Source-linked AI summary
Spectral band selection for vegetation properties retrieval using Gaussian processes regression
Jochem Verrelst, Juan Pablo Rivera, Anatoly Gitelson, Jesus Delegido, José Moreno, Gustau Camps-Valls
TL;DR
Hyperspectral band selection is challenging because correlated, redundant bands can impair regression and because automated operational tools for vegetation-property retrieval are limited. The paper introduces GPR-BAT within ARTMO’s MLRA toolbox, sequentially removing least-contributing bands to identify informative wavelengths and compact band sets. The reported conclusion is that wise band selection is required for optimal vegetation-properties mapping, with CV improving from 0.55 to 0.79 for LCC and from 0.88 to 0.94 for gLAI.
Problem
Correlated and redundant hyperspectral bands can cause over-fitting and limited transfer to other scenarios, while few band-selection methods address vegetation-property regression operationally.
Method
GPR-BAT integrates Gaussian processes regression into ARTMO’s MLRA toolbox and sequentially removes the least contributing band during model development.
Results
CV from 0.55 to 0.79 for LCC and 0.88 to 0.94 for gLAI.
Takeaways & Limitations
GPR-BAT identifies informative bands and the least number of bands that preserve optimized accurate predictions for vegetation-properties mapping.
Takeaways & Limitations
The meaningfulness of the best-performing bands depends on the quality of the introduced dataset, and two-band indices can be affected by multi-collinearity.
Abstract
from arXiv · showhide
With current and upcoming imaging spectrometers, automated band analysis techniques are needed to enable efficient identification of most informative bands to facilitate optimized processing of spectral data into estimates of biophysical variables. This paper introduces an automated spectral band analysis tool (BAT) based on Gaussian processes regression (GPR) for the spectral analysis of vegetation properties. The GPR-BAT procedure sequentially backwards removes the least contributing band in the regression model for a given variable until only one band is kept. GPR-BAT is implemented within the framework of the free ARTMO's MLRA (machine learning regression algorithms) toolbox, which is dedicated to the transforming of optical remote sensing images into biophysical products. GPR-BAT allows (1) to identify the most informative bands in relating spectral data to a biophysical variable, and (2) to find the least number of bands that preserve optimized accurate predictions. This study concludes that a wise band selection of hyperspectral data is strictly required for optimal vegetation properties mapping.
1. Introduction
Hyperspectral data create band-selection challenges because many bands are correlated, noisy, redundant, and potentially problematic for regression. The paper proposes GPR-BAT to automate informative-band identification and determine compact band sets for vegetation-property retrieval.
- Motivation: Highly correlated, noisy, and redundant bands can cause statistical problems, over-fitting, limited transferability, and reduced prediction accuracy.These issues are especially relevant when sample sizes are small relative to the number of available bands.
- Motivation: Band selection can reduce spectral dimensionality, improve regression fit and processing speed, and clarify relationships between spectra and vegetation properties.Selecting specific spectral regions may also minimize signals from secondary responses.
- Band-selection challenge: Finding the best subset of spectral bands is NP-complete, with many local minima and resulting numerical and computational difficulties.The task is framed as selecting bands that capture most information for a particular problem.
- Existing methods: Filter methods converge faster but may select poorly for the training learner, whereas wrapper methods retrain the learner for each band set and can be computationally intensive.Wrapper methods use the learning machine’s output as the selection criterion.
- Research gap: Most prior imaging-spectroscopy band-selection studies address classification, while few target regression and vegetation-property estimation.Existing retrieval-oriented band-ranking studies remained experimental and were not directly applicable to operational hyperspectral processing.
- Contribution: GPR-BAT analyzes band-specific information for a biophysical variable with little user interaction and identifies both informative bands and the optimal number of bands.The study applies it to hyperspectral datasets and image data for automated and optimized vegetation-properties mapping.
3. ARTMO and GPR-BAT
The paper integrates GPR-BAT into ARTMO’s MLRA toolbox for automated spectral band analysis. Sequential backward removal identifies contributing bands while tracking validation performance and the smallest band set retaining robust results.
- ARTMO and GPR-BAT: GPR-BAT is introduced as a GPR-based band analysis tool within ARTMO’s MLRA toolbox.The implementation extends ARTMO with GPR and automated band-selection functionality.
- GPR-BAT procedure: The procedure repeatedly removes the least contributing band, retrains and validates a new GPR model, and continues until one band remains.This sequential backward band removal identifies the most sensitive final band and band combinations for the variable under consideration.
- Outputs: The toolbox stores band rankings and validation statistics including R2, RMSE, and NRMSE during sequential band removal.Outputs can be queried and plotted through the graphical interface.
- Validation: With k-fold cross-validation, training data are split into equal folds, validation accuracies are averaged, and statistics such as standard deviation and min-max are calculated.Band removal can use sums of σb values or σb rankings.
- Purpose: GPR-BAT is designed to identify the minimum number of bands needed to retain robust results and the most sensitive wavelengths.The GUI reports validation statistics versus band count, associated wavelengths, and relative-band frequencies when cross-validation is used.
