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Linear and Nonlinear Imaging
Spectrometer Denoising Algorithms
Assessed Through Chemistry Estimation
David G. Goodenough1,2, Geoffrey S. Quinn3,
Piper L. Gordon2, K. Olaf Niemann3 and Hao Chen1
1Pacific
Forestry Centre, Natural Resources Canada, Victoria, BC
2Department of Computer Science, University of Victoria, Victoria, BC
3Department of Geography, University of Victoria, Victoria, BC
© July 2011
Linear and Nonlinear Denoising Algorithms
Assessed Through Chemistry Estimation
 Objective: To compare linear and non-linear methods of denoising
hyperspectral data; do we always need non-linear methods?
 Data collection: Study area, sample collection, data/sensor characteristics
 Pre-processing: Orthorectification and radiometric calibration
 Processing: Contextual filter, spectral transformations, PLS regression,
Chlorophyll-a and Nitrogen estimation
 Analysis:
 30 x 30 m Plot-level
 2 x 2 m Tree-level
 Conclusions
© July 2011
Data collection:
The Greater Victoria Watershed District (GVWD)
14 plots, 140 trees
© July 2011
Data collection:
AISA Hyperspectral Data Acquisition
 Acquisition date
 September 11, 2006
 Spectral data
 Range: 395 - 2503nm
 492 spectral bands
 Mean sampling interval:
2.37nm (VNIR <990nm)
6.30nm (SWIR>1001)
 Mean FWHM:
2.37nm (VNIR)
6.28 (SWIR)
 Spatial data
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300 spatial pixels
FOV: 22°
IFOV: 0.076°
Imaging rate: 40f/s
Flight speed: 70m/s
Along track sampling: 1.75m
Flight altitude: 1500m
2m resolution
© July 2011
Data collection:
Lidar Data Acquisition
 Acquisition date
 Concurrent with AISA acquisition
 Sensor characteristics
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Discrete return LIDAR system
1064 nm
FOV: 20°
Footprint: ~25 cm (variable)
Pulse rate: 100+ Khz
Scan rate: 15 to 30 Hz
Flight speed: 70 m/s
Flight altitude: 1500m
Posting density: ~1.2/m2
 Data
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Applanix 410 IMU/DGPS system
First and last return x, y, z positions
Range accuracy: 5 to 10 cm
Rasterized to 2m resolution
corresponding to AISA data
 Canopy height, digital surface and bare
earth models are derived
© July 2011
Data pre-processing:
Radiometric and Geometric Correction
 Geometric distortions (non-uniform distance and direction) caused by platform
altitude, attitude (roll, pitch and yaw) and surface relief
 Traditional DEM orthorectification at fine resolutions introduce
significant errors in tree canopy positions
 Accurate positioning is vital for high resolution datasets
and fine scale patterns and processes
 The lidar RBO (range based orthorectification),
reduces misregistration issues caused by layover
of the reflected surface.
 Atmospheric corrections performed by
ATCOR-4 (airborne) software applying
sensor and atmospheric parameters to
sample MODTRAN LUT and provide
correction factors
 Empirical line calibration performed to
reduce residual errors
© July 2011
AISA
(B,G,R: 460,550,640nm)
draped over LIDAR DSM
Nonlinearity of Hyperspectral
 Hyperspectral data is non-linear
T. Han and D. G. Goodenough, "Investigation of Nonlinearity
in Hyperspectral Imagery Using Surrogate Data Methods,"
Geoscience and Remote Sensing, IEEE Transactions on, vol.
46, pp. 2840-2847, 2008.
 Minimum Noise Fraction (MNF)
 Popular linear noise removal technique
 Non-linear Local Geometric Projection Algorithm
(NL-LGP)
 Will it outperform MNF denoising for foliar chemistry
prediction?
© July 2011
Denoising: Linear and Nonlinear
AISA image
180 m x 170 m area
True colour
Inverse MNF denoised
NL-LGP denoised
Reflectance - MNF
NL-LGP - Reflectance
Difference
Images
RGB: 1736, 1303, 1089nm
© July 2011
NL-LGP Algorithm
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Construct state vectors in phase space
