International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B7. Istanbul 2004
1.2 Potential for a new approach
The limitations of previous methods call for the evaluation of
novel spectral analytical approaches. Within laboratory
spectroscopy methods for decomposing spectra and modelling
component absorption features have recently emerged which
hold considerable promise for quantifying plant pigments. One
approach that appears to be particularly appropriate is wavelet
analysis (WA).
WA was developed independently in several scientific fields
but interchanges between these during the last decade have led
to a diverse range of applications of this signal processing
technique. The potential of WA in image processing has been
recognised with new techniques in image compression,
classification, archiving and enhancement. Recent studies in
laboratory spectroscopy have shown that WA offers several
advantages over previous spectral approaches. Wavelets are
functions that satisfy certain mathematical requirements and are
used in representing data or other functions. Approximation
using superposition of functions is the basis of Fourier Analysis
(FA), however, in WA data is processed data at different scales
or resolutions. Observing a spectrum through a large ‘window’
identifies gross features and through a small ‘window’ small
features. The sines and cosines of FA are, by definition, non-
local and poor at approximating spectra with sharp
discontinuities (such as vegetation reflectance). WA is able to
use more appropriate functions to capture local spectral features
as it can decompose into components that are well localised in
both time and frequency domains, while FA can only
characterise frequency information (Strang and Nguyen, 1996).
WA of a spectrum yields a vector of wavelet coefficients that
are assigned to different frequency bands. Each band expands
over the complete wavelength domain and responds to a certain
frequency range of the spectrum. By selecting appropriate
wavelet coefficients a spectral model can be established by
regression of the coefficients against component chemical
concentrations.
WA was initially applied in laboratory spectroscopy for
quantifying glucose concentrations in solutions of varying
protein (present in larger quantities with more dominant
absorption features than glucose) and temperature (McNulty
and Mauze, 1998). The results were comparable to Partial Least
Squares regression (PLS) when calibration and prediction data
sets contained the same protein concentration, but WA
outperformed PLS when protein concentrations differed. The
study highlighted the potential of WA to quantify
concentrations based on localised absorption features from a
mixture of compounds and that the approach is extendible
beyond the calibration data set. It also showed how appropriate
wavelet basis functions (or ‘mother wavelets’) can be selected
from the multitude available based the correspondence between
their shape and that of absorption features of components of
interest, this gives the procedure a sound physical basis and
chemical (pigment) specificity. The ability of WA to remove
the effects of background spectral variation when quantifying
concentrations of components with fine absorption from
mixtures has also been demonstrated (Mittermayr ef al., 2001).
This offers potential for removing the effects of broader
absorption features from the narrower features of specific
pigments and for dealing with factors which affect broader
regions of vegetation reflectance spectra such as leaf or canopy
structure and soil/litter response. Importantly, the resilience of
WA to low frequency background noise can be tuned by
choosing the appropriate number of vanishing moments in the
wavelets and WA can deal with difficult situation where
background varies between calibration and prediction data sets
(Mittermayr et al., 2001). Furthermore, due to the localisation
of wavelets, the wavelet coefficient can be chosen by chemical
knowledge, e.g. the position and width of absorption bands.
Conversely chemical knowledge can be discovered by selecting
wavelet coefficients according to statistical measures (e.g.
correlation, prediction errors etc.) and the localisation of
coefficients indicate wavelength regions related to the analyte
under investigation (Mittermayr er al, 2001). This is important
in the context of plant pigments which display differing
absorption spectra in vivo and in vitro.
Further evidence of the robustness of the approach is provided
by spectroscopic studies that have used WA to remove
background signals, noise and specular reflectance to produce
accurate estimates of chemical concentrations by preserving
fine spectral features of components, unlike other
filtering/smoothing algorithms which attenuate and distort the
absorption features of interest (Cai et al., 2001). The capacity of
WA for noise suppression and insensitivity to background
spectral variations has recently been exploited in quantitative
remote sensing for the extraction of significant spectral features
in AVIRIS data for vegetation type discrimination and the
selection of width of smoothing and operator used for
calculating spectral derivatives (Bruce and Li, 2001). Moreover,
work on the classification of canopy reflectance spectra to
discriminate crops and weeds has shown that WA is accurate
and robust with respect to variations in % canopy cover and
soil/litter properties (Huang er al., 2001).
1.3 Aims
The work reported in this paper forms part of a wider project
aimed at developing a generic technique for quantifying
vegetation pigment concentrations from hyperspectral
remotely-sensed data. Specifically, the research will investigate
the ability of WA to provide a method that is able to determine
accurately Chl a and b, and Cars.
2. METHODS
The initial evaluation reported here, focussed on the application
of WA to data sets collected by the author for previously
published research — thereby facilitating a comparison with
previous spectral approaches.
2.1 Data sets used
The data sets used were acquired using a common set of
principles. Reflectance spectra of leaves and canopies were
acquired with a spectroradiometer then immediately after the
pigment determinations were conducted by extraction using an
organic solvent followed by spectrophotometric analysis. In the
case of canopies, pigment concentrations obtained from leaf
samples were scaled up to the canopy level using leaf area
index data collected in situ. The vegetation types used were
broadleaved deciduous tree leaves (and stacks thereof) at
various stages of senescence (see Blackburn, 1998a + 1999),
bracken canopies (Blackburn, 1998b) and matorrral bushland
canopies (Blackburn and Steele, 1999). Details of the methods
and instrumentation used can be found in these papers.
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