- Scope: Although emphasized for vegetation properties, GPR-BAT can be applied to measured or modeled surface biophysical or geophysical variables associated with spectral data.This broadens the stated application scope beyond the case studied here.
4. Global Sensitivity Analysis
The study compares data-driven GPR-BAT band rankings with variance-based global sensitivity analysis of PROSAIL. The sensitivity analysis samples the full input space and estimates each vegetation variable’s total contribution to model-output variance.
- Rationale: GPR-BAT is a statistical, data-driven method whose meaningfulness and performance depend on the quality of the introduced dataset.The paper therefore compares its best-performing bands against global sensitivity analysis.
- Sensitivity analysis: Variance-based global sensitivity analysis evaluates the relative importance of input variables across the full input-variable space.It can identify influential variables through first-order and total sensitivity effects.
- Experimental setup: The analysis uses PROSAIL, combining PROSPECT4 and SAIL, with vegetation inputs sampled by Latin Hypercube sampling.The sampled variables span the min-max boundaries listed in Table 1.
- Experimental setup: 1000 samples across 7 input variables produced 9000 directional-reflectance simulations from 400 to 2500 nm at 1 nm increments.Only total-order sensitivity effects were considered and expressed as percentages.
5. Case studies
GPR-BAT is illustrated using two hyperspectral datasets: a field dataset collected in Nebraska, United States, and the airborne SPARC campaign over Barrax, Spain.
- Datasets: The first case study uses a field hyperspectral dataset collected in Nebraska, United States.The dataset contains biophysical variables and associated spectra for illustrating GPR-BAT’s utility.
- Datasets: The second case study uses the airborne SPARC campaign dataset collected over Barrax, Spain.SPARC is the named airborne campaign used in the study.
5.1. UNL field hyperspectral dataset
The UNL dataset comprised maize and soybean field observations from eastern Nebraska, combining canopy and leaf-level measurements with hyperspectral reflectance data. Measurements covered multiple field-years, crop-management regimes, and growing-season conditions.
- Study site: The study site comprised three approximately 65-ha fields at the University of Nebraska-Lincoln Agricultural Research and Development Center near Mead, Nebraska.
- Study site: The fields included continuous irrigated maize, irrigated maize/soybean rotation, and rain-fed maize/soybean rotation under best management practices.
- Study site: The dataset contained 16 maize and 8 soybean field-years, with maximal green leaf area index ranging from 4.3 to 6.5 m2/m2 for maize and 3.0 to 5.5 m2/m2 for soybean.
- Field measurements: Leaf reflectance was measured from 400 to 900 nm using a leaf clip, and red-edge chlorophyll index values were computed from averaged reflectance scans.
- Field measurements: Analytical chlorophyll extraction established a relationship between red-edge chlorophyll index and leaf chlorophyll content, with RMSE < 38 mg/m2 and NRMSE below 4.5%.
- Field measurements: Field-level reflectance consisted of 278 maize and 145 soybean spectra collected from 2001 through 2008 using top-of-canopy radiometers covering 400 to 1100 nm with 2.0 nm resolution.
5.2. SPARC field and HyMap dataset
The SPARC field dataset covered diverse crops and canopy conditions, while HyMap supplied corrected airborne hyperspectral reflectance linked to sampling-unit measurements of vegetation properties.
- Study site: The SPARC-2003 campaign measured biophysical parameters within 108 elementary sampling units across nine crop types.
- Study site: The dataset encompassed different crop types, growing phases, canopy geometries, and soil conditions, with no differentiation between crops in the analysis.
- Field measurements: The two principal vegetation variables were leaf area index and canopy water content; LAI values were assigned per sampling unit from 24 measurements.
- Field measurements: Canopy water content was calculated as the product of LAI and leaf canopy content, with leaf water content based on fresh and dry biomass measurements.
- HyMap dataset: HyMap acquired 125 contiguous bands between 430 and 2490 nm, with 11–21 nm bandwidths and 5 m pixel size.
- HyMap dataset: A top-of-canopy reflectance dataset was prepared for the centre point of each elementary sampling unit and its corresponding LAI value.
5.3. Experimental setup
The experimental setup used repeated cross-validation and sequential backward band removal to assess sensitive spectral bands and reduce each model to a single band.
- Validation: A k-fold cross-validation SBBR procedure repeated each iteration with different training and validation pools so every sample served in validation.
- Validation: The procedure used k=10 for the Nebraska dataset of 263 samples and k=4 for the SPARC dataset of 100 samples, producing validation subsets of about 25 samples.
- Validation: Goodness-of-fit statistics were averaged across the k validation runs, including CV, RMSECV, NRMSECV, standard deviation, and min-max rankings.
- Band selection: The accumulated rankings identified the least contributing band, which was removed iteratively until only one band remained.
- Implementation: Training and validation processing speed was logged, and analyses were performed on a 64-bit Intel Core i7-4700MQ processor with 16 GB memory.
