MCM-AWARE TWIN-LEAST-SQUARE GAN FOR HY-PERSPECTRAL ANOMALY DETECTION Anonymous

Abstract

Hyperspectral anomaly detection under high-dimensional data and interference of deteriorated bands without any prior information has been challenging and attracted close attention in the exploration of the unknown in real scenarios. However, some emerging methods based on generative adversarial network (GAN) suffer from the problems of gradient vanishing and training instability with struggling to strike a balance between performance and training sample limitations. In this work, aiming to remedy the drawbacks of existing methods, we present a novel multi-scale covariance map (MCM)-aware twin-least-square GAN (MTGAN). Instead of the widely used single-scale Gaussian hypothesis background estimation, in MTGAN, we introduce the MCM-aware strategy to construct multi-scale priors with precise second-order statistics, thereby implicitly bridging the spatial and spectral information. Thus, we reliably and adaptively represent the prior of HSI to change the priors-lack situation. Moreover, we impose the twin-least-square loss on GAN, which helps improve the generative ability and training stability in feature and image domains, overcoming the gradient vanishing problem. Finally, the network enforced with a new anomaly rejection loss establishes a pure and discriminative background estimation. Experiments demonstrate that the average detection accuracy of MTGAN reaches 0.99809, which is superior to the state-ofthe-art algorithms.

1. INTRODUCTION

Hyperspectral image (HSI) appears as a three-dimensional (3D) data cube, two dimensions of which show the spatial information of materials, and the other reveals hundreds of contiguous bands to perceive each scene (Yokoya et al., 2012) . Among a wealth of HSIs interpretation techniques in practical situations, anomaly detection has many potential applications in video surveillance, activity recognition, and scene understanding, etc (Lanaras et al., 2015; Eyal et al., 2019; Tu et al., 2020) . However, due to the insufficient prior information, inaccurate labels, complex scenes, and unbalanced samples, it is high-cost and sometimes infeasible to accurately detect different types of anomalies in HSI. Consequently, hyperspectral anomaly detection without any priors is a challenging task and is of great importance. Deep learning-based methods have powerful and unique advantages in modeling and characterizing complex data (Stanislaw et al., 2020) . A lot of research has appeared in the field of anomaly detection, which can be roughly divided into three categories: supervised, semi-supervised, and unsupervised. However, due to the difficulty of annotation and collection of label training, supervised methods are rarely applied (Grnitz et al., 2013; Raghavendra & Sanjay, 2019) . Semi-supervised work aims to break the dilemma between the number of samples and detection performance, but it still requires pure background training samples (Blanchar et al., 2010; Wu & Prasad, 2018) . On the one hand, unsupervised learning based hyperspectral anomaly detection has become a new trend (Schlegl et al., 2017; Zhang et al., 2019) . On the other hand, the detection performance is limited due to the lack of prior knowledge. Therefore, we propose an MCM-aware strategy to adaptively obtain reliable and stable pseudo-labeled prior information to alleviate these problems. Concretely, motivated by the observations mentioned above, we estimate the priors and model the background with multi-scale covariance matrices as the necessary preparation fed into the MTGAN model, which generates discriminative representations with second-order statistics in covariance pooling and is conducive to exploiting the intrinsic spatial-spectral information of HSI. The progress of MCM-aware priors construction strategy is illustrated in Figure 1 . Furthermore, though GAN performs well in anomaly detection tasks according to the literature, the real objective of GAN is supposed to capture more separable latent features between background and anomalies instead of minimizing the pixel-wise reconstruction error (Gong et al., 2020) . The gradient vanishing problem, which is partly caused by the hypothesize that the discriminator as a classifier with the sigmoid cross-entropy loss function in regular GANs, is not conducive to the generation of background and discrimination of anomalies. Hence, to facilitate the training stability and alleviate the gradient-vanishing problem, we present twin-least-square loss to perform background modeling in feature and image domains. Accordingly, we can solve the problem of gradient vanishing and enhance the representation directly aiming at the reconstruction of each pixel. In light of the difficulties of the separability between the anomaly and background, we also impose an anomaly rejection loss to avoid anomalies contamination in background estimation. In this way, the network can reconstruct resembled background dictionaries, but dramatically changed anomalies, thereby increasing the degree of difference between them and endow better detection accuracy. To verify the effectiveness of the proposed method, we implement evaluations on five public HSI data sets. In MTGAN, the average AUC scores of (P d , P f ) and (P f , τ ) are 0.99809 and 0.00518, respectively, which outperform previous state-of-the-art methods. To summary, our contributions are mainly three-fold: • To solve the problem of insufficient samples that previous methods suffer from, we propose an MCM-aware strategy to reliably and adaptively generate prior dictionaries. In specific, we calculate a series of multi-scale covariance matrices, taking advantage of the second-order statistics to naturally model the distribution with integrated spectral and spatial information. • The twin-least-square loss is introduced into both the feature and image domains to overcome the gradient vanishing problem. Meanwhile, the generative ability and training stability can be improved, which can fit the characteristics of high-dimension and complexity of HSI data. • To further reduce the false alarm rate, we design a novel anomaly rejection loss to enlarge the distribution diversity between background regions and anomalies, aiming to distinguish between background and anomalies. Experimental results illustrate that the AUC score of (P f , τ ) in MTGAN is one order of magnitude lower than other state-of-the-art methods.

2. RELATED WORK

For traditional methods, the RX method assumes that each spectral channel is Gaussian-distributed, and the pixel is L-dimensional multi-variate Gaussian distributed (Guo et al., 2014; Luo et al., 2019; Ahmed et al., 2020) . As a non-RX based methods, the ADLR method obtains abundance vectors by spectral decomposition and constructs a dictionary based on the mean value clustering of abundance vectors (Qu et al., 2018) . The PAB-DC model imposed with low-rank and sparse constraints considers the homogeneity of background and the sparsity of anomalies to construct the dictionaries (Huyan et al., 2019) . The emerging typical algorithm AED removes the background mainly by attribute filtering and difference operation. Additionally, the LSDM-MoG method combines the mixed noise models and low-rank background to characterize complex distributions more accurately (Li et al., 2020) . However, these conventional methods are based on single-scale Gaussian assumption and cannot represent complex and high-dimensional data sets well, leading to the exploration of deep learning-based methods (Ben et al., 2014) .



Figure 1: The progress of MCM-aware priors construction strategy.

