Abstract:
A system and method for assessing the probability of detection of a target of a hyperspectral sensing system. The system is adapted to calculate the probability of detection of targets based on various sensor parameters, atmospheric conditions, and a specified combination of targets and backgrounds for a given false alarm rate. The system may be executed, for example, on an IBM compatible PC to allow the user to optimize the hyperspectral sensor and subsequent signal processing to a particular set of backgrounds and targets. The sensor models, atmospheric models and target and background profiles are initially applied to the system in the form of the databases. As such, the system enables the user to select among the various parameters to optimize a hyperspectral sensor and the subsequent signal processing for a particular set of parameters.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a hyperspectral analysis tool and more particularly to a method for assessing the performance (i.e. the probability of detecting a target) of a hyperspectral sensing system. 
     2. Description of the Prior Art 
     Various tracking systems are known in the art which detect and track objects or targets of interest. Examples of such tracking systems are disclosed in U.S. Pat. Nos. 4,465,940; 5,129,525; 5,323,987; 5,333,815; and 5,445,453 as well as “A System for the Processing and Analysis of Multi- and Hyperspectral Data” by Lurie et al,  SIG Technology Review , Winter 1994, pages 43-58, hereby incorporated by reference. In particular, infrared, multispectral and hyperspectral systems are known. These sensors detect the spectral radiance of an object, and in particular, the reflected light intensity and wavelength reflected from an object of interest. Infrared systems are known to detect infrared radiation in a single band. However, there are problems with such infrared detection systems. For example, the infrared band may contain a relatively strong background signal which approximates or even exceeds the expected intensity level of the target of interest. Even though such systems utilize threshold detectors, the detection threshold must be set relatively close to the background clutter signal which can result in relatively low detection rates. Accordingly, multispectral and hyperspectral detection systems have been developed to overcome this problem. Such multispectral and hyperspectral detection systems operate on a plurality of spectral bands and are thus able to provide relatively higher detection rates. For example, a multispectral detector may operate at about 10 or more frequency bands while a hyperspectral sensor may operate at a 100 or more frequency bands. Examples of multispectral sensing systems are disclosed in commonly-owned U.S. Pat. Nos. 5,300,780; 5,479,255; and 5,528,037. Hyperspectral sensors are discussed in “A System for the Processing and Analysis of Multi- and Hyperspectral Data” supra. 
     Unfortunately, relatively simple countermeasures, such as camouflage, flares, or in-band sources, are known to reduce the effectiveness of multispectral sensors. As such, systems have been developed for optimizing the performance of multispectral sensors. For example, as set forth in commonly-owned U.S. Pat. No. 5,528,037, the integration time as well as the bands are selected to optimize the signal-to-noise ratio of a multispectral sensor. The system disclosed in the &#39;037 patent is adapted to be utilized with a relatively small number of bands (i.e. 10 or less) each with large noise where the objective is detection of a single target against all other backgrounds. Even with such optimization, the performance of such multispectral systems still falls below the performance by hyperspectral sensing systems. This higher performance can be attributed to higher spectral resolution and ability to discriminate among subtle spectral differences. Thus, hyperspectral sensors are becoming in more demand. Unfortunately, there are no known systems suitable for assessing the performance of hyperspectral sensors. As such, hyperspectral sensing system performance has heretofore not been able to be assessed. Thus, there is need for providing a method for assessing the performance of a hyperspectral sensing system. 
     SUMMARY OF THE INVENTION 
     Briefly, the present invention relates to a system and method for assessing the probability of detection of a target of a hyperspectral sensing system. The system is adapted to calculate the probability of detection of targets based on various sensor parameters, atmospheric conditions, and a specified combination of targets and backgrounds for a given false alarm rate. The system may be executed, for example, on an IBM compatible PC to allow the user to optimize the hyperspectral sensor and subsequent signal processing to a particular set of backgrounds and targets. The sensor models, atmospheric models and target and background profiles are initially applied to the system in the form of databases. As such, the system enables the user to select among the various parameters to optimize a hyperspectral sensor and the subsequent signal processing for a particular set of parameters. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     These and other advantages of the present invention will be readily understood with reference to the following specification and attached drawings, wherein: 
     FIG. 1 is a spectral diagram of an exemplary target and background. 
     FIG. 2 is a block diagram of the hyperspectral analysis system in accordance with the present invention. 
     FIG. 3 is a flow chart for the hyperspectral analysis system and process in accordance with the present invention 
    
    
     DETAILED DESCRIPTION 
     The hyperspectral analysis system in accordance with the present invention enables the performance (i.e. probability of detection of a target) of a hyperspectral sensing system to be assessed for different user-selected combinations of target and background combinations as well as different atmospheric conditions. In particular, for various user-selected combinations of hyperspectral signatures for different targets and backgrounds, the system is able to compute a signal-to-noise ratio (SNR) and a probability of detection, P d , to enable the performance of the hyperspectral sensing system to be assessed, which heretofore has been unknown. 
     A block diagram of the hyperspectral analysis system is illustrated in FIG.  2  and generally identified with the reference numeral  20 . As mentioned above, the inputs to the system  20  are user selectable to enable the system performance to be assessed for different parameters. These inputs may be initially stored in the form of databases, for example, on a diskette. The system may be executed on an IBM compatible PC, for example. 
     Initially, hyperspectral signatures for various targets and background clutter, identified as R 1 , R 2 , R 3 , . . . R n , are applied to the system. The spectral signature is the reflectivity of an object as a function of wavelength. As is known in the art, hyperspectral signatures for various backgrounds of interest are generated by known hyperspectral sensing systems with no targets present. Similarly, a hyperspectral signature may be generated for each target of interest by itself or against a reference background. As discussed above, such hyperspectral signatures are in the form of reflectivity as a function of wavelength. These hyperspectral signatures are digitized and stored. Exemplary hyperspectral signatures are illustrated in FIG.  1 . The solid line represents a target while the dashed line represents a background. 
     The sensor parameters as well as the atmospheric parameters are also user defined. These sensor parameters include the spectral range or frequency range of each band of the hyperspectral sensor, the range or distance between the sensor and the object to be sensed, the aperture of the sensor as well as the footprint or pattern of the field of view of the hyperspectral sensor. Such sensor parameters are well known in the art and are disclosed in, for example, Volume 4, “Electro-optical Systems Design, Analysis, and Testing”, Michael Dudzik, SPIE Optical Engineering Press, 1993, hereby incorporated by reference. 
     In order to enable the system to assess the performance of a hyperspectral sensor under different atmospheric conditions, various atmospheric parameters may be initially input to the system as discussed above so that they are user selectable. These atmospheric parameters include solar illumination, atmospheric transmission and atmospheric radiance. Determination of the atmospheric parameters is well known in the art, for example, as disclosed in Dudzik, op cit, and Volume 1, “Sources of Radiation”, George Zissis, Ed., SPIE Optical Engineering Press, 1993, hereby incorporated by reference. Such atmospheric parameters can be generated by the system by executing public domain software such as MODTRAN, as provided by the United States Government. Also sensor operating conditions, which include the operating altitude of the sensor, and whether the sensor is looking down or to the side are also input into the system  20 . 
     Referring to FIGS. 2 and 3, after all of the user-defined data, as discussed above, is initially input into the system  20 , the system  20  enables a user to select the target and background spectra R 1 , R 2 , R 3 , . . . R n  from the stored target and background signatures in step  32  (FIG.  3 ). In addition, the operating altitude and the atmospheric conditions as well as the sensor parameters are either selected from stored data or input by the user. The selected hyperspectral signatures for the target and background spectra are read and interpreted to match the user-selected spectral range and number of bands. 
     As discussed above, the hyperspectral signatures represent surface reflectivities from the target or background of interest. These surface reflectivities are converted to spectral photo-electrons in the detector array by a function block  22  using (FIG. 2) equation (1) below in step  34  (FIG.  3 ). 
     
       
           S   i =(( IR   i   T /2π)+ IB ) d   2 ( A/r   2 )( tληρ )(Δλ)/( hc )  (1)  
       
