Wavelet Analysis of Soil Reflectance for the Characterization of Soil Properties

Wavelet analysis has proven to be effective in many fields including signal processing and digital image analysis. Recently, it has been adapted to spectroscopy, where the reflectance of various materials is measured with respect to wavelength. Reflectance spectra can cover broad wavelength ranges within which wavelength-specific reflectance values can be highly autocorrelated, making the use of traditional statistical procedures impractical for correlating the spectral information with the variable of interest. The spectra also need to processed prior to correlation to remove noise originating from instrument dynamics or atmospheric conditions. Wavelet analysis can provide a good technique to address the aforementioned problems, by reducing the number of necessary wavelengths to the most significant minimum, removing multi-collinearity among the spectral wavelengths, and filtering noise. This project applied wavelet analysis to hyperspectral near-infrared (NIR) and mid-infrared (MIR) reflectance spectra of soil materials, and evaluated its combined use with Multiple Linear Regression Analysis (MLR) and Partial Least Squares Regression (PLSR). Spectral analysis via wavelet decomposition and MLR provided cross validation R values of 0.41, 0.76, 0.48, 0.37, 0.02, 0.83 and 0.50 for soil pH, organic carbon, sand, silt, clay (%), and oxalate extractable Al and Fe (mg kg), respectively, with similar results obtained for wavelets + PLSR and PLSR alone. Wavelet analyses successfully reduced the number of wavelengths (predictors) used in the correlation of reflectance spectra with soil properties, and helped with the spectral characterization of certain soil analytes by incorporating different wavelet bases at different scales. INTRODUCTION Soil survey and characterization in the agricultural landscape can be hindered by the high cost of chemical and physical laboratory analyses, which are typically time consuming and labor intensive. While reflectance spectroscopy (in the NIR and MIR) has shown promise for rapid and cost-effective characterization of various soil parameters in both laboratory and in situ (Viscarra Rossel et al. 2006; Waiser et al. 2007), its accuracy is affected by methods of spectral preprocessing and choice of statistical procedures used to correlate spectra to soil parameters. Following initial use in geophysical applications in the early 1980s, wavelet transformation and analysis has become commonly employed in other fields, including applications in signal processing (noise removal, improvement of signal/noise ratio, signal compression), remote sensing (feature enhancement and extraction), and digital image analysis (edge detection and land structure classification). It has been reported to outperform other signal processing methods such as Fourier transformation and moving averages because of its ability to localize in both time and frequency domains (Kumar and Georgiou, 1997). The goals of this project were to: i) enhance characterization of soil properties using wavelet analysis of reflectance spectra; ii) reduce the dimension of necessary predictors (components of reflectance spectra); iii) test the prediction capability of obtained wavelet coefficients in the estimation of soil properties; and iv) compare the estimation accuracy of combined use of wavelet and Multiple Linear Regression (MLR) with results of the Partial Least Square Regression (PLSR) technique commonly used for calibrating soil reflectance to soil properties. MATERIAL AND METHODS Soil Samples Eighty-two soil samples (0-5 cm) were collected from pasture sites in northern Louisiana. The soils included Darley (fine, kaolinitic, thermic Typic Hapludult) and Ruston (fine-loamy, siliceous, thermic Typic Paleudult) series. Samples were air dried, ground to pass a 2 mm screen, and analyzed for pH; organic C (%); soil texture: sand, silt, clay (%); and oxalateextractable Al and Fe (mg kg). The quantity of soil constituents ranged as 4.93 to 6.41 (pH), 0.54 to 6.14 (% C), 45 to 95, 0 to 50, 0 to 15 (texture), 150 to 2708 (Al) and 256 to 28360 (Fe). VNIR-MID Infrared Spectra The air-dried ground samples were scanned in the NIR (1000 to 2500 nm) and MIR (2500 to 25000 nm) as described in McCarty et. al. (2002). All spectra were computed as log [1/Reflectance] with 64 co-added scans per spectrum. Discrete Wavelet Transformation (DWT) In wavelet transformation, a spectral signal with finite length is decomposed into two series: the first consisting of approximation coefficients (smooth waveform) that capture the overall variation and trend of the spectrum, and the second consisting of wavelet coefficients that capture the fine detail (high frequency part of the signal). The approximation coefficients (A(j,k)) are obtained as an inner product of the signal (f(n)) with a scaled and oriented (shifted) scaling function. The detail coefficients, D(j,k), (wavelet coefficients) are obtained as inner product of signal with scaled and shifted wavelet functions formulated as: