A Performance Analysis Method for Optical / SAR Cooperative Detection System Based on Mutual Information

Abstract

This invention discloses a performance analysis method for an optical / SAR cooperative detection system based on mutual information, relating to the field of remote sensing. Specifically, it includes four steps: Step 1, establishing a cooperative detection system model based on the imaging and target detection principles of the optical / SAR cooperative detection system; Step 2, analyzing the statistical characteristics of the input and output signals of the cooperative detection system under the assumption of a random field in the observation scenario; Step 3, deriving the mutual information expression between the target characteristics of the optical / SAR cooperative detection system and the remote sensing image based on information theory, to quantitatively evaluate the performance of the cooperative detection system; Step 4, through theoretical derivation, using mutual information to represent the upper bound of the target detection probability of the cooperative detection system, verifying the effectiveness of mutual information as a performance evaluation index. This invention provides a theoretical basis for evaluating the detection capabilities of multi-source remote sensing cooperative detection systems.

Description

Technical Field

[0001] This invention relates to the field of remote sensing, specifically a performance analysis method for optical / SAR cooperative detection systems based on mutual information. Background Technology

[0002] Optical imaging and synthetic aperture radar (SAR) imaging are two commonly used methods for acquiring remote sensing images.

[0003] Images obtained by optical remote sensing systems can reflect the spectral and spatial information of ground objects, which conforms to human visual habits. However, optical remote sensing systems cannot work properly in the absence of light or in the presence of clouds, rain, or fog.

[0004] SAR can operate around the clock and in all weather conditions and has a certain ability to penetrate the ground, but its images have problems such as speckle noise, and the amount of texture and ground feature radiation information obtained is insufficient, making interpretation difficult.

[0005] Optical imaging systems and SAR imaging systems acquire complementary information. Therefore, fusing different types of remote sensing information to enable multiple remote sensing systems to work together has become a solution to improve detection capabilities.

[0006] Current work on optical and SAR collaborative detection mostly involves fusing acquired remote sensing images to achieve target detection, recognition, and classification. However, there is limited research analyzing the performance of collaborative detection systems at the system level. Existing related work only models single optical or SAR systems and often uses metrics such as the minimum mean square error between the image and the distortion-free image, the signal-to-noise ratio of the remote sensing data, and the mutual information between the remote sensing image and the observed scene to evaluate system performance.

[0007] Remote sensing aims to obtain more information about the characteristics of targets in the observed scene from remote sensing images. Using the mutual information between remote sensing images and target characteristics as a system performance evaluation index can indicate how much target information is obtained from remote sensing images, characterize the information flow process between different levels of the system, and quantitatively represent the impact of background and noise on system performance. Summary of the Invention

[0008] This invention addresses the insufficient research on the performance analysis of optical / SAR cooperative detection systems in the field of optical and SAR remote sensing information fusion. It proposes a performance analysis method for optical / SAR cooperative detection systems based on mutual information. First, a model of the optical / SAR cooperative detection system is established based on imaging principles. Then, assuming the observed scene is a random signal, the statistical characteristics of the random signal after passing through the system are calculated. Next, the mutual information expression of the cooperative detection system is calculated based on the statistical characteristics of the input and output signals, serving as a performance evaluation index for the cooperative detection system. Finally, it is demonstrated that increasing mutual information contributes to improving the target detection probability, verifying the effectiveness of mutual information as a system evaluation index. This invention achieves the formula derivation and validity verification of the performance evaluation index for optical / SAR cooperative detection systems, solving the problem of insufficient research on analyzing the performance of optical / SAR cooperative detection systems from the perspective of remote sensing image acquisition, and providing a theoretical basis for the performance analysis and parameter optimization of optical / SAR cooperative detection systems.

[0009] The specific steps of the performance analysis method for the optical / SAR cooperative detection system based on mutual information are as follows:

[0010] Step 1: Establish an optical imaging system model, mathematically representing the process by which the imaging system detects the observed scene in the visible light band, receives signals from optical sensors, and performs imaging processing to obtain optical remote sensing images.

[0011] The acquired optical remote sensing images were obtained using S opti The two-dimensional function representation of (x, y) is as follows:

[0012]

[0013] G opti (x,y) represents the observation scene located at (x,y), with the y-axis pointing in the direction of platform motion and the x-axis pointing in a direction perpendicular to the platform velocity and parallel to the observation plane; h opti (x,y) is the impulse response of the optical system located at (x,y); δ(xd) x m)δ(yd y n) is a matrix array of impulse functions, representing spatial sampling, d x d y N represents the dimensions of a CCD pixel along the x and y axes, where m and n are integers representing the sequence numbers of different sampling units; opti (x,y) represents the receiver noise located at (x,y).

[0014] Step 2: Establish a SAR imaging system model to clarify the imaging process from the observation scene to the SAR remote sensing image in the microwave band.

[0015] SAR remote sensing images using function S SAR(η,τ) is expressed as follows:

[0016]

[0017] Among them G SAR (η,τ) represents the SAR observation scene at time (η,τ), where η and τ are the slow and fast times of the radar signal, respectively; h SAR (η,τ) represents the impulse response of the SAR imaging system at time (η,τ); N SAR (η,τ) represents the noise of the SAR receiver at time (η,τ).

[0018] Step 3: Target detection is performed using the maximum likelihood estimation method based on the optical remote sensing image and the SAR remote sensing image respectively, resulting in two corresponding target detection results. The two target detection results are then fused according to the decision fusion method to serve as the final decision result of the optical / SAR cooperative detection system.

[0019] The decision fusion method employs a fusion criterion that minimizes Bayesian risk to obtain the final decision result Φ(v). o ,v S )for:

[0020]

[0021] v o v S The results of target detection are shown in optical remote sensing images and SAR remote sensing images, respectively; H0 and H1 represent the hypotheses of no target and the presence of a target, respectively; P(v o |H0) indicates that the optical imaging system's decision result is v when the observed scene does not actually contain the target. o The probability of P(v). S |H0) indicates that the SAR imaging system, under the condition that the target is not actually included in the microwave band, has a decision result of v. S The probability of P(v). o |H1) indicates that the optical imaging system's decision result is v when the observed scene actually contains the target. o The probability of P(v). S |H1) indicates that the SAR imaging system, under the condition that the target is actually contained in the microwave band, has a decision result of v. S The probability of.

[0022] Step 4: Assuming the observation scene is a random field, analyze the effect of the optical / SAR cooperative detection system on the input signal to obtain the statistical characteristics of the remote sensing image output by the imaging system.

[0023] Specifically, it includes:

[0024] (1) Establish the signal model of the observation scenario G:

[0025] When a target is present in the observation scene, the remote sensing image obtained by the optical imaging system is denoted as S1. It contains the background and target components after passing through the system, as well as superimposed noise.

[0026] When there is no target in the observation scene, the remote sensing image obtained by the optical imaging system is denoted as S0, which includes the background component data after passing through the system and system noise.

[0027] In an optical imaging system, the background component of the observed scene is B. o (x,y) is a zero-mean Gaussian white noise random field, and the background component B of the observed scene is... o The power spectral density of (x,y) is P Bo Target component T o (x,y) can be represented as:

[0028] T o (x,y)=T o ′(x,y)+m o (4)

[0029] T o ′(x,y) is a zero-mean Gaussian white noise random field, and the power spectral density of the target component in the optical imaging system is P. To ;m o This represents the mean value of the target component in the optical imaging system.

[0030] In a SAR imaging system, the background component in the observed scene is B. S (x,y), its power spectral density is P BS Its target component T S (x,y) can be represented as:

[0031] T S (x,y)=T S ′(x,y)+m S (5)

[0032] T S ′(x,y) is a complex-valued zero-mean Gaussian white noise random field with power spectral density P. TS ;m S This is the complex mean of the target component in the SAR imaging system.

[0033] (2) Calculate the statistical characteristics of the random signal after it passes through the imaging system.

[0034] Based on the characteristics of a random signal after passing through a linear time-invariant system, the variance of the background component of a remote sensing image in an optical imaging system can be calculated as follows:

[0035]

[0036] MTF opti (u,v) is the modulation transfer function of the optical imaging system, which represents the transmission characteristics of the optical imaging system for signals of different spatial frequencies, where u and v are the spatial frequency components corresponding to x and y, respectively.

[0037] The formulas for calculating the mean and variance of the target components are as follows:

[0038] m So =MTF opti (0,0)m o (7)

[0039]

[0040] The SAR imaging system obtains the variance of the background component of the remote sensing image:

[0041]

[0042] P BS H represents the power spectral density of the background component of the scene observed by the SAR imaging system. SAR (u,v) is the transfer function of the SAR imaging system, which is the result of the two-dimensional Fourier transform of the impulse response of the SAR imaging system; u and v are the frequency components corresponding to the slow time and fast time of the radar signal, respectively.

[0043] The mean and variance of the target component are shown in the following formula:

[0044] m SS =H SAR (0,0)m S (10)

[0045]

[0046] P TS The power spectral density of the target components in the scene observed by the SAR imaging system;

[0047] When the variances of the real and imaginary parts of a SAR remote sensing image are equal, each being half the variance of the complex signal, the statistical characteristics of the complex data of the SAR remote sensing image are obtained.

[0048] Step 5: Calculate the mutual information between the target characteristics and the remote sensing image based on the statistical characteristics of the input and output signals of the optical / SAR cooperative detection system;

[0049] The target characteristics at a single pixel in an optical / SAR co-detection system and the mutual information I of the remote sensing image data when the target is present. co (T,S1); that is:

[0050] I co (T,S1)=I opti(T,S1)+I SAR (T,S1)(12)

[0051] I opti (T,S1) is the mutual information expression of the optical imaging system, specifically:

[0052]

[0053] I SAR (T,S1) is the mutual information expression of the SAR imaging system, specifically:

[0054]

[0055] and These represent the noise variances for optical and SAR imaging systems, respectively.

[0056] Step 6: Based on the Brettaniller-Huber boundary, establish the relationship between mutual information and target detection probability in the optical / SAR cooperative detection system, and verify the effectiveness of mutual information as an evaluation index for the optical / SAR cooperative detection system.

[0057] The system performs target detection using remote sensing data S. Based on the definition of total variational distance, the following inequality can be obtained for the target detection probability:

[0058]

[0059] Where f0(s) is the probability density function of remote sensing data when there is no target in the observed scene, and f1(s) is the probability density function of remote sensing data when there is a target in the observed scene. ||f0(s)-f1(s)|| TV Let f0(s) be the total variational distance between two probability density functions f0(s) and f1(s), representing the maximum difference between the two probability density functions in their domains.

[0060] Next, using the BH bound, the upper bound of the total variational distance is represented by the KL divergence between f0(s) and f1(s).

[0061] Next, we calculate the KL divergence expression for the optical / SAR cooperative detection system under the Gaussian distribution assumption, and substitute the mutual information into the expression. Finally, we obtain the upper bound of the target detection probability of the optical / SAR cooperative detection system expressed in terms of mutual information as follows:

[0062]

[0063] The upper bound is used as the maximum object detection probability to verify the effectiveness of mutual information.

[0064] The advantages of this invention are:

[0065] (1) A performance analysis method for optical / SAR cooperative detection system based on mutual information. Mutual information can be calculated by the statistical characteristics of the observation scene and remote sensing image. Using mutual information to evaluate the target detection performance of optical / SAR cooperative detection system is simple and is not affected by the target detection method.

[0066] (2) A performance analysis method for optical / SAR cooperative detection system based on mutual information provides a general method for modeling cooperative detection system and calculating mutual information. The system transfer function or system parameters can be changed according to the actual observation system to analyze the system performance.

[0067] (3) A performance analysis method for optical / SAR cooperative detection system based on mutual information. The mutual information of target characteristics and remote sensing images of optical / SAR cooperative detection system is used as the system performance evaluation index. Through theoretical derivation, it is proved that the increase of mutual information helps to increase the target detection probability of cooperative detection system, and the effectiveness of mutual information as a performance analysis index is verified. Attached Figure Description

[0068] Figure 1 This is a flowchart illustrating the steps of a performance analysis method for an optical / SAR cooperative detection system based on mutual information, as described in this invention.

[0069] Figure 2 This is the optical / SAR cooperative detection system model in this invention;

[0070] Figure 3 This is the optical imaging system model in this invention;

[0071] Figure 4 This is the SAR imaging system model in this invention;

[0072] Figure 5 This is the signal mathematical model in this invention;

[0073] Figure 6 This is the curve showing the change in mutual information of the cooperative detection system parameters in this invention.

[0074] Figure 7 This is the curve showing the relationship between the mutual information of the optical system and the target detection probability in this invention;

[0075] Figure 8 This is the curve showing the relationship between mutual information of the SAR system and the target detection probability in this invention;

[0076] Figure 9 This is the curve showing the relationship between mutual information and target detection probability in the optical / SAR cooperative system of this invention; Detailed Implementation

[0077] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments.

[0078] This invention discloses a performance analysis method for an optical / SAR cooperative detection system based on mutual information. The method includes modeling the optical / SAR cooperative detection system, analyzing the information flow process, calculating mutual information, and using mutual information to represent an upper bound on the target detection probability. First, the optical / SAR cooperative detection system is modeled, and its signal model is analyzed. Then, assuming the observation scene is a random signal, the statistical characteristics of the random signal after passing through the system are calculated. Next, based on the statistical characteristics of the input and output signals, the mutual information expression of the cooperative detection system is calculated as a performance evaluation index. Finally, the mutual information is used to represent the upper bound on the target detection probability to verify the effectiveness of mutual information as an evaluation index. Mutual information can not only provide direction for system optimization but also provide a theoretical evaluation basis for data processing in the cooperative detection system.

[0079] The specific process is as follows:

[0080] 1. Establish a model of the optical / SAR cooperative detection system.

[0081] The optical / SAR cooperative detection system is divided into an imaging system and a cooperative decision system. The imaging system detects the observed scene in the visible and microwave bands, receives signals from optical and SAR sensors, and then processes the echo signals to obtain remote sensing images. The principles of optical and SAR imaging are analyzed, mathematical models of both imaging systems are established, and the impulse response expression of the system from the observed scene to the final obtained remote sensing image is given. The cooperative decision system performs target detection based on the acquired optical and SAR images, employing a relatively simple parallel decision fusion method to obtain the target detection results of the cooperative detection system.

[0082] 2. Analyze the information flow process of the optical / SAR cooperative detection system.

[0083] Assuming the observation scene is a random field, we analyze the effect of the imaging system on the random signal. The observation scene includes a background component and a potentially present target component, and we assume that the target and background components follow a Gaussian distribution and are statistically independent. After passing through a linear imaging system, the target and background components still follow a statistically independent Gaussian distribution. Therefore, by calculating the effect of the imaging system on the variance and mean of the random signal, we can obtain the probability distribution of the output remote sensing image with and without the target.

[0084] 3. Calculate the mutual information between the target characteristics of the optical / SAR cooperative detection system and the remote sensing image.

[0085] The mutual information between target characteristics and remote sensing images represents how much information about target characteristics can be obtained from remote sensing images. Given the target components and statistical characteristics of the remote sensing images in the observed scene, the mutual information expression can be derived from the mutual information calculation formula. The mutual information of the optical / SAR cooperative detection system is used as a system performance evaluation index.

[0086] 4. Use mutual information to represent the upper bound of the target detection probability in the optical / SAR cooperative detection system.

[0087] Through theoretical derivation, the target detection probability of the optical / SAR cooperative system is linked to the divergence of remote sensing data with and without a target using the BH bound. Furthermore, based on the relationship between divergence and mutual information, mutual information is used to represent the upper bound of the target detection probability. It is demonstrated that increasing mutual information contributes to improving the target detection probability of the optical / SAR cooperative detection system.

[0088] The performance analysis method for the optical / SAR cooperative detection system based on mutual information, such as Figure 1 As shown, the specific steps are as follows:

[0089] Step 1: Establish an optical imaging system model, detect the observation scene in the visible light band, receive signals from the optical sensor, and perform imaging processing to obtain optical remote sensing images.

[0090] Optical imaging systems such as Figure 3 As shown, the system consists of an optical lens and a CCD array, and its impulse response is h. opti (x, y), where the y-axis points in the direction of platform motion, and the x-axis points in a direction perpendicular to the platform velocity and parallel to the observation plane. The modulation transfer function (MTF) of the optical imaging system is obtained by performing a two-dimensional Fourier transform on the impulse response. opti (u,v) is divided into the following parts:

[0091] MTF opti (u,v)=MTF lens (u,v)MTF CCD (u,v)MTF TDI (u,v) (1)

[0092] Where u and v represent spatial frequency variables. MTF lens (u,v) represents the modulation transfer function (MTF) of the optical lens system. CCD (u,v) represents the spatial integration effect of CCD pixels. MTF TDI (u,v) represents the image degradation caused by the unstable posture of the platform.

[0093] The modulation transfer function of each subsystem can be derived from the imaging principle theory or obtained by numerical fitting based on experimental results.

[0094] Then, the obtained remote sensing images are spatially represented by d x d y Interval sampling can produce spatially discrete images, d x d y Let N be the size of a CCD pixel along the x and y axes. Spatial discrete image superposition receiver noise N. opti (x,y), the final optical remote sensing image obtained using S opti (x,y) Two-dimensional function representation.

[0095] Remote sensing images and their two-dimensional spectrum S opti (u,v) can be represented as:

[0096]

[0097]

[0098] Among them G opti (x,y) represents the observation scene located at (x,y), and δ(xd) x m)δ(yd y n) is a matrix array of impulse functions, representing spatial sampling; m and n are integers, representing the indices of different sampling units; h opti (x,y) is the impulse response of the optical imaging system, which is formed by the cascade of the optical lens system, the spatial integration system of the CCD pixel, and the image degradation system caused by the unstable operating posture of the platform.

[0099] Step 2: Establish a SAR imaging system model and clarify the observation scene G in the microwave band. opti (x,y) to SAR remote sensing image S opti The imaging process of (x,y).

[0100] like Figure 4 As shown, the SAR imaging process includes the transmitted signal detection process and the imaging processing process. Since the SAR system response is spatially variable with target distance in the two-dimensional time domain, it is considered to use the location (0,R) at the center of the observation scene. mid The response of ) can be used as the system impulse response of SAR, and the impulse response h of SAR can be obtained. SAR The expression for (η,τ) is:

[0101]

[0102] In the above formula, η and τ represent the slow time and fast time of the radar signal, respectively. t (η,τ;R mid h represents the impulse response caused by electromagnetic wave reflection and platform motion. mτ(η,τ) is the range-oriented matched filter, h mη (η,τ) represents azimuth focusing processing.

[0103] Considering the motion of the platform, (0,R) mid The echo of the point target at point ) appears in the two-dimensional time domain in the form of the following equation:

[0104]

[0105]

[0106] Where P t This is the transmitted signal power. R(η,R) mid For (0, R) mid The distance between the point target at position () and the platform moving at different slow times. c is the speed of electromagnetic wave propagation in space; T p The duration of the transmitted signal is represented by γ; the linear modulation frequency of the transmitted signal is represented by γ; and the speed of the flight platform is represented by V.

