A limited-order markov hyperspectral real-time anomaly detection method

Abstract

This invention discloses a real-time anomaly detection method for hyperspectral data based on a finite-order Markov model, comprising: reading hyperspectral image data and initializing the number of rows; establishing a finite-order Markov model of inter-row information, calculating the information content of the current row i, and calculating the second derivative of the information content to determine whether the current row is an anomaly or a non-anomaly; establishing the state equation of the spectral vector correlation matrix R(n) of the hyperspectral data pixels; if it is an anomaly, replacing the first row of the original data with new data in the spectral vector correlation matrix R(n); if it is a non-anomaly, adding new data to the original data; and updating the inverse matrix R of the correlation matrix R(n). ‑1 (n); This invention performs detection on hyperspectral data and obtains the results of real-time local anomaly detection in hyperspectral images. It achieves local anomaly detection in hyperspectral images, avoids high-dimensional data storage and redundant computation, and has good local anomaly detection performance.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of hyperspectral image detection, and particularly relates to a hyperspectral real-time anomaly detection method based on limited-order Markov. BACKGROUND

[0002] Hyperspectral anomaly detection is a key problem in hyperspectral image analysis. Hyperspectral anomaly detection refers to unknown target spectrum prior knowledge, and according to the spectral characteristics difference between the target and the image background, the abnormal target is identified from the background.

[0003] According to the different operator statistical information, the anomaly detection algorithm can be divided into global anomaly detection and local anomaly detection. Using the statistics of the background pixels in the entire hyperspectral image is considered as a global method, which performs well in most cases, but due to the pollution of anomalies, the accuracy of background modeling and the complexity of calculation, the global method is not suitable for weak anomalies or complex background, and the performance of the global method is limited. In contrast, local anomaly detection using small neighborhood statistics has been widely studied recently. However, due to the sliding of the neighborhood window, the size of the window will directly affect the detection result, and the parameters set by humans are difficult to have universality, so how to adaptively determine the window size according to the hyperspectral image is a problem to be solved in hyperspectral local anomaly detection.

[0004] However, the high cost of hyperspectral data processing and the high time complexity limit its application in some industries that require high timeliness, such as environmental monitoring, disaster site detection, industrial production detection, etc. In other words, only the previous data and the data just acquired can be used, and the unacquired data samples cannot be used. In recent years, many real-time anomaly detection algorithms have been proposed in the field of hyperspectral anomaly detection to discover abnormal targets in time. Most of the hyperspectral real-time local anomaly detection operators use window model design. Although it can avoid the problem that the global method fails to detect due to the fact that the abnormal target only exists in a local range and is submerged in a global range. However, while improving the accuracy of anomaly detection, the computational cost is also increased, and multiple parameters need to be determined, such as window size selection. The appropriateness can be measured through a large number of experimental tests, but the anomaly conditions of each data set are different, and the size of the abnormal target in the actual industrial scene is difficult to determine in advance. In addition, the traditional line-by-line real-time anomaly detection algorithm uses all the data samples before the data sample to be detected. When the hyperspectral imager scans a large area of data, due to the need to store redundant data, it is still computationally expensive and will affect the fast processing of the target. Unfortunately, so far, the storage of appropriate data sample size has received little attention in real-time processing. Therefore, how to select the appropriate data range for real-time processing and faster processing is the key to improving the effect of hyperspectral local anomaly real-time detection, and has more practical value. SUMMARY

[0005] In view of the problems in the prior art, the present application discloses a real-time anomaly detection method based on limited-order Markov hyperspectral, which specifically comprises the following steps:

[0006] S1: reading hyperspectral image data X and initializing row number i;

[0007] S2: establishing a limited-order Markov model of inter-row information quantity, calculating the information quantity H(X i ) of the current row i, and calculating the second derivative value of the information quantity to determine whether the current row is an abnormal row or a non-abnormal row;

[0008] S3: establishing a state equation of a spectral vector correlation matrix R(n) of the hyperspectral data pixel points, if it is an abnormal row, R(L(new)) replaces the first row of the original data with new data, and if it is a non-abnormal row, the correlation matrix adopts R(L(n)) to add new data to the original data;

[0009] S4: updating the inverse matrix R -1 (n) of the correlation matrix R(n) by using the Woodbury identity formula;

[0010] S5: detecting the hyperspectral data by using a real-time local anomaly method based on limited-order Markov row-by-row processing, and finally obtaining the result of real-time local anomaly detection of the hyperspectral image.

[0011] Further, the calculation formula of the information quantity H(X i ) of the current row i is as follows:

[0012]

[0013] Wherein, X iBB is the correlation matrix of the B bands of the i-th row of the hyperspectral image X, x ii is the diagonal element of the X iBB matrix.

[0014] Further, when the n-th row of the current hyperspectral image discovers an anomaly, if it is an abnormal row, R(L(new)) replaces the first row of the original data with new data, and the calculation formula of the correlation matrix R(L(new)) is as follows:

[0015]

[0016] Wherein, R(L(n-1)) represents the correlation matrix of the data samples of the first n-1 rows of the hyperspectral image, R(L n ) represents the correlation matrix of the data samples of the n-th row, and R(L m ) represents the correlation matrix of the data samples of the m-th row.

[0017] Further, when the current hyperspectral image does not find the abnormality in the nth row, the correlation matrix uses R(L(n)) to add new data to the original data, and the calculation formula of the correlation matrix R(L(n)) is as follows:

[0018]

[0019] Further, the inverse matrix R -1 (n) of the correlation matrix R(n) is updated by using the Woodbury identity, and when the hyperspectral image finds the abnormality in the nth row, the inverse of R(L(new)) is calculated, and R(L(new)) is divided into two parts, that is, * The calculation formula of the inverse of R

[0020]

[0021] Wherein, I represents the unit matrix;

[0022] Then, R -1 (L(new)) is calculated, and the calculation formula is as follows:

[0023]

[0024] Further, the inverse matrix R -1 (n) of the correlation matrix R(n) is updated by using the Woodbury identity, and when the hyperspectral image does not find the abnormality in the nth row, the inverse of R(L(n)) is calculated, and the expression is as follows:

[0025]

[0026] Further, the real-time local anomaly method using finite-order Markov row-by-row correlation matrix is used to detect the hyperspectral data needing real-time detection processing, and when the current hyperspectral image finds the abnormality in the nth row, the formula is as follows:

[0027]

[0028] Wherein, The detection value of the current state is represented, The detection value of the previous state is represented;

[0029] Further, the real-time local anomaly method using finite-order Markov row-by-row correlation matrix is used to detect the hyperspectral data needing real-time detection processing, and when the current hyperspectral image does not find the abnormality in the nth row, the formula is as follows:

[0030] ​

[0031] wherein, represents a detection value of a current time state, represents a detection value of a last time state.

[0032] Due to the adoption of the technical scheme, the application provides a hyperspectral real-time anomaly detection method based on a limited-order Markov, which judges whether a current row is an abnormal row by calculating the information amount of the current row, and adaptively determines the size of a local background region according to the limited-order Markov thought. Based on the R-anomaly detection (R-AD) of a correlation matrix, two different correlation matrix representations are designed for the dynamically updated limited-order local sample, the Woodbury identity is used to update the suppressed background statistics, and the corresponding update equation with the causal recursive characteristic is derived to realize the real-time local anomaly detection, so as to further reduce the time consumption and improve the detection ability. The application realizes the local anomaly detection of the data acquired by the push-broom hyperspectral image sensor, realizes the real-time processing at the same time, avoids the high-dimensional data storage and repeated calculation, solves the real-time problem of the anomaly detection to a certain extent, and has a good local anomaly detection effect. BRIEF DESCRIPTION OF DRAWINGS

[0033] In order to more clearly illustrate the technical solutions of the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments or prior art description will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments described in the present application, and those skilled in the art can also obtain other drawings according to these drawings without creating any creative labor.

