Small infrared target detection based on low-rank and sparse representation
Introduction
Infrared imaging guide is one of the most accurate guide manners in the precision guide weapons. Thus, infrared small target detection is one of the key techniques for infrared guidance systems and is thus a popular topic of research for military applications. On one hand, small targets are usually submerged in background clutter and heavy noise with low Signal Noise Ratio (SNR) because of the long observation distance during the transmission and scattering in the atmosphere. On the other hand, the targets in the images appear as dim points which make the targets have no obvious feature and texture information useful. Therefore, infrared small target detection becomes difficult because of these two factors [1].
Thus far, methods of infrared target detection can be classified into two categories [2]: detection based on single frame and detection based on sequential frames. The sequential detection methods are processed on the basis of the prior information of the target and background. Thus, these methods cannot achieve satisfactory performance because information can hardly be obtained in military applications. Moreover, the capability of sequential methods commonly depends on the results of single frame detection. Given these characteristics, single frame detection algorithms have attracted considerable attention from researchers, who have proposed various single frame detection methods. These detection methods can be divided into two classes.
One class is the detection of targets using image filtering [3], [4], [5], [6]. This type of algorithms enhances targets by estimating the background through filtering, such as the max-mean filter, max-median filter, top-hat filter, and TDLMS filter. These filters can preserve the edges of structural backgrounds and remove clutter by predicting backgrounds and subtracting the filtered image from the original image. However, these methods suffer from a high false-alarm rate caused by the low SNR of infrared images. Another type of method is detecting targets by using machine learning theory. These methods transform the detection task into a pattern recognition problem to facilitate the application of some powerful mathematical tools, such as PCA [7], PPCA [8], NLPCA [9] and Fisher linear discriminator [10]. These methods also generate the model or extract the features of targets by using training samples. Such details are used to determine the target location.
There are many detection methods based on single-frame proposed in the open literature. Zhao et al. [11] presented a detection algorithm based on the sparse representation. This method improve and optimize the target representation by modeling the small targets as a combination of certain target samples which are generated using Gaussian Intensity Model and employ the thresholding to sparsity concentration index to locate the target position. But the SR method focuses target modeling and is lack of description ability for background. Shao et al. [12] presented a method using the contrast mechanism of human visual system which improved the algorithm proposed by Kim in [13]. This method uses a morphological processing to make the targets distinguished easily from background and locate the true target through threshold segmentation. Gao et al. [14] proposed a detection method based on the IPI model. This algorithm transforms the detection task into an optimization problem which recovers low-rank and sparse matrices and can be solved effectively by low-rank theory. Although this method only employs one low-rank subspace assumption of background which usually comes from a mixture of multi-low-rank subspaces, but it works better if there are heavy noise and clutter in the images with highly heterogeneous background. Chen et al. [15] proposed a detection method based on peer group filter (PGF), bi-dimension empirical mode decomposition (BEMD) and local inverse entropy. In this method, the PGF is used to remove the noise and enhance the target, then, the proposed BEMD can estimate the background and locate the target by removing the background and segmenting the intrinsic mode functions using the local inverse entropy. Based on the BEMD, Chen et al. [16] also proposed a spatial–temporal detection method. Such method combines the advantages of time-domain difference and BEMD, which is based on sequential images.
On the basis of the original data drawn from several low-rank subspaces, Low-Rank Representation (LRR) [17] was recently proposed for subspace segmentation or recovery. LRR can decompose the data matrix into the clean matrix described by the self-expressive dictionary with low-rank coefficients and the sparse noise. Considering the underlying structure revealing and background modeling ability of LRR with large errors or outliers, we propose a low-rank and sparse representation (LRSR) model in this paper. This model adds the sparse representation of the special structure into the LRR. Infrared small target detection method based on LRSR is also presented. This method employs sparse representation for the small target on the basis of the low-rank decomposition of an infrared image to separate the target from noise. The background, noise, and target can be modeled by using the proposed method. Thus, the proposed method has better detection performance than baseline algorithms, as demonstrated by the experiment results.
The remainder of this paper is organized as follows. Section 2 describes the robust principal component analysis and low-rank representation model. Section 3 presents the proposed LRSR with its solution, complexity, and convergence. Section 4 provides a detailed description of infrared dim and small target detection method, which is proposed on the basis of LRSR. Section 5 presents the experimental results and the comparisons between the proposed method and conventional algorithms. Section 6 provides the conclusions and future works.
Section snippets
Low-rank representation
Considering the given observation matrix was generated from a low-rank matrix with some of its entries corrupted by an additive error , the original data can be recovered by the following regularized rank minimization problem which is adopted by the established robust principal component analysis (RPCA) method [18]where is a parameter and indicates a certain regularization strategy, such as the squared Frobenius norm used for
Model of LRSR
An infrared image with small target is typically composed of three components, namely, background, target and noise. Generally, the background of the infrared image is transitions slowly and also has the property of non-local self-correlation, the target and noise are small with respect to the whole image. Thus, the infrared image can be regarded as the superposition of low-rank background component and sparse target-noise component. The infrared image has been decomposed by RPCA into
LRSR based small target detection
As mentioned earlier, an infrared image can be viewed as combination of three components, such as background, target, and noise. Thus, we decompose the original infrared image into three components images by using LRSR model. Then, the target location is determined by thresholding the target image. The whole method of small target detection based on LRSR is depicted in Fig. 2, and the steps of the detection method are as follows:
- 1.
Image data reconstruction. Given that the small infrared target is
Design of experiments
Three groups of experiments are designed to evaluate the target detection performance. The first group is single target detection experiments. Six real images with different backgrounds are decomposed, and the detection results are obtained directly using the proposed method. The second group of experiments is for the infrared sequences with some synthetic targets. We embed small synthetic targets, which are generated from five real targets, into the images chosen from four real sequences.
Conclusion and future work
In this paper, a novel model called LRSR is presented based on low-rank representation combining the sparse representation theory. On the basis of the LRSR model, we proposed a small target detection method which can transform the detection task into separation process of background, noise and target components by solving LRSR. The results of the three groups of experiments validated that the proposed method has better detection performance and greater robustness to different noises than
Conflict of interest
There is no conflict of interest.
Acknowledgments
This work is supported by National Natural Science Foundation of China (Grant No. 61102170). We thank Liu for providing the source codes of LRR. We are also very grateful to the editor and anonymous reviewers for their constructive comments and suggestions that help improve the quality of this manuscript.
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