[0107] It can be observed that the response function of a point target changes with the target distance R in the two-dimensional time domain, using the observation scene center distance R. mid The response curve at a given point represents the response of the entire observation scenario, which can simplify the system response to a non-space-variable state.

[0108] The range-direction receiving filter uses a conjugate flip of the transmitted signal. After range compression, the signal should be focused in the azimuth direction. In principle, this can be achieved using h... t (η,τ;R mid ) and h mτ The conjugate flip of the (η,τ) convolution result is used as the azimuth focusing function; this can be used to obtain the SAR remote sensing image S. SAR (η,τ) and its spectrum S SAR (u,v) is:

[0109]

[0110] S SAR (u,v)=G SAR (u,v)H SAR (u,v)+N SAR (u,v) (8)

[0111] In a SAR system, u and v represent time-frequency variables, and the impulse response h... SAR The two-dimensional Fourier transform of (η,τ) yields H. SAR (u,v), G SAR (η,τ) represents the SAR observation scene corresponding to time (η,τ), h SAR(η,τ) represents the impulse response of the SAR imaging system at time (η,τ); it includes the diffusion effect of point targets on the two-dimensional data caused by electromagnetic backscattering and platform motion, as well as the range filtering and azimuth focusing effects of imaging processing. N SAR (η,τ) represents the noise of the SAR receiver at time (η,τ).

[0112] Step 3: Target detection is performed using the maximum likelihood estimation method based on the optical remote sensing image and the SAR remote sensing image respectively, resulting in two corresponding target detection results. The two target detection results are then fused according to the decision fusion method to serve as the final decision result of the optical / SAR cooperative detection system.

[0113] like Figure 2 The diagram illustrates the modeling of an optical / SAR cooperative detection system, comprising an imaging system and a cooperative decision system. The imaging system is modeled following the "source-channel-destination" model in communication systems. The observation scene serves as the source for the remote sensing system, the imaging system as the channel, and the remote sensing image obtained through imaging processing as the destination. The cooperative decision system performs target detection based on the optical and SAR images, yielding the target detection result of the cooperative detection system.

[0114] The optical / SAR collaborative decision-making system employs a parallel decision fusion method. The collaborative decision-making system fuses the decision results from the optical and SAR subsystems according to certain criteria to obtain the final decision result of the collaborative detection system. The single-system target detection method uses the maximum likelihood method.

[0115]

[0116] Where s refers to the remote sensing data used for target detection, and f S0 (s), f S1 (s) refer to the probability density functions of remote sensing data with and without a target, respectively. The decision fusion method employs minimizing the Bayesian risk C. F P fa -C D P d Integration criteria:

[0117]

[0118] P fa Let P be the false alarm probability. d For the probability of a target being correctly detected, C F -C D These are their respective loss coefficients. Let H0 and H1 represent the detection result vectors of the two subsystems. H0 and H1 represent the hypotheses of no target and with target, respectively. P(v|H1) represents the probability that the decision result of the two systems is v under the hypothesis that a target exists. If the target exists, then accept the H1 hypothesis; otherwise, accept the H0 hypothesis.

[0119] Further assuming that the decisions of the two systems are independent, that is, under the same assumptions, the decision results of the optical system and the SAR system are independent. It is also assumed that the loss coefficients for different errors are equal. The fusion criterion for the subsystem decision vector v can be obtained as follows:

[0120]

[0121] The decision fusion method employs a fusion criterion that minimizes Bayesian risk to obtain the final decision result Φ(v). o ,v S )for:

[0122]

[0123] v o v S The results of target detection are shown in optical remote sensing images and SAR remote sensing images, respectively; H0 and H1 represent the hypotheses of no target and the presence of a target, respectively; P(v o |H0) indicates that the optical imaging system's decision result is v when the observed scene does not actually contain the target. o The probability of P(v). S |H0) indicates that the SAR imaging system, under the condition that the target is not actually included in the microwave band, has a decision result of v. S The probability of P(v). o |H1) indicates that the optical imaging system's decision result is v when the observed scene actually contains the target. o The probability of P(v). S |H1) indicates that the SAR imaging system, under the condition that the target is actually contained in the microwave band, has a decision result of v. S The probability of.

[0124] Step 4: Assuming the observation scene is a random field, analyze the effect of the optical / SAR cooperative detection system on the input signal to obtain the statistical characteristics of the remote sensing image output by the imaging system.

[0125] Specifically, it includes:

[0126] (1) Establish the signal model of the observation scenario G:

[0127] like Figure 5 As shown, the observation scene G is modeled as a random signal, containing a background component B and potentially a target component T. The background and target components are statistically independent. The observation scene signal is processed by an imaging system and noise is superimposed to finally obtain a remote sensing image S.

