Optimal Waveband of Multispectral for Infrared Target Detection
Aiming at the low signal to noise ratio (SNR) and weak anti-interference problem of single band detection, we use a method called Joint Skewness-Kurtosis figure (JSFK) to select the optimal waveband. Firstly, the expression of infrared signal detection is given and the coupling and random characteristics of the detection process are analyzed. Then based on the statistical theory and utilizing the non-Gaussian distribution characteristic of JSKF method, the optimal wavebands of multispectral are selected. From the selection results, the wavebands selected by the JSKF method distribute dispersively in the band 2 m~15 m μ μ and have strong complementarity, which can better reflect the multispectral characteristics of target radiation. Finally, the wavebands selected by the IABC, ECA and JSKF methods are respectively fused by the PCA method. The experiment results show that the fusion effect of JSKF method is superior to the IABC and ECA methods. Besides, the JSKF method can realize real-time processing of multispectral signals detected by the airborne, which is significant for infrared target detection. Introduction In multispectral detections, spectral signature describes the infrared radiation characteristics and reveals the intrinsic property of target and background. Utilizing such wealth of spectral and spatial information greatly improves the performance of the target detection and recognition, and even extends the detection technology to a new frontier [1]. In complex environment, the infrared spectral can be affected by the target original radiation, atmospheric transmission, detector noise and multi-reflection of electromagnetic waves, so there exists the phenomenon of “One object, different spectrum” [2,3]. In the face of single spectrum detecting defects, such as low detection probability, more infrared details loss and weak anti-interference ability, multispectral detection technology may make up for the shortage. The multispectral signals detected at the same time have significant differences in the aspect of SNR, contrast degree and radiation intensity. Utilizing these differences with spatio-temporal correlation and complementary information to fuse different infrared signals can obtain more comprehensive and clear description of target [4]. However, as for the information processing, multispectral signals can cause the problem of large data processing, so using all the infrared bands to make data classification not only processes in low efficiency, but also reduces the detection accuracy because of the influence of vast noise jamming bands or low SNR bands [5,6]. Since the limitation of current information interpretation capability, the optimal band selection for detection is the primary problem to solve. Optimal detection wavebands can expand the difference between target and background and even have a high anti-interference ability [7-9]. Over the past few years, band selection for specific target had become a hot topic in the field of military defense. Yanke Xv working in Northwestern Polytechnical University analyzed the band selection for early warning detection system [10]. Professor Wei Zhang working in Harbin Institude of Technology systematically studied the detecting bands for space-based early warning system [11]. Later, in the Changchun Institute of Optics and Fine Mechanics, Zhi Wan proposed a novel approach of band selection for marine target detection [12]. The studies mentioned above mainly focus on single band selection and use the SNR index to evaluate the optimal band selection, while the detection process has coupling and random 5 characteristics. The infrared signals easily submerge in noise and the SNR becomes lower, which brings difficulties to signal processing. In fact, the noise presents Gaussian distribution with accumulation characteristic and the target is a singular signal, so by signal fusion can provide more viability for multispectral detection. Based on the multispectral detection and statistical theory, we use the Joint Skewness-Kurtosis figure (JSKF) method to select optimal bands. Finally, we compare this method with other methods and obtain better detectable effect. Optimal Wavebands Selection for Target Detection Take the airborne target for example. The infrared spectral distribution of aerial target is complicated and the radiation characteristic always changes along with the flight altitude, working states of engine, etc., which makes single waveband detection more difficult to detect the infrared signals. In multispectral detection system, the infrared signals detected can be expressed as: ( ) ( ) ( ) 1 1 i j n m i j x t s t n t λ λ = = = + ∑ ∑ (1) where ( ) x t denotes total input signal; ( ) i s t λ and ( ) i n t λ are respectively single band signals of target and background. As for the multispectral signals, most of the background signals obey an approximate Gaussian distribution according to the central limit theorem, while the target signals are singular points existing in the background signals. Then the signal model of target is further given by ( ) ( ) ( ) 0 0 = i s t a t t t t λ δ ⋅ ; ( ) 0 a t t is the pulse amplitude and ( ) 0 t t δ is the pulse signal at 0 t time. The pulse amplitude a can not be decided by one factor and it is closely associated with target radiation, background radiation and atmospheric transmittance. 0 5 10 15 0 100 200 300 400 500 Wavelength/(μm) R a d ia ti o n i n te n s it y /( W /s r) Target radiation intensity Background radiation intensity Radiation intensity received 0 5 10 15 0 0.2 0.4 0.6 0.8 1 Wavelength/(μm) A tm o s p h e ri c t ra n s m it ta n c e Figure 1. Radiation intensity. Figure 2. Atmospheric transmittance. Fig. 1 indicates that target and background radiation are not continuous in the waveband 2 m~15 m μ μ and Fig. 2 indicates that the atmospheric transmittance has selection characteristics for radiation wavebands. So the infrared signal detection is a coupling process and we needs to select the optimal wavebands based on the coupling analysis of the characteristics of airborne targets, background, atmosphere and detection systems. The target signal detection is to look for the singular signals greatly deviating from the Gaussian distribution [13]. The Skewness defined third central moment and the Kurtosis defined fourth central moment respectively measure the asymmetry and steepness of random distribution [14]. Compared with the traditional evaluating indexes like first central moment and second central moment, the Skewness and Kurtosis not only can reflect the degree of random variables deviating from the normal distribution but also measure the difference size among different waveband signals, which is a good method for waveband selection [15]. Assume the random variable x has second to fourth central moment and they are defined as: 6 ( ) ( ) ( ) 2 2 2 3 3 4 4 = = = m E x E x m E x E x m E x E x σ  − =       −       −       (2) Therefore, the Skewness and Kurtosis are further respectively expressed as 3 3 / S m σ = and 4 4 / K m σ = ; σ denotes variance. In the Normal distribution, the S value equals 0 and K value equals 3. The larger the Skewness is, the more asymmetric the variable is; the higher the Kurtosis is, the steeper the density distribution curve is. So the values of S and K determine the target information amount. The discrete expression of Skewness and Kurtosis are as follows ( ) ( ) ( ) ( ) 3/2 3 2