Hyperspectral Derivative Analysis

Table of Contents

• Introduction
  
• Methodology
  
• DX Implementation
  
• Result
  
• Conclusion
  
• Acknowledge
  
• References

Introduction

Among the techniques developed in spectroscopy, derivative spectroscopy is particularly promising for use with remotely sensed data. Derivatives of the second order or higher should be relatively insensitive to variations in illumination. At the typical spectral sampling interval of hyperspectral systems, derivatives should also be relatively insensitive to sunlight and skylight. Nonetheless, few researchers so far have addressed applications of spectral derivatives in remote sensing.[6][9][10] Although some of these studies have used high order derivatives, [11][12] first and second order derivatives have been the most common. In addition, most of the studies using spectral derivative analysis were directly toward specific applications.[10][13][14]

The purpose of this project is to develop an algorithm for derivative analysis of hyperspectal data and then implement modules for IBM Data Explorer as a general hyperspectral derivative tool that will treat hyperspectal data as truly spectrally continuous data based on the algorithm. It is hoped that with this exploratory tool, the user would be able to proceed general hyperspectral derivative analysis and extract useful spectral features from the spectra for advanced analysis. More important, these operations would be performed with no needs to assume that the data consisted of homogeneous pixels or were generated in highly controlled environments.

Methodology

After smoothing, the resultant smoothing spectra can be then passed into the derivative module. In this study, derivatives are estimated using a finite divided difference scheme, or "finite approximation". The advantage of finite approximation is that the derivatives can be computed according to different finite band resolutions (band separations) to extract special spectral features of interest at different spectral scales. The first and second derivatives are estimated by:
(2)
(3)

Accordingly, higher order derivatives are computed iteratively and any order of derivative is accessible using finite approximation. In general, the n-th order of derivative is:
(4)
where j=(2*i+n)/2, if (2i+n) is even, or j=(2*i+n+1)/2, if (2i+n) is odd, i.e. if the resultant derivative falls between sampling points, it is assigned to the point at next larger wavelength or wave number. The coefficients, Ck are calculated using an iteration scheme.
As the band separation increases, the magnitude of derivatives is usually depressed -a quasi-smoothing effect.[15] This is because the derivatives are normalized by a power of band separation (Equation-4). To facilitate visual comparison of the derivatives as band separation increases, the derivatives can be "enhanced" by replacing the denominator of Equation-4 with the band separation, regardless the order of derivatives.

DX Implementation

The key issue of the implementation is to allow users to flexibly assign various parameters, such as bandwidth for (smoothing), band separation (for derivative computation), to proceed derivative analysis for extracting desired spectral features or exploring the spectra to detect useful information. If you want to try these modules, please go to the program page to download the archives.

Result

Conclusion

Modules developed in this study have been limited to deal with hyperspectral data so far. Improvement and extensions for algorithms toward a more solid analysis tool would be worthwhile. These include the improvement of programming techniques to accelerate the process and reduce memory requirement, incorporating other smoothing and derivative methods, and extend the modules for more general applications on spectral analysis. It is also desired to reinforce these modules for dealing with hyperspectral imagery such as the AVIRIS (Airborne Visible/Infrared Imaging Spectrometer) images.

Acknowledge

References