[0128] When a target is present in the observation scene, the remote sensing image obtained by the optical imaging system is denoted as S1. It contains the background and target components after passing through the system, as well as superimposed noise.

[0129] When there is no target in the observation scene, the remote sensing image obtained by the optical imaging system is denoted as S0, which includes the background component data after passing through the system and system noise.

[0130] In an optical imaging system, the background component of the observed scene is B. o (x,y) is a real-valued zero-mean Gaussian white noise random field, and the background component B of the observed scene is... o The power spectral density of (x,y) is P Bo Target component T o (x, y) is a superposition of zero-mean Gaussian white noise and non-zero constants; expressed as:

[0131] T o (x,y)=T o ′(x,y)+m o (13)

[0132] T o ′(x,y) is a zero-mean Gaussian white noise random field, and the power spectral density of the target component in the optical imaging system is P. To ;m o This represents the mean value of the target component in the optical imaging system.

[0133] In SAR imaging systems, since SAR is a coherent system, its observation scene should be a complex random field; the background component in the observation scene is B. S (x,y) is a complex Gaussian white noise random field with power spectral density P. BS Its target component T S (x,y) can be represented as:

[0134]

[0135] T S ′(x,y) is a complex-valued zero-mean Gaussian white noise random field with power spectral density P. TS ;m S This is the complex mean of the target component in the SAR imaging system.

[0136] (2) Calculate the statistical characteristics of the random signal after it passes through the imaging system.

[0137] Based on the characteristics of a random signal after passing through a linear time-invariant system, the variance of the background component of a remote sensing image in an optical imaging system can be calculated as follows:

[0138]

[0139] MTF opti (u,v) is the modulation transfer function of the optical imaging system, which represents the transmission characteristics of the optical imaging system for signals of different spatial frequencies, where u and v are the spatial frequency components corresponding to x and y, respectively.

[0140] The formulas for calculating the mean and variance of the target components are as follows:

[0141] m So =MTF opti (0,0)m o (16)

[0142]

[0143] Similarly, the variance of the background component of complex remote sensing images can be obtained using SAR imaging systems:

[0144]

[0145] P BS H represents the power spectral density of the background component of the scene observed by the SAR imaging system. SAR (u,v) is the transfer function of the SAR imaging system, which is the result of the two-dimensional Fourier transform of the impulse response of the SAR imaging system; u and v are the frequency components of the radar signal in slow time and fast time, respectively.

[0146] The mean and variance of the target component are shown in the following formula:

[0147] m SS =H SAR (0,0)m S (19)

[0148]

[0149] P TS This represents the power spectral density of the target component in the scene observed by the SAR imaging system.

[0150] When the variances of the real and imaginary parts of a SAR remote sensing image are equal, each being half the variance of the complex signal, the statistical characteristics of the complex data of the SAR remote sensing image can be obtained.

[0151] Step 5: Based on the statistical characteristics of the input and output signals of the optical / SAR cooperative detection system, calculate the target characteristics of the optical / SAR cooperative detection system and the mutual information of the remote sensing image;

[0152] The current calculation involves determining the target characteristics at a single pixel in the optical / SAR cooperative detection system and the mutual information I between the remote sensing image data and the presence of the target. co (T,S1).

[0153] Assuming the observation scene is statistically independent in the optical and microwave bands, the mutual information of the optical / SAR cooperative system is the sum of the mutual information of the subsystems, i.e.:

[0154] I co (T,S1)=I opti (T,S1)+I SAR (T,S1)(21)

[0155] Mutual information can be expressed as the entropy of the remote sensing image data when the target is present minus the conditional entropy of the remote sensing image data given the target components. Assuming that the target components, background components, and noise in the observed scene are statistically independent, we can obtain:

[0156] I(T,S1)=H(S1)-H(B+N)(22)

[0157] B represents the background component, and N represents the noise component.

[0158] Assuming that the target characteristics, background components, and noise of the optical system all follow a Gaussian distribution, the mutual information I of the optical imaging system is obtained. opti The expression for (T,S1) is:

[0159]

[0160] The noise variance of the optical system is further derived as follows:

[0161]

[0162] The remote sensing data used for decision-making in SAR imaging systems is complex data, and its mutual information I... SAR The formula for calculating (T,S1) is as follows:

[0163]

[0164] in Let V be the noise variance of the SAR imaging system.

[0165] Changing the CCD pixel size of the optical system, the signal bandwidth of the SAR system, and the noise power of the cooperative detection system can sequentially yield the following results: Figure 6 The curves showing the mutual information variation of the cooperative detection system are shown in (a), (b), and (c). To reflect the effect of noise signals, the system noise power is chosen to be on the same order of magnitude as the background component power in the remote sensing image. It can be observed that changing the optical or SAR imaging system parameters affects the system's information acquisition capability, thereby altering the system's mutual information. Therefore, mutual information can serve as an indicator for system performance analysis and provide guidance for optimizing system parameters.

[0166] Step 6: Based on the Bretagnolle–Huber Bound (BH Bound), establish the relationship between the mutual information of the optical / SAR cooperative detection system and the target detection probability. Use the mutual information to represent the upper bound of the target detection probability of the optical / SAR cooperative detection system, and then use it to verify the effectiveness of the evaluation index of the optical / SAR cooperative detection system.

[0167] like Figure 5 As shown, the presence or absence of a target in the observed scene is represented by a binary random variable V. This indicates the detection results of the collaborative detection system. The probability that is the same as V is the target detection probability of the detection system. The system performs target detection using remote sensing data S. Based on the definition of total variational distance, the following inequality can be obtained for the target detection probability:

[0168]

[0169] Where f0(s) is the probability density function of remote sensing data when there is no target in the observed scene, and f1(s) is the probability density function of remote sensing data when there is a target in the observed scene. ||f0(s)-f1(s)|| TV Let f0(s) be the total variational distance between two probability density functions f0(s) and f1(s), representing the maximum difference between the two probability density functions in their domains.

[0170] Next, using the BH bound, the upper bound of the total variational distance is represented by the KL divergence between f0(s) and f1(s):

[0171]

[0172] Where D KL (f0(s)||f1(s)) represents the KL divergence of remote sensing data with and without a target.

[0173] Next, we calculate the KL divergence expression for the optical / SAR cooperative detection system under the Gaussian distribution assumption, which is:

[0174]

[0175] Substituting the mutual information into expression (28), we can obtain the upper bound of the target detection probability in the optical imaging system represented by the mutual information:

[0176]

[0177] Similarly, we can obtain the upper bound of the target detection probability of the SAR imaging system represented by mutual information:

[0178]

[0179] For collaborative systems that use joint variables from optical and SAR remote sensing images for target detection, the upper bound of the target detection probability can be calculated as follows:

[0180]

[0181] Simulations of the upper bound of target detection probability in optical systems, SAR systems, and cooperative systems can yield results such as... Figure 7 , 8 As shown in Figure 9, it can be observed that the upper bound of the target detection probability represented by mutual information is always greater than the target detection probability calculated using the aforementioned collaborative decision system detection method. With the increase of mutual information, both the upper bound of the target detection probability and the detection probability increase, and the difference between the two tends to decrease.

[0182] This invention establishes a model of an optical / SAR cooperative detection system and analyzes the statistical characteristics of the random signals input and output of the imaging system. It provides an expression for the mutual information between target characteristics and remote sensing images, serving as a quantitative performance evaluation index for the cooperative detection system. Finally, through theoretical derivation, a theoretical upper bound for the target detection probability of the optical / SAR cooperative detection system is obtained, verifying the effectiveness of mutual information as a system evaluation index. This invention utilizes mutual information, which is easily calculated and unaffected by the detection method, as a system performance evaluation index, demonstrating its practicality. Furthermore, changing the system transfer function allows for application to the performance evaluation of other detection systems, showcasing its versatility. The theoretical derivation of using mutual information to represent the upper bound of the target detection probability verifies that increasing mutual information contributes to increasing the target detection probability, proving the effectiveness of mutual information as an evaluation index for cooperative detection systems.

