Use of Derivative Calculations and Minimum Noise Fraction Transform for Detecting and Correcting the Spectral Curvature Effect (Smile) in Hyperion Images

Abstract

Earth Observing-1 Hyperion data were found to be relatively noisy and to contain significant cross-track spectral curvature nonlinearity disturbances, known as the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">smile/frown</i> effect. A method for the correction of spectral curvature effects (smile) in Hyperion images, termed <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">trend line smile correction</i> (TLSC), is presented. The method is based on the assumption that there is a partial correlation between data spectral nonuniformity, due to the smile and eigenvalues gradient that mostly appears in the first minimum noise fraction (MNF) image (MNF-1). However, MNF-1 consists of both spatial and spectral information. Therefore, it is hypothesized that adaptation applied to MNF-1, according to exclusively spectrally derived parameters (e.g., atmospheric absorption features) can account specifically for the smile effect in the data. A set of normalization factors, calculated from the spectral derivative at the right-hand side of the O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> absorption feature (760 nm), MNF-1 and the moderate-resolution atmospheric transmittance radiative transfer model, are used to scale the initial MNF-1. The image is corrected after the inverse conversion of the MNF to radiance space. The methodology was tested on four different Hyperion scenes and consistently outperformed other tested methods by up to nine times. As a result, thematic mapping, using the TLSC-corrected reflectance data cube, was shown to be consistent with the geology maps of the study area.