Linear and Nonlinear Imaging Spectrometer Denoising Algorithms Compared

1. 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 Linear and Nonlinear Imaging Spectrometer Denoising Algorithms Assessed Through Chemistry Estimation

2. 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-level • 2 x 2 m Tree-level • Conclusions

3. Data collection:The Greater Victoria Watershed District (GVWD) 14 plots, 140 trees

4. 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 • 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

5. Data collection:Lidar Data Acquisition • Acquisition date • Concurrent with AISA acquisition • 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

6. 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 Data pre-processing:Radiometric and Geometric Correction AISA(B,G,R: 460,550,640nm) draped over LIDAR DSM

7. 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.

8. 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

9. 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.

10. 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)

11. Plot-Level Chemistry Comparison Process AISA 2m data Chemistry ground data Reflectance chemistry predictions Averaging Partial Least Squares (PLS) Regression AISA 30m data MNF denoised chemistry predictions NL-LGP denoising Inverse MNF denoising PLS Regression MNF denoised data NL-LGP denoised chemistry predictions PLS Regression NL-LGP denoised data

12. 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

13. Plot-Level Average R-squaredValues for Nitrogen

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

15. PLS Plot-Level Chlorophyll-a (μg/mg)

16. 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

17. Tree-Level Chemistry Comparison Process Chemistry ground data Reflectance chemistry predictions Partial Least Squares (PLS) Regression AISA 2m data MNF denoised chemistry predictions NL-LGP denoising Inverse MNF denoising PLS Regression MNF denoised data NL-LGP denoised chemistry predictions PLS Regression NL-LGP denoised data

18. 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

19. 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

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

21. PLS Tree-Level Chlorophyll-a (μg/mg)

22. 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 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

23. 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

24. 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.