Claims

1. A performance analysis method for an optical / SAR cooperative detection system based on mutual information, characterized in that, The specific steps are as follows: Step 1: Establish an optical imaging system model, detect the observation scene in the visible light band, receive signals from the optical sensor, and perform imaging processing to obtain optical remote sensing images; The acquired optical remote sensing images are used The two-dimensional function is represented by the following expression: (1) For located The observation scene The axis points in the direction of platform movement. The axis points in a direction perpendicular to the platform velocity and parallel to the observation plane; The optical system is located in The impulse response; It is a matrix array of impulse functions, representing spatial sampling. , For CCD pixels in shaft and Dimensions in the axial direction , Take an integer to represent the sequence number of the different sampling units; For located Receiver noise; Step 2: Establish a SAR imaging system model to clarify the imaging process from the observation scene to the SAR remote sensing image in the microwave band; SAR remote sensing image functions The expression is as follows: (2) in for The SAR observation scene corresponding to the time. , These represent the slow and fast times of the radar signal, respectively. for The impulse response of the SAR imaging system at any given moment; for The noise level corresponding to the SAR receiver at any given moment; Step 3: Target detection is performed using the maximum likelihood estimation method based on the optical remote sensing image and the SAR remote sensing image respectively, resulting in two corresponding target detection results. The two target detection results are then fused according to the decision fusion method to serve as the final decision result of the optical / SAR cooperative detection system. Step 4: Assuming the observation scene is a random field, analyze the effect of the optical / SAR cooperative detection system on the input signal to obtain the statistical characteristics of the remote sensing image output by the imaging system; Specifically, it includes: (1) Establish the observation scenario Signal model: When a target exists in the observed scene, the remote sensing image obtained by the optical imaging system is denoted as... It contains the data of the background and target components after passing through the system, as well as the superimposed noise; When there is no target in the observed scene, the remote sensing image obtained by the optical imaging system is denoted as It includes the background component data after passing through the system and system noise; In an optical imaging system, the background component of the observed scene is: It is a zero-mean Gaussian white noise random field, and the background component of the observed scene. The power spectral density is ; target component Represented as: (4) It is a zero-mean Gaussian white noise random field, and the power spectral density of the target component in the optical imaging system is: ; This represents the mean value of the target component in the optical imaging system. In a SAR imaging system, the background component in the observed scene is: Its power spectral density is Its target component Represented as: (5) It is a complex-valued zero-mean Gaussian white noise random field with a power spectral density of... ; This is the complex mean of the target component in the SAR imaging system; (2) Calculate the statistical properties of the random signal after it passes through the imaging system; Based on the characteristics of a random signal after passing through a linear time-invariant system, the variance of the background component of a remote sensing image in an optical imaging system can be calculated as follows: (6) Let be the modulation transfer function of the optical imaging system, representing the transmission characteristics of the optical imaging system for signals of different spatial frequencies. , They are respectively , The corresponding spatial frequency components; The formulas for calculating the mean and variance of the target components are as follows: （7） (8) The SAR imaging system obtains the variance of the background component of the remote sensing image: (9) The power spectral density of the background component of the scene observed by the SAR imaging system; Let be the transfer function of the SAR imaging system, and be the result of the two-dimensional Fourier transform of the impulse response of the SAR imaging system. , These are the frequency components corresponding to the slow and fast times of the radar signal, respectively. The mean and variance of the target component are shown in the following formula: (10) (11) The power spectral density of the target components in the scene observed by the SAR imaging system; When the variances of the real and imaginary parts of a SAR remote sensing image are equal, each being half the variance of the complex signal, the statistical characteristics of the complex data of the SAR remote sensing image are obtained. Step 5: Calculate the mutual information between the target characteristics and the remote sensing image based on the statistical characteristics of the input and output signals of the optical / SAR cooperative detection system; Step 6: Based on the Brettaniller-Huber boundary, establish the relationship between mutual information and target detection probability in the optical / SAR cooperative detection system, and verify the effectiveness of mutual information as an evaluation index for the optical / SAR cooperative detection system.

2. The performance analysis method for an optical / SAR cooperative detection system based on mutual information as described in claim 1, characterized in that, In step three, the decision fusion method employs a fusion criterion that minimizes Bayesian risk to obtain the final decision result. for: (3) , The results of target detection are shown in optical remote sensing images and SAR remote sensing images, respectively. , These are the assumptions of no goal and having a goal, respectively; This indicates that the optical imaging system makes a decision when the observed scene does not actually contain the target. The probability of; This indicates that the SAR imaging system, under the condition that the target is not actually included in the microwave band, makes the following decision: The probability of; This indicates that the optical imaging system, when the observed scene actually contains the target, makes the following decision: The probability of; This indicates that the SAR imaging system, under the condition that the target is actually contained in the microwave band, has the following decision result: The probability of.

3. The performance analysis method for an optical / SAR cooperative detection system based on mutual information as described in claim 1, characterized in that, In step five, the target characteristics at a pixel in the optical / SAR collaborative detection system and the mutual information of the remote sensing image data when the target is present are considered. ;Right now: (12) For the target component; The mutual information expression for an optical imaging system is as follows: (13) The mutual information expression for the SAR imaging system is as follows: (14) and These represent the noise variances for optical and SAR imaging systems, respectively.

4. The performance analysis method for an optical / SAR cooperative detection system based on mutual information as described in claim 3, characterized in that, In step six, the system performs target detection using remote sensing data. Based on the definition of total variational distance, the following inequality for the target detection probability can be obtained: (15) in It refers to remote sensing data used for target detection. Let be the probability density function of remote sensing data when there is no target in the observed scene. Let be the probability density function of remote sensing data when there are targets in the observed scene; For two density functions and The total variational distance between the two probability density functions represents the maximum difference between them in their domains; using bivariate random variables Indicates whether a target exists in the observed scene; This indicates the detection results of the collaborative detection system; Then, using the BH boundary, use and The KL divergence represents the upper bound of the total variational distance; Next, we calculate the KL divergence expression for the optical / SAR cooperative detection system under the Gaussian distribution assumption, and substitute the mutual information into the expression. Finally, we obtain the upper bound of the target detection probability of the optical / SAR cooperative detection system expressed in terms of mutual information as follows: (16) The upper bound is used as the maximum object detection probability to verify the effectiveness of mutual information.

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