Simultaneous and constrained calibration of multiple hyperspectral images through a new generalized empirical line model

The empirical line (EL) calibration method is commonly used for atmospheric correction of remotely sensed spectral images and recovery of surface reflectance. The current EL-based methods are applicable to calibrate only single images. Therefore, the use of the EL calibration is impractical for imaging campaigns, where many (partially overlapped) images are acquired to cover a large area. In addition, the EL results are unconstrained and an undesired reflectance with negative values or larger than 100% can be obtained. In this paper, we use the standard EL model to formulate a new generalized empirical line (GEL) model. Based on the GEL, we present a novel method for simultaneous and constrained calibration of multiple images. This new method allows for calibration through multiple image constrained empirical line (MIcEL) and three additional calibration modes. Given a set of images, we use the available ground targets and automatically extracted tie points between overlapping images to calibrate all the images in the set simultaneously. Quantitative and visual assessments of the proposed method were carried out relatively to the off-the-shelf method quick atmospheric correction (QUAC), using real hyperspectral images and field measurements. The results clearly show the superiority of MIcEL with respect to the minimization of the difference between the reflectance values of the same object in different overlapping images. An assessment of the absolute accuracy, with respect to 11 field measurement points, shows that the accuracy of MIcEL, with an average mean absolute error (MAE) of ∼11%, is comparable with respect to the QUAC.