1. Introduction
With the rapid development of remote sensing technology, the spatial resolution, spectral resolution and time resolution of remote sensing image have greatly improved, which facilitates a wide range of applications [
1,
2,
3,
4]. Remote sensing image contains abundant information, of which the processing and analyzing can help people in not only military but also civilian applications, such as disaster control, land planning, urban monitoring, traffic planning, target tracking, etc. [
5,
6,
7]. For all these applications, target detection is the necessary and key step. The targets are usually large objects, such as aircraft, ship, building, etc., which can provide more valuable object for further analyzing. However, the object detection is usually human, animal and other small objects, and the target is not limited to one specific category. Research of fast identification and precise interpretation on particular target has very important strategic significance [
8,
9].
Therefore, target detection has received considerable attention and has always been the research hotspot in remote sensing in the past decades [
10,
11,
12,
13]. A number of target detection algorithms emerged along with the development of remote sensing. Most of these algorithms tend to suppress background information and highlight target to enhance the target itself, e.g., adaptive coherence estimator (ACE) [
9,
14], match filter (MF) [
14], adaptive match filter (AMF) [
9,
15,
16,
17,
18], spectral angle mapper (SAM) [
17], independent component analysis (ICA) [
18], and constrained energy minimization (CEM) [
19,
20]. Stephanie et al. pointed out that ACE is known to be the generalized likelihood ratio test (GLRT) in partially homogeneous environments, when the covariance matrix of the secondary data is proportional to the covariance matrix of the vector under test [
21]. Similar to ACE, MF and AMF, which consider target detection as the problem of hypothesis testing, they often employ the local background statistics. Actually, target and background usually follow different probability models, and the generalized likelihood ratio test (GLRT) is used to detect target. The SAM algorithm treats both spectra of target and background as vector, and then calculates the spectral angle between them. It is an automated method that can directly compare image spectra to a known spectrum (usually measured by a spectrometer in the lab or field) or an end member. This algorithm is insensitive to illumination, because the SAM uses vector direction instead of vector length. William et al. proposed a CEM algorithm to map the ferruginous sediments. They pointed out that CEM, which is conducted pixel-by-pixel, could maximize the response of target signature and meanwhile suppress the response of undesired background signatures, so that the target and background can be discriminated easier [
19]. Actually, CEM constructs a finite-impulse response (FIR) filter, which minimizes the output energy under constraint that the filter’s response to spectral signature of target is unity [
22]. Although these methods have achieved impressive performance and been widely used, more and more complicated background will make the detection accuracy declined unexpectedly. Therefore, many improved algorithms are developed for further improving the detection performance under different situation. Shuo et al. proposed both sparse CEM and sparse ACE algorithms using the
-norm regularization term to restrict the output to be sparse [
23]. They hope that the output of detection is sparse, since target of interests usually occupy a few pixels (or even subpixels) in real remote sensing images. Geng et al. proposed a novel ACEM, and they proved that ACEM is mathematically equivalent to MF (matched filter). They concluded that the classical MF is always superior to the CEM operator [
24]. Zheng et al. proposed a new hierarchical method called hierarchical CEM (hCEM) to suppress the backgrounds while preserve the target spectra with the purpose of boosting the performance of traditional target detector [
25]. In practice applications, target spectra are always diverse, and most existing methods perform a hard constraint on the target spectrum, which will bring more difficulties to detect target accurately. Consider the situation, Shuo et al. proposed a target detection algorithm by employing an inequality constraint, which is more robust to spectral diversity, as they made a soft constraint on target spectrum to cover more styles [
26]. Geng et al. also proposed a Clever eye (CE) [
27] method that can automatically search the best data origin to move the data cloud to, and find the optimal direction to project the data on. Accordingly, CE can always obtain lower output energy than CEM and MF. Wang et al. proposed a two-time detection scheme by employing principal component CEM and matrix taper CEM simultaneously [
28].
The methods described above only concerned one kind of spectrum, which is obviously not consistent with actual situation. Most remote sensing images, which include multiple targets or target itself, possess multiple spectrum characteristics. To detect all kinds of targets in a single image simultaneously, Chein et al. developed several multiple target detection approaches, e.g., Multiple-target CEM (MTCEM), Sum CEM (SCEM), and Winner-Take-All CEM (WTACEM) [
29]. These methods utilized only the known target spectral information but not the background spectral information. Considering both target and background spectrum as a priori information, several detection methods utilized both target and background spectral information were proposed to obtain better performance. Orthogonal subspace projection (OSP), based on linear mixed model [
30], aimed at eliminating the background signatures. Matched subspace detector (MSD) assumes both target and background spectrum obey the Gaussian distribution [
31], with the same-scaled identity covariance matrix and differ only in their means [
32]. A novel Symmetric Sparse Representation (SSR) method has been presented to solve the band selection problem in hyperspectral imagery (HSI) classification by Sun et al. [
33]. The above methods analyzed both target and background spectrum, however, they did not do anything to further increase the difference between target and background spectral information, which probably lead to the false positive rate unexpectedly increasing as the variability of spectral information.
