted.","DOI":"10.14358\/PERS.79.7.653"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"212","DOI":"10.1016\/j.rse.2004.03.006","article-title":"Wavelet transform applied to EO-1 hyperspectral data for forest LAI and crown closure mapping","volume":"91","author":"Pu","year":"2004","journal-title":"Remote Sens. Environ"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"1192","DOI":"10.1785\/0120000916","article-title":"Source description of the 1999 Hector Mine, California, Earthquake, Part I: Wavelet domain inversion theory and resolution analysis","volume":"92","author":"Ji","year":"2002","journal-title":"Bull. Seismol. Soc. Am"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1029\/95RS03130","article-title":"Wavelet-based methods for the nonlinear inverse scattering problem using the extended born approximation","volume":"31","author":"Miller","year":"1996","journal-title":"Radio Sci"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1016\/j.isprsjprs.2006.12.004","article-title":"Feature extraction of hyperspectral images using wavelet and matching pursuit","volume":"62","author":"Hsu","year":"2007","journal-title":"ISPRS J. Photogramm"},{"key":"ref_45","unstructured":"Walker, J.S. (1999). A Primer on Wavelets and Their Scientific Applications, Chapman and Hall\/CRC."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"674","DOI":"10.1109\/34.192463","article-title":"A theory for multi-resolution signal decomposition: The wavelet representation","volume":"11","author":"Mallat","year":"1989","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1016\/S0168-1923(01)00284-2","article-title":"A practical scheme for correcting multiple scattering effects on optical LAI measurements","volume":"110","author":"Leblanc","year":"2001","journal-title":"Agric. For. Meteorol"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"166","DOI":"10.1016\/j.agrformet.2005.09.009","article-title":"Determining digital hemispherical photograph exposure for leaf area index estimation","volume":"133","author":"Zhang","year":"2005","journal-title":"Agric. For. Meteorol"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1016\/j.agrformet.2006.08.005","article-title":"Leaf area index measurements at Fluxnet-Canada forest sites","volume":"140","author":"Chen","year":"2006","journal-title":"Agric. For. Meteorol"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1080\/01621459.1979.10481634","article-title":"Influential observations in linear regression","volume":"74","author":"Cook","year":"1979","journal-title":"J. Amer. Statist. Assoc"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1016\/0034-4257(93)90022-P","article-title":"Inversion of the PROSPECT + SAIL Canopy reflectance model from AVIRIS equivalent spectra: Theoretical study","volume":"44","author":"Jacquemoud","year":"1993","journal-title":"Remote Sens. Environ"},{"key":"ref_52","unstructured":"Serbin, S.P. (2012). Spectroscopic Determination of Leaf Nutritional, Morphological, and Metabolic Traits. Ph.D. Dissertation, University of Wisconsin-Madison, Madison, WI, USA,."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"126","DOI":"10.1016\/j.rse.2008.08.008","article-title":"Short-term assessment of burn severity using the inversion of PROSPECT and GeoSail models","volume":"113","author":"Santis","year":"2009","journal-title":"Remote Sens. Environ"},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"330","DOI":"10.1016\/j.ymssp.2008.05.014","article-title":"On the energy leakage of discrete wavelet transform","volume":"23","author":"Peng","year":"2009","journal-title":"Mech. Syst. Signal Pr"},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1016\/S0034-4257(99)00056-5","article-title":"Direct and indirect estimation of leaf area index, F(Apar), and net primary production of terrestrial ecosystems","volume":"70","author":"Gower","year":"1999","journal-title":"Remote Sens. Environ"},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1016\/j.agrformet.2003.08.027","article-title":"Review of methods for in situ leaf area index determination\u2014Part I. Theories, sensors and hemispherical photography","volume":"12","author":"Jonckheere","year":"2004","journal-title":"Agric. For. Meteorol"},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1016\/j.agrformet.2003.08.001","article-title":"Review of methods for in situ Leaf Area Index (LAI) determination Part II. estimation of LAI, errors and sampling","volume":"121","author":"Weiss","year":"2004","journal-title":"Agric. For. Meteorol"},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"644","DOI":"10.1016\/j.agrformet.2007.11.015","article-title":"Estimation of leaf area and clumping indexes of crops with hemispherical photographs","volume":"148","author":"Demarez","year":"2008","journal-title":"Agric. For. Meteorol"},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"723","DOI":"10.1093\/treephys\/25.6.723","article-title":"Allometry and evaluation of in situ optical LAI determination in scots pine: A case study in Belgium","volume":"25","author":"Jonckheere","year":"2005","journal-title":"Tree Physiol"}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/5\/6\/2639\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:46:59Z","timestamp":1760219219000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/5\/6\/2639"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,5,24]]},"references-count":59,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2013,6]]}},"alternative-id":["rs5062639"],"URL":"https:\/\/doi.org\/10.3390\/rs5062639","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2013,5,24]]}}}