6. Experimental results
Across the UNL field and Barrax SPARC datasets, GPR-BAT identified compact band subsets that maintained or improved vegetation-property retrieval accuracy while reducing processing time. The most informative bands differed by property and dataset, and uncertainty estimates helped assess image-wide retrieval performance.
- 6.1. UNL field hyperspectral dataset: LCC and gLAI retrieval: Using all hyperspectral bands did not produce the best UNL retrievals; reducing the input generally improved stability and substantially reduced processing time.Processing took 19 s with hyperspectral data versus less than a second with fewer than 10 remaining bands.
- 6.1. UNL field hyperspectral dataset: LCC and gLAI retrieval: UNL accuracies remained high with only 3 bands for LCC and 2 bands for gLAI, whereas single-band models performed worst.For LCC, stable results were maintained to 9 bands; for gLAI, high accuracies persisted to 7 bands before remaining high through the two-band configuration.
- 6.1. UNL field hyperspectral dataset: LCC and gLAI retrieval: UNL LCC benefited from bands near 482, 500, 564, 710, and 714 nm, with additional informative bands in the 878-980 nm NIR region; gLAI favored 406 nm, 746 nm, and 792-878 nm.The LCC rankings also showed a distinct low-σb informative region around 720 nm.
- 6.2. Barrax SPARC dataset: LAI and CWC retrieval: For the Barrax SPARC dataset, LAI accuracies stayed stable to 4 bands and CWC to 6 bands, while one-band models produced the worst results.High accuracies remained through three bands for LAI and four bands for CWC.
- 6.3. Interpretation of sensitive bands: GPR-BAT identified sensitive bands from training data and paired them with uncertainty estimates to assess retrieval performance across entire images.Sensitive-band interpretation linked selected wavelengths to chlorophyll, LAI, LCC, dry matter, and liquid-water influences across spectral regions.
7. Discussion
The discussion finds that GPR-BAT identifies informative band combinations and supports reducing hyperspectral data while preserving strong vegetation-property predictions. Results also show that spectral selection must account for noise, redundancy, absorption regions, and variable co-variations.
- GPR-BAT identified sensitive bands for remotely predicting LCC and best-performing bands within 1157-1419 nm.The identified bands occurred in a strong LCC absorption region.
- Vegetation properties such as LAI, LCC, and CWC relate to broad spectral regions, so resampling narrowband data to broader bandwidths can be beneficial.The discussion gives 10 nm and HyMap-resolution resampling as examples.
- The HyMap results suggest that optimized LAI can be reached with few, specifically 4, well-identified bands.
- Single-band selection can be misleading because low σb values may reflect poorer SNR rather than lower vegetation information; GPR-BAT is therefore recommended as a more robust method.The discussion links irregular σb behavior from 900 nm onward to detector SNR limitations.
- Using all bands or reducing to superspectral data below 50 bands can both yield top-performing models, provided multispectral bands are correctly located across the spectral range.
- For tested variables, two best-performing bands produced suboptimal results, making two-band indices unsuitable for hyperspectral data.
- Full-spectrum analysis can identify more powerful band combinations, and using fewer well-identified bands can improve predictive accuracies and processing speed.SPARC HyMap analysis took a few minutes, while mapping took less than a minute.
- A red-edge band between 700-750 nm was crucial for each variable, while GPR-BAT also identified bands outside expected absorption regions through variable co-variations.
8. Conclusions
The study implements GPR-BAT in ARTMO to identify informative spectral bands and the smallest band sets retaining high predictive accuracy for vegetation properties. Across two hyperspectral datasets, selected-band models outperformed models using all wavebands, with best performance generally requiring four to nine bands.
- Tool and procedure: GPR-BAT was implemented in ARTMO’s MLRA toolbox as an automated tool for spectral band analysis using Gaussian processes regression.The procedure sequentially removes the least contributing band while developing a GP regression model, tracking goodness-of-fit validation and band rankings.
- Tool and procedure: The tool identifies informative bands and the least number of bands that preserve high predictive accuracy for surface biophysical or geophysical variables.These objectives support optimized and automated vegetation-property mapping after selecting the best-performing regression model.
- Datasets and findings: GPR-BAT was applied to field and airborne hyperspectral datasets covering crop variables including LCC, gLAI, LAI, and CWC.The field dataset covered 400–1000 nm measurements from maize and soybean, while the airborne HyMaP dataset covered 430–2490 nm across various crop types.
- Datasets and findings: Using all hyperspectral wavebands did not produce the most accurate GP regression models, particularly for the 301-band field dataset.Reducing the number of bands with GPR-BAT improved performance for that dataset.
- Datasets and findings: CV increased from 0.55 to 0.79 for LCC and from 0.88 to 0.94 for gLAI after band reduction.These values report the improvement associated with reducing bands in the field hyperspectral dataset.
- Datasets and findings: For each considered variable, top performance occurred with four to nine bands, including a red-edge band and bands in relevant absorption regions.The findings support selecting informative bands rather than retaining the full hyperspectral waveband set.