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Automatic Endmember Bundle Unmixing Methodology for Lunar Icarus 319 (2019) 349–362 Contents lists available at ScienceDirect Icarus journal homepage: www.elsevier.com/locate/icarus Automatic endmember bundle unmixing methodology for lunar regional T area mineral mapping ⁎ Jihao Yina, Chenyu Huanga, Xiaoyan Luo ,a, Qian Dub a Beihang University, 37 Xueyuan Road, Haidian District, Beijing 100191, China b Department of Electrical and Computer Engineering, Mississippi State University, Starkville, MS 39762, USA ARTICLE INFO ABSTRACT Keywords: The mineral distribution on lunar surface can contribute to studying lunar evolution, while abundance quan- Linear hyperspectral unmixing tification is still challenging. Unmixing on spectral reflectance data is an effective way for mineralresource Spectral variation explanation, especially in hardly accessible area. In regional area unmixing, some existing unmixing models Endmember bundle extraction mainly rely on spectral libraries, which limits the scene adapability in the absence of some prior information. Lunar mineral mapping Meanwhile, spectral variation is a common phenomenon but often neglected, which may lead to subsequent abundance inversion errors. In this paper, we address a novel automatic image-based endmember bundle un- mixing model, which is called AEBU, to solve these problems. Differently from many unmixing algorithms using a single spectrum to represent a type of mineral, we accommodate spectral variation and construct a set of spectra, i.e., endmember bundle, to represent each material, which will allow for comprehensive endmember expression. The endmember bundles are extracted from the imagery and regarded as a spectra catalog for abundance inversion to avoid the dependence on spectral library. The proposed AEBU model contains two major steps: image-based endmember bundle construction and abundance inversion. To construct endmember bundles effectively, we use pixel-wise sparse representation to extract image pixels as endmember candidates, andthen analyze the shape feature of candidate spectra to separate endmember bundles. In abundance inversion, we consider the extracted endmember bundles as existing spectra library and propose a block sparse representation- based algorithm to automatically select reasonable endmembers for per-pixel unmixing. The performance of AEBU is compared with the state-of-the-art bundle unmixing algorithms on simulated lunar data. The experi- mental results demonstrate excellent performance of the proposed AEBU. Finally, we map the mineral dis- tribution on lunar regional areas by AEBU using interference imaging spectrometer (IIM) data collected by ChangE-1 and moon mineralogy mapper (M3) data collected by Chandrayaan-1, and unmix the Cuprite data to show more application of AEBU. 1. Introduction global mapping and regional area mapping (Bras and Erard, 2003). Global maps of the mineral distribution on the moon are mainly based As the only natural satellite of the Earth, the exploration of the on Hapke radiative transfer analysis (Moussaoui et al., 2008): for ex- moon has a significant meaning to study the origin and evolution ofthe ample, some researchers (Lucey, 2004) mapped the distribution of e.g., Earth (Bharti et al., 2014). There exist many satellites including the clinopyroxene, orthopyroxene, olivine, and plagioclase with five bands SELENE launched by Japan in September 2007, ChangE-1 Lunar Orbiter UVVIS data of Clementine. Regional area mapping pays more attention launched on 24th October 2007 by China, Chandrayaan-1 launched on to the fine research of material distribution on craters and maria. With 22nd October 2008 by India and USAs Lunar Reconnaissance Orbiter/ only five bands of Clementine it is difficult to achieve this mission, Lunar Crater Observation and Sensing Satellite (LRO/LCROSS) laun- while hyperspectral data of IIM onboard ChangE-1 and M3 onboard ched on 18th June 2009, which are important to recent lunar ex- Chandrayaan-1 (Pieters et al., 2009) make it more feasible. ploration missions (Jin et al., 2013). Since several moonshot projects Hyperspectral unmixing is an effective approach to estimate mineral have been achieved till now, a large amount of data is waiting for composition and distribution for large scale areas (Kruse et al., 1985). analysis (Yan et al., 2010). An important task of lunar exploration In general, spectral mixture models can be linear or nonlinear. Linear program is mineral mapping, which can be divided into two categories: spectral mixture model (LSMM) is widely adopted and it is suitable for ⁎ Corresponding author. E-mail addresses: [email protected] (J. Yin), [email protected] (C. Huang), [email protected] (X. Luo), [email protected] (Q. Du). https://doi.org/10.1016/j.icarus.2018.09.005 Received 22 December 2017; Received in revised form 5 September 2018; Accepted 5 September 2018 Available online 25 September 2018 0019-1035/ © 2018 Elsevier Inc. All rights reserved. J. Yin et al. Icarus 319 (2019) 349–362 Fig. 1. The study areas are shown in yellow boxes, the red line is IIM data and the blue line is M3 data. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) medium or low resolution imagery. The major principle of linear spectral variability due to different illumination conditions, variable spectral mixture model is that mineral spectrum features linearly grain size and due to the presence of elemental substitution (Jin et al., combine in proportion to their area fractions and the fractions are 2013; Hiroi and Pieters, 1994; Pilorget et al., 2016). A single spectrum considered as abundance. The mathematical formular of linear spectral may not represent an endmember well in practical applications, espe- mixture model is cially in complex geographical environments (Bateson et al., 2000), and x= aE + n (1) neglecting spectral variation is the major reason of error in abundance inverse model. Therefore, using endmember bundle to represent a where a is the abundance vector of x, E denotes the endmembers material is an alternative and effective approach. spectra of the image and n is the noise vector. Since the lunar surface is Several endmember bundle based algorithms have been proposed composed of minerals and lack of vegetation, we focus on linear spec- recently. For example, Somers et al. (2012) proposes an endmember tral mixture model in this paper. bundle extraction algorithm called EIBE to automatically extract end- Endmembers are spectral signatures of tconstituent materials in an member bundles from imagery, which randomly selects endmember image scene. The mainstream unmixing methods are based on a given candidates from imagery, and then clusters them into bundles. Using catalog of endmember spectra like USGS spectral library to select these extracted endmember bundles as a spectral library, abundances endmember spectra for mapping, in which the spectral adaptability is are estimated via multiple endmember spectral mixture analysis limited by fixed library. In recent years, researchers tend to extract (MESMA) method (Roberts et al., 1998). The process of endmember endmembers from the image, i.e., image-based endmember spectra for bundle extraction in Somerss algorithm ignores spatial homogeneity of mapping (Plaza et al., 2009). These image-based endmember extraction material distribution, assuming similar distribution of minerals in algorithms can not only reduce the cost of extensive spectrometric neighboring pixels. Thus the block-area endmember candidates ex- measurements, but also share the same atmospheric effects with un- traction in EIBE may lead to inaccurate endmember bundle extraction mixed data (Keshava and Mustard, 2002). They mainly contain two and affect subsequent abundance estimation. An improved endmember categories based on whether there exist pure pixel or not per end- bundle extraction method proposed in Xu et al. (2015) considers spatial member in the image. If there exists pure endmember pixels in the and spectral information called SSEBE in this paper, combining the image, the classical endmember extraction algorithms include pixel pixel purity index (PPI) (Boardman et al., 1995) and homogeneity index purity index (PPI) (Boardman et al., 1995), iteration error analysis (HI) for candidate endmembers selection. However, PPI captures the (IEA) (Wang et al., 2014), vertex component analysis (VCA) endmembers lying in the boundary of data simplex and may fail to (Nascimento and Dias, 2005) and N-FINDR (Winter, 1999). With non- extract other variable endmembers within the simplex (Uezato et al., pure-pixel existing hypothesis, the representative algorithms are 2016). These endmember bundle extraction methods classify end- minimum volume-constrained nonnegative matrix factorization (MVC- member bundles by k-means (Hartigan and Wong, 1979) with spectral NMF) (Jia and Qian, 2009) and minimum volume simplex analysis value characteristics. However, spectral value may not be a highly (MVSA) (Li and Bioucas-Dias, 2009). In addition, some unmixing discriminant feature to distinguish spectra into different classes. For methods take advantage of statistic models and consider homogeneous example, some numerically similar spectra belong to different classes, mixture of pixels in statistic formulation, such as the Bayesian model while the same-class spectra vary greatly in value (Zhang et al., 2010). based unmixing algorithm (Chen et al., 2016; Moussaoui et al., 2008). In addition, these endmember bundle-based algorithms estimate Generally, most unmixing
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