Specify the neighbourhood of these state vectors
Find projection directions
Project the state vectors on these directions, reducing
noise
D. G. Goodenough, H. Tian, B. Moa, K. Lang, C. Hao, A.
Dhaliwal, and A. Richardson, "A framework for efficiently
parallelizing nonlinear noise reduction algorithm," in
Geoscience and Remote Sensing Symposium (IGARSS),
2010 IEEE International, pp. 2182-2185.
© July 2011
Minimum Noise Fraction
 Estimates noise in the data and in a Principal
Components Analysis (PCA) of the noise covariance
matrix
 Noise whitening models the noise in the data as
having unit variance and being spectrally uncorrelated
 A second PCA is taken
 Resulting MNF eigenvectors are ordered from highest
to lowest signal to noise ratio (noise variance divided
by total variance)
© July 2011
Plot-Level Chemistry Comparison
Process
AISA 2m data
Chemistry
ground data
Averaging
AISA 30m data
NL-LGP
denoising
Partial Least
Squares (PLS)
Regression
Inverse MNF
denoising
PLS
Regression
MNF
denoised data
PLS
Regression
NL-LGP
denoised data
© July 2011
Reflectance
chemistry
predictions
MNF
denoised
chemistry
predictions
NL-LGP
denoised
chemistry
predictions
Spectral Transformation for
Comparing Chemistry Predictions
 Mean R2 values for the transformation types are
output by the PLS program
 Large standard deviations, overlapping between
original reflectance, MNF and NL-LGP denoised
 2nd derivative (2 points left) has one of the highest
mean R-squared values
 The most accurate predictions from PLS regression
are output for each transformation type
 2nd derivative (2 points left) gave best prediction for
all 3 spectra types and both Nitrogen and Chlorophyll-a
chemistry
© July 2011
Plot-Level Average R-squared
Values for Nitrogen
© July 2011
Plot-Level Non-current
Nitrogen (% dry weight)
© July 2011
PLS Plot-Level Chlorophyll-a
(μg/mg)
© July 2011
Moving from
Plot-Level to Tree-Level
 Original reflectance predicts chemistry with greater
accuracy than denoised reflectance
 Averaging from 2 x 2 m pixels to 30 x 30 m pixels
 Preprocessing of the data (orthorectification and
radiometric calibration)
 To find if there is non-linear noise at the 2 m level
(tree-level) the process is repeated with original, nonaveraged AISA 2 m data
© July 2011
Tree-Level Chemistry Comparison
Process
Chemistry
ground data
AISA 2m data
NL-LGP
denoising
Partial Least
Squares (PLS)
Regression
Inverse MNF
denoising
PLS
Regression
MNF
denoised data
PLS
Regression
NL-LGP
denoised data
© July 2011
Reflectance
chemistry
predictions
MNF
denoised
chemistry
predictions
NL-LGP
denoised
chemistry
predictions
Tree-Level Chemical Analysis
 Spectra were extracted from the positions of each tree
in the plot data (2m by 2m pixels)
 Chemistry predictions were generated for the ten trees
in each of the 14 plots, against the averaged
chemistry measurement for their plot
 2nd derivative of reflectance (2 points left) gave the
best R2 values and was used for the chemistry
predictions
© July 2011
Tree-Level Chemistry Comparison
140 Trees
Predicted
Chemistry
for each of…
14 Plots
AISA 2m reflectance
MNF denoised
vs
NL-LGP denoised
Averaged
Measured
Chemistry
© July 2011
PLS Tree-Level Non-current
Nitrogen (% dry weight)
© July 2011
PLS Tree-Level Chlorophyll-a
(μg/mg)
© July 2011
Conclusions:
Linear and Non-Linear Denoising Algorithms
 For plot-level applications, denoising is not necessary
 The averaging process is effective for removing noise
 For tree-level applications, use of a non-linear denoising method is
better for mapping chemistry
 Nitrogen
 Chlorophyll
 Non-Linear 0.811 ± 0.047
 Non-Linear 0.818 ± 0.054
 MNF 0.679 ± 0.061
 MNF 0.691 ± 0.061
 Original Reflectance
0.775 ± 0.051
 Original Reflectance
0.758 ± 0.054
© July 2011
Conclusions:
Linear and Non-Linear Denoising Algorithms
 MNF does not improve chemistry predictions, further
supporting the non-linearity of hyperspectral data
 The application of PLS regression to forest chemistry mapping
remains our most reliable method for chemistry estimation
 R2 of ~0.9 for plot-level
 R2 of ~0.8 for tree-level
© July 2011
Acknowledgements:
Hyperspectral applications for forestry
We thank:
• The University of Victoria for its support.
• Natural Resources Canada (NRCan), the Canadian Space
Agency (CSA), and Natural Sciences and Engineering
Research Council of Canada (NSERC) (DGG) for their
support.
• The Victoria Capital Regional District Watershed Protection
Division for its logistical support.
• The audience for their attention.
© July 2011