     
     where the individual components of vectors I and T, defined below, are applied to R i  by band (multiply row by row) and where R i  is the surface reflectivity of the target/background i, S i  approximates the photo-electron spectrum of the target/background i; I is the solar irradiance, T is the atmospheric transmission; B is the atmospheric radiance due to haze and scatter, d is the ground sample distance; A is aperture area; t is the integration time; η is the detector&#39;s quantum efficiency; ρ is the throughput of the optical system; h is Planek&#39;s constant; c is the speed of light in vacuum; λ is the wavelength; Δλ is the spectral width of the band; and r is the range to ground. The quantity S i  is a template vector. The terms I, R i , T, B, λ, η, and ρ represent column vectors having a size equal to the number of hyperspectral bands. 
     In order to optimize the performance of the system, the sensor noise covariance K is determined in step  36  by a function block  24 . The sensor noise covariance K is based upon a sensor noise model that includes the shot noise combined with other noise sources, such as the analog-to-digital (A/D) quantization noise, dark current noise, read out noise and electronic noise. One of the templates S b  is selected as a background for the determining the shot noise. The determinization of the sensor shot noise as well as the other noise terms is well known in the art, for example, as disclosed in U.S. Pat. No. 5,528,037, Whitsitt. 
     The sensor noise covariance K and the spectral templates S are applied to a function block  26  which computes a template strength covariance matrix provided by equation (2) below in step  38 . 
     
       
           K   α =( S   T    K   −1    S ) −1   (2)  
       
     
     where S represents the photo-electron templates, K represents the sensor noise covariances, and K α  represents the covariance of the template strengths. The covariance of measurement template strengths K α  is based on a model as set forth below. In particular, a pixel measurement b may be modeled as set forth in equation (3) below. 
     
       
           b=Sα+N   (3)  
       
     
     where S is a matrix of m×1 templates S i  as given in equation (4) below. 
     
       
         S=[S 1 , S 2 , . . . S n ]  (4)  
       
     
     and α is a n×1 vector of template strengths as given in equation (5) below.              α   =     [           α   1               α   2             ⋮             α   n           ]             (   5   )                                
     N is sensor noise with covariance K. 
     Equation (3) may be best understood with reference to an example. In particular, consider two classes of background spectra, such as soil and grass, represented by template vectors S 1  and S 2  and a target template target vector represented by the spectrum S 3 . Assume that the template vectors S 1 , S 2  and S 3  correspond to template strengths α 1 , α 2  and α 3 , respectively. As such, when the sensor is over soil, the respective template strengths for α 1 , α 2  and α 3  are 1, 0, 0, respectively. Similarly, when the sensor is over grass the respective template strengths for α 1 , α 2  and α 3  are 0, 1, 0, respectively. When the sensor is over a target, the respective template strengths α 1 , α 2  and α 3  are 0, 0, 1 respectively. 
     The template strengths for a given spectrum are computed by a weighted least squares method, which is well known in the art. Equation (6) may be used to determine the template strengths. 
     
       
         α=( S   T   K   −1    S ) −1    S   T    K   −1   b.   (6)  
       
     
     In order to determine the signal-to-noise ratio of the system it is necessary to compute the covariance of the template strengths as indicated by the function block  26 . The covariance of the templates strengths is based on the noise from the sensor noise model  24  for a given spectrum. For example, assuming a target template strength of 1, equation (2) is used to determine the template strength covariance. In particular, the diagonal terms in the covariance matrix represented by equation (2) represent the individual α i  covariances in the estimate represented by equation (6). These covariances of the template strengths are then used to determine the signal-to-noise ratio (SNR) as indicated in step  40 . It is convenient to define template SNR for each template under the same condition α i =1. The SNR is defined by equation (7) below; 
     
       
           SNR   i =1/{square root over (( K   α ) i )}  (7)  
       
     
     where (K α ) i  is the i th  diagonal component of Kα. 
     Thus, for a template strength, as an example, for a target as discussed above of 1, and a covariance of a template strength computed to be 0.01, then the SNR is 10. The signal-to-noise ratio may then be applied to a threshold detector  30  (FIG. 2) along with a desired false alarm rate signal to provide a probability of detection P d  as set forth in step  42 . As such, for a given SNR and given desired false alarm rate, the system  20  can compute the probability of detection P d  of a target in the presence of numerous simultaneous background spectra, with a simple threshold detector. The probability of the detection of a target P d  for hyperspectral sensor was heretofore unknown. 
     Off-diagonal terms in the template strength covariance are a measure of similarity between templates. This feature allows further optimization of hyperspectral systems by giving designers a method of choosing the best template sets to enhance detection and discriminate among multiple target and background types. A feature of equation (6) is that template strength α is measured in a dimension orthogonal to all other templates, reducing variability in performance due to uncertainty in template strength. 
     Obviously, many modifications and variations of the present invention are possible in light of the above teachings. Thus, it is to be understood that, within the scope of the appended claims, the invention may be practiced otherwise than as specifically described above.