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An Improved CEM Target Detection Algorithm for Hyperspectral Images
DOI: 10.12677/APP.2019.92007, PDF, HTML, XML, 下载: 807  浏览: 3,390

Abstract: Target detection algorithm based on constrained energy minimization (CEM) is widely used in hyperspectral target detection. An improved CEM target detection algorithm is proposed. In this method, spectral reordering and first order derivation of hyperspectral data sets are firstly used to increase the difference between target and background. The similarity between target spectral and spectral points of data set is calculated, and the pixels with high similarity are removed when the autocorrelation matrix of CEM algorithm is obtained with the suppression of target by autocorrelation matrix reduced. To further suppress the background, a logarithmic operator is added. Finally, experiments on synthetic hyperspectral data and real hyperspectral data show that the proposed algorithm can recognize camouflaged targets effectively, and is applicable to small targets and large area targets detection.

1. 引言

2. CEM算法

1993年Halsayi [7] 提出了CEM算法。它使用一个有限的脉冲响应(Finite impulse response, FIR)来限制目标光谱，同时保证滤波器的输出能量最小。对于一个高光谱数据集 $S=\left[{r}_{1},{r}_{2},{r}_{3},\cdots ,{r}_{N}\right]$ ，每个像元的光谱矢量为 ${r}_{i}={\left[{r}_{i1},{r}_{i2},{r}_{i3},\cdots ,{r}_{iL}\right]}^{T}$ ，其中N为高光谱数据集中像元总数目，L为波段数。我们的目的是设计一个线性滤波器 $w={\left[{w}_{1},{w}_{2},{w}_{3},\cdots ,{w}_{L}\right]}^{T}$ ，它保证目标光谱的输出为1，同时限制背景输出最小。

$\left\{\begin{array}{l}\underset{w}{\mathrm{min}}\frac{1}{N}\left(\underset{i=1}{\overset{N}{\sum }}{y}_{i}^{2}\right)=\underset{w}{\mathrm{min}}{w}^{T}Rw\\ {d}^{T}w=1\end{array}$ (1)

${D}_{CEM}=\frac{{R}^{-1}d}{{d}^{T}{R}^{-1}d}$ (2)

3. 改进的CEM算法

1) 光谱重排可以增加变化趋势相似的光谱曲线的差异性 [8] 。对给定目标光谱d进行单调递增(递减)进行排序，数据集中所有像元按照d的排序方式进行重新排序。目标光谱重排后变为 ${d}^{*}={\left[{d}_{k1},{d}_{k2},{d}_{k3},\cdots ,{d}_{kL}\right]}^{T}$ ，其它像元重排后变为 ${r}_{i}^{*}={\left[{r}_{ik1},{r}_{ik2},{r}_{ik3},\cdots ,{r}_{ikL}\right]}^{T}$

2) 一阶微分可以反应光谱曲线的斜率及斜率变化情况，从而增强光谱曲线在坡度上的差异性 [9] 。一阶微分对大气效应也有一定的抑制作用。目标光谱和像元光谱一阶微分计算公式如(4) (5)所示。

${d}_{L-1}={\left[{d}_{k2}-{d}_{k1},{d}_{k3}-{d}_{k2},{d}_{k4}-{d}_{k3},\cdots ,{d}_{kL}-{d}_{kL-1}\right]}^{T}$ (4)

${r}_{i}^{L-1}={\left[{r}_{ik2}-{r}_{ik1},{r}_{ik3}-{r}_{ik2},{r}_{ik4}-{r}_{ik3},\cdots ,{r}_{ikL}-{r}_{ikL-1}\right]}^{T}$ (5)

3) 计算一阶微分处理后的目标光谱与各个像元光谱的相似度。此处使用余弦值度量光谱之间的相似性。目标与第i个像元之间余弦值计算公式如(6)所示。

$sim〈i,d〉=\frac{{\left({d}_{L-1}\right)}^{T}{r}_{i}^{L-1}}{‖{d}_{L-1}‖‖{r}_{i}^{L-1}‖}$ (6)

4) 对计算后的相似度值进行由大到小排序，设置阈值th。在计算自相关矩阵 $R=\left({\sum }_{i=1}^{N}{r}_{i}{r}_{i}^{T}\right)/N$ 时，相似度值最大为 $sim〈\mathrm{max}〉$ ，相似度在 $\left[sim〈\mathrm{max}〉-th,sim〈\mathrm{max}〉\right]$ 之间的像元点不计入计算之内。当 $sim〈\mathrm{max}〉-sim〈i,d〉$ 大于 $th$ 时，分界相似度值 $TH=sim〈i,d〉$ 。从而求得改进后的自相关矩阵 ${R}^{*}$

5) 只有当目标在数据集中的量较大时，修正后的自相关矩阵 ${R}^{*}$ 才能更好地对背景进行抑制，当目标在数据集中只占由少量像元，甚至仅有一个像元时，修正后的自相关矩阵 ${R}^{*}$$R$ 几乎没有差别，对背景没有显著抑制作用，结果与CEM算法没有什么差别。为进一步抑制背景，我们引入对数算子 ${\mathrm{log}}_{TH}^{sim〈i,d〉}$

${D}_{\text{MCEM}}={\mathrm{log}}_{TH}^{sim〈i,d〉}\frac{{R}^{*}{}^{-1}d}{{d}^{T}{R}^{*}{}^{-1}d}$ (7)

4. 试验及结果分析

4.1. 成高光谱试验

$t=\left(car+n*bac\right)/\left(n+1\right)+sa$ (8)

car为汽车的标准光谱，bac为背景光谱，sa为噪声，通常为高斯白噪声。此处我们取n = 6。目标植入坐标分别为(50, 50)、(50, 100)、(50, 150)、(100, 50)、(100, 100)、(100, 150)、(150, 50)、(150, 100)、(150, 150)。背景光谱、汽车标准光谱和伪装目标光谱如图5所示。

Figure 1. Flow chart of MCEM algorithm

Figure 2. Hyperspectral panorama

Figure 3. Green area

Figure 4. White car

Figure 5. Target and background normalized spectra

(1) RX (2) ACE (3) CEM (4) MCEM

Figure 6. Test results of four algorithms

Table 1. Comparisons of algorithmic performance

4.2. 真实高光谱试验

Figure 7. The target area

Figure 8. The yellow fabric target

Figure 9. Target detection results of algorithms

Table 2. Comparisons of algorithmic performance

5. 结论

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