Multiple Aerosol Unmixing by the Split Bregman Algorithm

Abstract

For more than a decade, the U.S. government has been developing laser-based sensors for detecting, locating, and classifying aerosols in the atmosphere at safe standoff ranges. The motivation for this work is the need to discriminate aerosols of biological origin from interferent materials such as smoke and dust using the backscatter from multiple wavelengths in the long wave infrared (LWIR) spectral region. Through previous work, algorithms have been developed for estimating the aerosol spectral dependence and concentration range dependence from these data. The range dependence is required for locating and tracking the aerosol plumes, and the backscatter spectral dependence is used for discrimination by a support vector machine classifier. Substantial progress has been made in these algorithms for the case of a single aerosol present in the lidar line-of-sight (LOS). Often, however, mixtures of aerosols are present along the same LOS overlapped in range and time. Analysis of these mixtures of aerosols presents a difficult inverse problem that cannot be successfully treated by the methods used for single aerosols. Fortunately, recent advances have been made in the analysis of inverse problems using shrinkage-based <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -regularization techniques. Of the several <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -regularization methods currently known, the split Bregman algorithm is straightforward to implement, converges rapidly, and is applicable to a broad range of inverse problems including our aerosol unmixing. In this paper, we show how the split Bregman algorithm can successfully resolve LWIR lidar data containing mixtures of bioaerosol simulants and interferents into their separate components. The individual components then can be classified as bio- or nonbioaerosol by our SVM classifier. We illustrate the approach through data collected in field tests over the past several years using the U.S. Army FAL sensor in testing at Dugway Proving Ground, UT.