In the state-of-the-arts, the methods based on sparse representation still report satisfactory performance in recent years, especially in classification and target detection [
34,
35,
36,
37,
38]. These methods usually need to construct two dictionaries, the target dictionary and union dictionary that contains both target and background. Then, they use these two dictionaries to sparsely represent the spectral information and get the sparse coefficient to obtain reconstruction error. The quality of the dictionaries plays an important role in the detection performance, especially the background dictionary, which is always difficult to obtain. An effective way to construct the dictionary is to build a dual concentric window [
37], which is an adaptive local dictionary method. It needs to set the window sizes in advance, however, there is no specific method to choose the appropriate size. For the purpose of reducing the impact of target pollution, another method based on learning has been proposed. Although there are many algorithms about constructing dictionary, how to construct an effective dictionary is still a difficult problem. The target spectral is always more intuitive with small amount, and the background spectral is always complicated and large. Thus, the target dictionary is easier to get while the background dictionary is more difficult to obtain.
To solve the above problems, in this paper, a novel sparse weighted-based constrained energy minimization (SWCEM) target detection method is proposed. Based on the constrained energy minimization (CEM) algorithm, the proposed method first introduced the effective sparse representation to weight the spectral characteristics with sparse information, which can effectively increase the difference between target and background spectrum. Since the spectrums are always diverse, target may possess similar spectrum characteristics with background. It will make the target detection more difficult. Unlike the CEM algorithm, which only uses the spectral information of original target and background pixels, the proposed SWCEM method adaptively assigned weights to each pixel according to their reconstruction error matrix of sparse representation. It adaptively assigned greater weight to target pixel, and smaller weight to background pixel, which can effectively increase the difference between target pixels and background pixels. Then, comparing with the exist sparse representation based methods, the SWCEM algorithm only needs to construct target dictionary, and calculate the similarity between spectrums of pixels and recovery of residual. Since the sparse weighted procedure could improve the identification degree between target and background, we do not need to establish the background dictionary that is hard to get. It makes the similarity measure more scientific and accurate.
The remainder of this paper is organized as follows:
Section 2 introduces the proposed sparse weighted CEM (SWCEM) method in detail.
Section 3 describes the dataset we employed and illustrates the performance of the proposed method. Then,
Section 4 analyzes and discusses the experimental results. Finally, conclusions are exhibited in
Section 5.
4. Discussion
To further discuss the detection performance objectively, the receiver operating characteristic (ROC) [
27,
42] curves are employed to evaluate and analyze the experimental results. Several popular detection methods are also employed to validate the performance of the proposed method.
The ROC curves describe the varying relationship of detection probability and false alarm rate [
27], i.e., describe the value of detection probability and false alarm rate corresponding to different threshold condition. The ROC curves provide a more intuitive and comprehensive performance evaluation method for target detection algorithms. The false alarm rate (
Fa) and the probability of detection (
Pd) are defined as follows:
where
is the number of false alarm pixels,
is the total number of background pixels,
is the number of correct detection target pixels, and
is the number of total true target pixels. The larger the area surrounded by the ROC curve is, the better the detection performance is.
For more comprehensively, the evaluate procedure is still conducted on the above datasets, and the proposed method is compared with several classical and popular detection methods.
Figure 12 shows the ROC curves of different algorithms on first dataset with two scenes. The ROC curves are built based on the same scene and hypothesis. The classical CEM, improved hCEM, popular SAM, and recently proposed CE, MPCEM are employed here to compare with the proposed methods. We can see that the proposed algorithm can obviously obtain higher detection probability at lower false alarm rates, and the ROC curves further prove that the SWCEM algorithm outperforms the other popular algorithms. For more intuitively, we calculated the area under ROC curves, which are shown in
Table 1 and
Table 2. We can conclude that the proposed method indeed achieves the highest area value, which means more significant performance.
Then, the ROC curves of different algorithms tested on the second dataset are presented in
Figure 13. From the curves, we can obviously see that the proposed algorithm also can obtain better detection result than the other methods, with a flatter with more stable detection probability rate. We calculated the area under the ROC curves similarly, and recorded them in
Table 3. In
Table 3, the proposed method also covers the largest area, which effectively improves the detection performance of the classical CEM and outperforms the other methods.
We then present the ROC curves of all the methods on the third and fourth dataset in
Figure 14 and
Figure 15. All the curves are nearer the upper left corner in
Figure 14, as the third dataset possesses relatively more obvious target characteristics. Furthermore, we find that the proposed SWCEM algorithm can still achieved the best detection result coherently with the first two datasets, and the ROC curve of the proposed method presents more competitive detection rate under the same false alarm rate. Under the same condition, the areas under the ROC curves of these methods are shown in
Table 4 and
Table 5. These area values can further verify the effectiveness of the proposed method, which report highest value in the table.
According to the above discussion, we can find that these statistical results give the perspective that the proposed SWCEM is more effective and robust on detection task comparing with the exist works. It can achieve significant performance on different datasets under uniform hypothesis and parameters setting. The ROC curves and area value demonstrate the high detection sensitivity of the proposed method. Considering its complexity, we also analyzed the detection time of these methods, and the proposed SWCEM also reports competitive computation time compared to the existing methods, while only a little more than original CEM. This is because of the introduction of sparse weighted item, which needs to adaptively calculate and assign.
The method we proposed can be easily extended to multiple target detection tasks, with only a few constraints added. In our experiments, airplanes are very representative of the target, because the plane’s wing and back on the plane’s spectrum information is not very similar. It is like a multitasking detection task, and we have introduced two of different sparse constraints to accommodate this problem. These constraints can be manually labeled or acquired from labeled data, and the proposed method adaptively computes multiple weights by using sparse encoding constraints from different destinations. Once the constraint is changed, the target function should be rebuilt and recalculated to achieve different target detection results. How to balance these constraints is a problem to be considered in the future. In addition, the detection efficiency can be further improved by introducing some fast optimization methods.