Collaborative-guided spectral abundance learning with bilinear mixing model for hyperspectral subpixel target detection
Introduction
Hyperspectral remote sensing system can acquire and record the radiance of the Earth’s surface objects or scenes within each pixel area in vast spectral wavelength bands, providing hyperspectral images (HSIs) containing a large number of contiguous spectral bands (Bioucas-Dias et al., 2013, Manolakis et al., 2003, Wu et al., 2018). These contiguous spectral bands present rich spectral information that can be used to distinguish various ground cover materials (Axelsson et al., 2016, Goetz, 2009, Landgrebe, 2002, Su et al., 2020, Xie et al., 2018). With this characteristic, hyperspectral images have been widely used in many fields, covering agriculture, military, and mineralogy (Manolakis and Shaw, 2002, Yue et al., 2021). In these fields, the detection of specific materials or objects of interest, such as precision agriculture, military and civilian target detection, and mineral exploration, attracts considerable attention due to real-world applications (Boubanga-Tombet et al., 2018, Eismann et al., 2009, Lu et al., 2020). Such detection tasks make hyperspectral target detection become an important topic in remote sensing image processing (Dong, Du et al., 2015, Nasrabadi, 2014, Zhu et al., 2019).
Target detection in hyperspectral imagery is to identify whether the target of interest exists for each pixel based on the known spectrum of the target (Bioucas-Dias et al., 2013, Du and Zhang, 2014, Xie et al., 2019). In general, the known spectrum is acquired from the spectral library or selected from the training sample, usually, one spectrum of the target signature is enough (Healey and Slater, 1999, Li et al., 2022, Manolakis and Shaw, 2002). Target detection in hyperspectral imagery is quite different from that in other optical remote sensing images. For example, target detection in high-resolution remote sensing images detects specific ground objects with the bounding box boxing out the targets, which is a box-level target detection task (Li et al., 2020, Xia et al., 2018). Conversely, target detection in hyperspectral imagery is more like a pixel-level detection task that labels every pixel as the background or target, which is essentially a binary classification problem (Du et al., 2016, Manolakis et al., 2013, Zhao et al., 2021). However, compared with a large number of background pixels, the number of target pixels only occupies a very small fraction, which does not allow the overall classification error for a good tool to measure the hyperspectral target detection performance. Consequently, most existing methods that perform target detection in hyperspectral imagery are formed according to the Neyman–Pearson criterion, maximizing the detection probability in the fixed false alarm rate (Chang and Du, 2004, Nasrabadi, 2014).
As early as the 1980s, exploiting hyperspectral images to detect specific targets of interest emerged. In the early stage, people construct target detectors based on simple spectrum matching where the pixel with higher spectral similarity to the prior target spectrum is more likely to be labeled as the target. Spectral angle mapper (SAM) (Kruse et al., 1993), Spectral information divergence (SID) (Chang, 1999), and spectral matched filter (SMF) (Nasrabadi, 2008) are the detectors of this category. After that, machine learning theory has been applied to target detection in hyperspectral images, and extensive robust hyperspectral target detectors based on machine learning theory emerged, such as kernel-based algorithms (Jiao and Chang, 2008, Kwon and Nasrabadi, 2004), representation-based target detectors (Bitar et al., 2019, Chen et al., 2011, Li et al., 2015, Zhang et al., 2015), and metric and manifold learning-based methods (Dong, Zhang et al., 2015, Zhang et al., 2013). In recent years, exploiting deep learning methods to solve the target detection problem in hyperspectral imagery is mainstream. These methods design deep networks to extract spectral and spatial features to distinguish the difference between targets and background, thus allowing for target pixel identification. For example, HTD-net design a multi-layer convolutional neural network to distinguish target-background and target–target pixel pairs (Zhang et al., 2020), while TSCNTD constructs an effective deep learning-based target detection method using two-stream convolutional networks (Zhu et al., 2020).
The aforementioned detection methods are mainly designed for full-pixel target detection in hyperspectral images, where target pixels are considered as pixels that contain single target spectral information. However, due to the limitation of spatial resolution and target size, targets in the image scene often appear as subpixel targets which are the mixed pixels containing the target of interest and other background materials. In this case, the detection performance of the above full-pixel target detection methods could be limited, and the process of detection turns out to be the subpixel target detection task in hyperspectral imagery. In the open literature, different methods have been investigated to solve the subpixel target detection problem in hyperspectral images. According to different background description models, structural background description methods and nonstructural background methods are investigated. Matched subspace detector (MSD) (Scharf & Friedlander, 1994), adaptive matched subspace detector (AMSD) (Manolakis et al., 2001), and orthogonal subspace projector (OSP) (Chang, 2005) are the category of structural background description methods, while adaptive coherence/cosine estimator (ACE) (Kraut & Scharf, 1999), hybrid unstructured detector (HUD) (Broadwater & Chellappa, 2007), and non-parametric adaptive matched filter (Matteoli et al., 2020) are the category of nonstructural background description detectors. Moreover, to achieve robust performance, more attempts have been made at hyperspectral subpixel target detection. For example, to improve the background reconstruction, a pixel reconstruction-based subpixel target detection model (Song et al., 2021) is presented, it tries to obtain accurate background endmembers and reconstruct the input hyperspectral image to detect subpixel targets. A double dictionary-based nonlinear representation method (Wang et al., 2022) constructs double dictionaries to consider the spatial characteristics of the target and background for subpixel detection. Two subpixel target detectors are presented based on a multiple-instance learning framework, which aims to learn a discriminative prime target signature by maximizing the posterior detection statistics of subpixel hyperspectral targets (Jiao et al., 2022). It should be noted that some sparse and collaborative-based detectors, such as the sparsity-based target detector (STD) (Chen et al., 2011) and the combined sparse and collaborative representation detector (CSCR) (Li et al., 2015), although they are designed for the full-pixel target detection, they still have a certain capability of detecting subpixel targets.
Despite great advances in subpixel target detection for hyperspectral images, most of the existing subpixel target detectors are constructed based on the linear mixing model (LMM), assuming that different endmembers interact with the incident radiation in a linear way at a subpixel level (Gao et al., 2022, Ling et al., 2022, Manolakis et al., 2001, Yang et al., 2018). However, due to the multiple scattering during hyperspectral imaging, the linear mixing model cannot illustrate the multiple materials interactions that are nonlinear and widespread in real-world hyperspectral images, which could result in unsatisfactory performance in real-world hyperspectral image subpixel target detection. To alleviate this problem, we develop a new collaborative-guided spectral abundance learning model (denoted as CGSAL) for subpixel target detection in hyperspectral images based on a bilinear mixing model (BMM) in this paper. BMM is capable of illustrating multiple materials interactions by modeling virtual endmembers and their abundance, which can help to achieve good accuracy for modeling nonlinear scattering accounts for multiple materials interactions and contribute to more accurate model learning. Moreover, to emphasize the contributions of different endmembers and the collaborative relationships between them, we impose a collaborative constraint term on the proposed model, which is beneficial to spectral abundance learning of the target of interest and allows for precise subpixel target detection. The main contributions of this study are summarized as follows:
- (1)
We present a novel collaborative-guided spectral abundance learning method with the bilinear mixing model for hyperspectral subpixel target detection. The proposed CGSAL detector can model multiple materials interactions with regard to the nonlinear scattering in the process of hyperspectral imaging, so as to reach good accuracy for spectral abundance learning, which can help detect subpixel targets accurately.
- (2)
We propose to add a collaborative term to the spectral abundance learning model to emphasize the collaborative relationships between different endmembers. Under the condition of the limited number of samples in the endmember dictionary, the collaborative term can demonstrate the contributions of different endmembers, thus allowing for precise spectral abundance learning of the target.
The remainder of this work is organized as follows. Section 2 presents the proposed CGSAL method for hyperspectral subpixel target detection, including the collaborative-guided spectral abundance learning model, and its numerical solution algorithm. In Section 3, Experiments and analyses conducted on three real-world hyperspectral image datasets are provided, including detection performance evaluation and comparison, and parameters analyses. Finally, the conclusion of this article is drawn in Section 4.
Section snippets
Proposed CGSAL method
In this section, the proposed CGSAL method for hyperspectral subpixel target detection is detailedly described. We first introduce the collaborative-guided spectral abundance learning approach, in which we learn the spectral abundance of the target of interest to detect subpixel targets based on the bilinear mixing model and we add a collaborative term to emphasize the collaborative relationships of endmembers for accurate spectral abundance learning. We then provide the numerical solution
Experimental results and analysis
To evaluate the subpixel target detection performance and test the robustness and effectiveness of the proposed CGSAL method, extensive experiments and analyses conducted on three real-world and one synthetic hyperspectral image datasets are provided in this section. First of all, we introduce the four datasets and provide the experiment setting details. We then present the detection performance comparison with respect to several valid hyperspectral target detectors and our proposed CGSAL
Conclusion
In this work, we propose a new subpixel target detector with a novel collaborative-guided spectral abundance learning model based on the bilinear mixing model for hyperspectral images. To model the multiple materials interactions, the proposed CGSAL presents the virtual endmember term for denoting nonlinear scattering in the processing of hyperspectral imaging. To further emphasize the collaborative relationships that contribute to illustrating the virtual endmember term between different
Declaration of Competing Interest
The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Bo Du reports financial support was provided by Wuhan University.
Acknowledgments
This work was supported in part by the National Natural Science Foundation of China under Grants 62225113, 61871299, and the Natural Science Foundation of Hubei Province under Grants 2018CFA050.
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