© July 2011

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, BC2Department of Computer Science, University of Victoria, Victoria, BC

3Department of Geography, University of Victoria, Victoria, BC

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Linear and Nonlinear Denoising AlgorithmsAssessed 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-level2 x 2 m Tree-level

Conclusions

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Data collection:The Greater Victoria Watershed District (GVWD)

14 plots, 140 trees

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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 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

Data collection:AISA Hyperspectral Data Acquisition

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Sensor characteristics 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 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

Acquisition date Concurrent with AISA acquisition

Data collection:Lidar Data Acquisition

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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 introducesignificant 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 layoverof 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

AISA(B,G,R: 460,550,640nm) draped over LIDAR DSM

Data pre-processing:Radiometric and Geometric Correction

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Nonlinearity of Hyperspectral

Hyperspectral data is non-linear

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?

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.

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Denoising: Linear and Nonlinear

AISA image180 m x 170 m area True colour

RGB: 1736, 1303, 1089nm

Difference Images

Inverse MNF denoised NL-LGP denoised

NL-LGP - ReflectanceReflectance - MNF

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NL-LGP Algorithm

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)

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Plot-Level Chemistry Comparison Process

AISA 30m data

AISA 2m data

MNF denoised data

NL-LGP denoised data

Averaging

Inverse MNFdenoising

NL-LGPdenoising

Reflectancechemistry predictions

MNF denoised

chemistry predictions

NL-LGP denoised

chemistry predictions

Chemistry ground data

Partial Least Squares (PLS)

Regression

PLSRegression

PLSRegression

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Spectral Transformation forComparing 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

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Plot-Level Average R-squaredValues for Nitrogen

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Plot-Level Non-current Nitrogen (% dry weight)

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PLS Plot-Level Chlorophyll-a (μg/mg)

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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, non-averaged AISA 2 m data

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Tree-Level Chemistry Comparison Process

AISA 2m data

MNF denoised data

NL-LGP denoised data

Inverse MNFdenoising

NL-LGPdenoising

Reflectancechemistry predictions

MNF denoised

chemistry predictions

NL-LGP denoised

chemistry predictions

Chemistry ground data

Partial Least Squares (PLS)

Regression

PLSRegression

PLSRegression

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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

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Tree-Level Chemistry Comparison

14 Plots

140 TreesPredicted Chemistry for each of…

MNF denoised

NL-LGP denoised

AISA 2m reflectance

AveragedMeasuredChemistry

vs

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PLS Tree-Level Non-current Nitrogen (% dry weight)

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PLS Tree-Level Chlorophyll-a (μg/mg)

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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

Non-Linear 0.811 ± 0.047

MNF 0.679 ± 0.061

Original Reflectance 0.775 ± 0.051

Chlorophyll

Non-Linear 0.818 ± 0.054

MNF 0.691 ± 0.061

Original Reflectance 0.758 ± 0.054

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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

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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.

Acknowledgements: Hyperspectral applications for forestry