[0034] Figure 1 The flowchart of the method provided by the application is shown in the figure;

[0035] Figures 2a-2c The ground truth map and the spectral reflectance diagram of the Segundo data set scene in the application are shown in the figure;

[0036] Figures 3a-3f The process diagram of the local anomaly detection result of the Segundo data set in the application is shown in the figure;

[0037] Figures 4a-4d The 3D ROC curve and its corresponding three 2D ROC curves of the local anomaly detection result of the Segundo data set in the application are shown in the figure. DETAILED DESCRIPTION

[0038] In order to make the technical solutions and advantages of the present application clearer, the technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application:

[0039] As Figure 1The method for real-time hyperspectral anomaly detection based on a limited-order Markov model specifically comprises the following steps:

[0040] (1) initialization;

[0041] read the hyperspectral image data X, initialize the row number i;

[0042] (2) establish a limited-order Markov model of the information amount between rows;

[0043] calculate the information amount H(X i ) of the current row i, and calculate the second derivative value of the information amount, and determine whether the current row is an abnormal row or a non-abnormal row;

[0044] (3) establish a state equation of the spectral vector correlation matrix R(n) of the hyperspectral data pixel points, if it is an abnormal row, R(L(new)) replaces the first row of the original data with new data, and if it is a non-abnormal row, the correlation matrix adopts R(L(n)) to add new data to the original data;

[0045] (4) update the inverse matrix R -1 (n) of the correlation matrix R(n) by using the Woodbury identity formula;

[0046] (5) detect the hyperspectral data by using the real-time local anomaly method of the limited-order Markov correlation matrix row by row, and finally obtain the result of real-time local anomaly detection of the hyperspectral image.

[0047] Real hyperspectral data experiment

[0048] The following will follow the above method steps, and a set of public real hyperspectral image data sets will be used to test and illustrate the method for real-time hyperspectral anomaly detection based on a limited-order Markov model, and the application effect analysis and evaluation.

[0049] 1. Segundo data set and parameter setting

[0050] This section takes the Segundo real hyperspectral image scene as the experimental object, and the experimental scene is a hyperspectral image of Segundo, California, USA, collected by an AVIRIS sensor, as shown in Fig. 2(a), the scene size is 250x300 pixel vectors, and the AVIRIS imager can obtain 224 wavebands. The ground real image is shown in Fig. 2(b). The spectral reflectivity is shown in Fig. 2(c).

[0051] 2. Experimental evaluation index

[0052] The proposed algorithm is evaluated by using a 3D-ROC curve, and the AUC of(P D , PF ), AUC of (P D , τ) and AUC of (P F , τ) to verify the effectiveness of the proposed algorithm, and compare the original RXD, RT-CR-RXD and the proposed FMLRT-RAD algorithm. The 3D-ROC curve and the corresponding three 2D-ROC curves are shown in Figures 4(a)-4(d).

[0053] 3. Experimental result analysis and evaluation

[0054] The results of the experiment of the real hyperspectral image data based on the limited order Markov hyperspectral real-time anomaly detection method provided by the application are shown in Table 1, and the corresponding detection result process images are shown in Figures 3(a)-3(f).

[0055] According to the real-time local anomaly detection result, the following conclusions can be obtained:

[0056] (1) The FMLRT-RAD proposed can accurately detect the position and shape of different size anomalies, such as airplanes, vehicles, etc. in different scenes. In the initial stage of detection, the image is generally light in color, but once the system detects the anomaly, the background is suddenly suppressed, and the brightness value of the abnormal pixel is also significantly increased.

[0057] (2) FMLRT-RAD obtains the initial abnormal range by analyzing the amount of information of the current row and the previous rows. According to the detected abnormal information, only part of the rows and the current data are selected to generate the detection result in the operation process. This processing method of local information can not only better preserve the abnormal information, but also effectively suppress the background interference, and realize the accurate detection of different size anomalies in different scenes.

[0058] (3) The FMLRT-RAD algorithm shows excellent detection effect on the data set, not only significantly reduces the data storage overhead, but also can realize real-time data processing. This fully shows that the algorithm has wide application potential.

[0059] (4) The algorithm only needs to store the information of the last time and the data of the current pixel to be processed in the running process, without storing the entire huge spectral data, which is particularly suitable for applications that cannot delay to make decisions until the entire scene is obtained, and paves the way for hardware implementation of actual application of hyperspectral image detection.

[0060] Table 1 Comparison of AUC values of abu-beach-4 data set anomaly detection results

[0061]

[0062] The present application is directed to the principle of line-by-line imaging of pushbroom hyperspectral imager, adopts the finite-order Markov model, discusses the abnormal line data recognition method, and applies it to the local anomaly detection field, proposes a finite-order Markov hyperspectral real-time anomaly detection method (FMLRT-RAD) method, so as to obtain the abnormal detection result of the current line while obtaining the line-by-line information of the pushbroom hyperspectral imager. In addition, we use Woodbury identity to introduce the line-by-line recursive updating mechanism, which effectively avoids the repeated calculation of the processed line information, and instead updates the operator in a recursive way to obtain the detection result of the current line. Only the state of the last time and the information of the current pixel to be detected need to be stored during the operation of the algorithm, and the complete high-dimensional spectral data does not need to be stored, thereby significantly reducing the data storage requirement and avoiding repeated inverse operation. The experimental results of a set of real public hyperspectral data set prove that the present application realizes the synchronization of data acquisition and processing while ensuring the performance of local anomaly detection. This provides strong theoretical support for the actual hyperspectral image real-time local anomaly detection system. At the same time, it fully proves the effectiveness of the finite-order Markov hyperspectral real-time anomaly detection method provided by the present application.

[0063] The above description is only the preferred embodiment of the present application, but the protection scope of the present application is not limited thereto, any person skilled in the art can make equivalent replacement or change according to the technical solution and the inventive concept of the present application within the technical range disclosed by the present application, which should be covered within the protection scope of the present application.

Claims

1. A real-time anomaly detection method based on finite-order Markov hyperspectral imaging, characterized in that... include: Read hyperspectral image data X and initialize row number i; Establish a finite-order Markov model of inter-line information content, and calculate the information content H(X) of the current row i. i ), and calculate the information content H(X) i The second derivative of ) is used to determine whether the current row is an abnormal row or not; Establish the state equation of the spectral vector correlation matrix R(n) of hyperspectral data pixels. If it is an abnormal row, the spectral vector correlation matrix R(n) replaces the first row of the original data with the new data. If it is a non-abnormal row, the new data is added to the original data. Update the inverse matrix R of the correlation matrix R(n) using the Woodbury identity. -1 (n); A real-time local anomaly R-AD operator with finite-order Markov line-by-line processing was used to detect hyperspectral data, and the results of real-time local anomaly detection in hyperspectral images were finally obtained. According to the real-time local anomaly R-AD operator for finite-order Markov line-by-line processing, the formula for detecting an anomaly in the nth row of the current hyperspectral image is as follows: (7) in, The detection value represents the current state. The detected value represents the state at the previous moment; According to the real-time local anomaly R-AD operator based on finite-order Markov line-by-line processing, when no anomalies are found in the nth row of the current hyperspectral image, the formula is as follows: in, The detection value represents the current state. The detected value represents the state at the previous moment.

2. The real-time anomaly detection method based on finite-order Markov hyperspectral imaging according to claim 1, characterized in that: The information content H(X) of the current row i. i The calculation formula for ) is as follows: Among them, X iBB Let x be the correlation matrix of the B bands in the i-th row of the hyperspectral image X. ii It is X iBB The diagonal elements of a matrix.

3. The real-time anomaly detection method based on finite-order Markov hyperspectral imaging according to claim 1, characterized in that: Using a finite-order Markov model of inter-row information in hyperspectral images, if an anomaly is found in the nth row of a hyperspectral image, the correlation matrix of the data samples in the first n-1 rows of the hyperspectral image is denoted as R(L(new)), and its expression is as follows: Where R(L(n-1)) represents the correlation matrix of the first n-1 rows of data samples in the hyperspectral image, R(L n R(L) represents the correlation matrix of the data sample in the nth row. m () represents the correlation matrix of the data sample in the m-th row; Using a finite-order Markov model of inter-row information in hyperspectral images, the correlation matrix R(L(n)) of the first n rows of data samples is calculated as follows when no anomalies are found in the nth row of the current hyperspectral image:

4. The real-time anomaly detection method based on finite-order Markov hyperspectral imaging according to claim 1, characterized in that: Update the inverse matrix R of the correlation matrix R(n) using the Woodbury identity. -1 When an anomaly is found in the nth row of the hyperspectral image (n), invert R(L(new)) and divide R(L(new)) into two parts, i.e. First, for R * The formula for finding the inverse is as follows: Where I represents the identity matrix; Calculate R again -1 (L(new)) is calculated using the following formula: When no anomalies are found in the nth row of the hyperspectral image, the inverse of R(L(n)) is expressed as follows:

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