Anomaly detection method based on multi-scale relative total variation collaborative representation of airborne hyperspectral images

Abstract

The present invention relates to a multi-scale relative total variation collaborative representation anomaly detection method for airborne hyperspectral images in the field of airborne hyperspectral image processing, comprising: obtaining a surrounding spatial neighborhood pixel set through a double window, and solving the partial derivatives of the spatial neighborhood set in the x and y directions, the weighted sum of the absolute values ​​of the gradients at all pixels, and the absolute value of the weighted sum of the gradients, to obtain structural information and texture information of different scales of the spatial neighborhood, and fusing the structural information to obtain structural information of the relative total variation at multiple scales; calculating the Tikhonov regularization matrix, and applying constraints to the weight vector that the sum is 1 and that minimizes the second norm of the weight vector; deriving the weight vector according to the constraints and the regularization matrix, and multiplying it with the structural information to obtain the result of the pixel to be detected being represented by the spatial neighborhood set, and then subtracting it from the original image to obtain a residual image. The present invention has a small probability of being misjudged as a background pixel when the pixel to be detected is an abnormal pixel, and at the same time, the accuracy of the abnormal detection rate is high.

Description

Technical Field

[0001] The present invention relates to an airborne hyperspectral image multi-scale relative total variation joint collaborative representation anomaly detection method in the field of airborne hyperspectral image processing. Background Art

[0002] Airborne hyperspectral image anomaly detection is crucial for drones to perform reconnaissance missions. After acquiring hyperspectral images, drones directly perform anomaly detection to quickly identify enemy equipment in the irradiated area and transmit the anomaly detection results to our command center through a wireless link. Compared with drones directly transmitting hyperspectral images to the ground for image analysis, the time it takes for our command center to obtain intelligence is greatly reduced, which can greatly improve our response time when there is an emergency. Multi-scale relative total variation compensates for the probability of the pixel to be tested being misjudged as a background pixel when it is an abnormal pixel, greatly improving the probability of anomaly detection in airborne hyperspectral images from the detection results, which is of great significance for our rapid and precise strike. Summary of the invention

[0003] The present invention mainly solves the problem that there is a high probability that the pixel to be tested is misjudged as an abnormal pixel in the hyperspectral collaborative representation anomaly detection algorithm. A method is proposed to apply a multi-scale relative total variation model to propose different scale texture information of the spatial neighborhood pixels of the pixel to be tested and only retain the structural information. The method is used to process the spatial neighborhood pixels, and the pixel to be detected is represented by a set of spatial neighborhood pixels, so that the abnormal pixels in the hyperspectral image can be represented.

[0004] The technical solution adopted by the present invention is:

[0005] A multi-scale relative total variation collaborative representation anomaly detection method for airborne hyperspectral images includes the following steps:

[0006] S1 sets the size of the inner and outer windows, takes the pixel to be detected in the hyperspectral image as the central pixel, and obtains the surrounding spatial neighborhood pixel set through the double window;

[0007] S2 applies a multi-scale relative total variation model to the spatial neighborhood pixel set to solve the partial derivatives of the spatial neighborhood set in the x-direction and the y-direction, the weighted sum of the absolute values ​​of the gradients of the pixels in the spatial neighborhood set at all pixels, and the absolute value of the weighted sum of the gradients of the pixels in the spatial neighborhood set at all pixels;

[0008] S3 obtains structural information and texture information of different scales of the spatial neighborhood according to the solution value of step (2);

[0009] S4 changes different inner and outer window sizes, returns to step S1, and enters step S5 after a set number of times;

[0010] S5 fuses the obtained structural information of different scales to obtain the structural information of relative total variation at multiple scales;

[0011] S6 calculates a Tikhonov regularization matrix using a distance-weighted Tikhonov regularization method according to the spatial relationship between each pixel in the spatial neighborhood pixel set and the pixel to be tested;

[0012] S7 imposes constraints on the weight vector such that the sum is 1 and the bi-norm of the weight vector is minimized;

[0013] S8, according to the constraints of step S7 and the Tikhonov regularization matrix obtained in step S6, derives the weight vector in the anomaly detection objective function and makes the derivative equal to zero, thereby obtaining the weight vector;

[0014] S9 multiplies the weight vector of the pixel to be tested by the structural information obtained in step S5 to obtain a result represented by the spatial neighborhood set of the pixel to be tested;

[0015] S10 performs a difference operation between the result of step S9 and the original image to obtain a residual image, that is, to identify abnormal pixels in the image.

[0016] Furthermore, the multi-scale relative total variation model described in step S2 is:

[0017]

[0018] Among them, Φ x (i) Φ y (i), θ x (i) and Θ y (i) are respectively expressed as:

[0019]

[0020]

[0021]

[0022]

[0023] g i,j It is expressed as:

[0024]

[0025] In the formula, Ω is the fusion parameter, N is the number of pixels in the spatial neighborhood set, S i is the structural information result image, I i is the spatial neighborhood set, λ is the weight parameter, ξ is a positive number, and Represent the partial derivatives in two directions, Φ x (i) and Φ y (i) is the weighted sum of the absolute values ​​of the gradients of all pixels in the neighborhood of pixel i, Θ x (i) and Θ y (i) is the absolute value of the weighted sum of the gradients of all pixels in the neighborhood of pixel i, j is the pixel in the neighborhood R(i) of pixel i, x i and i Represents the x direction and y direction of pixel i, respectively. j and j represents the x and y directions of pixel j, g i,j It means that the Gaussian weight function is operated on pixel i and pixel j, and δ is the scale of the spatial window.

[0026] Compared with the prior art, the present invention has the following advantages:

[0027] 1. In the existing hyperspectral image collaborative representation anomaly detection algorithm, when the pixel to be detected is an abnormal pixel and there are abnormal pixels of the same nature as the pixel to be detected in its neighboring spatial set, the pixel to be detected is often misjudged as a background pixel and the purpose of abnormal pixel detection cannot be achieved. Before the collaborative representation algorithm detects abnormal pixels, the present invention first performs multi-scale relative total variation processing on the spatial neighbor set, eliminates the texture information in the spatial neighborhood set, and only retains the structural information in the spatial neighborhood set, which can avoid the situation where the pixel to be detected is misjudged as a background pixel when it is an abnormal pixel to the greatest extent.

[0028] 2. Since the types of objects in different images have different scales, the present invention improves the relative total variation model and adopts a multi-scale relative total variation model. The advantage is that it can better adapt to the types of objects of different scales and can also be better applied to various different scenes in practical applications, thereby being able to more accurately detect abnormal pixels in the image. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 is a schematic diagram of the collaborative representation method of the present invention;

[0030] Figure 2 It is a schematic diagram of the results of applying the multi-scale relative total variation model of the present invention;

[0031] Figure 3 This is a graph of anomaly detection results when the present invention is applied to airborne hyperspectral images. DETAILED DESCRIPTION

[0032] The present invention will be further explained below in conjunction with the accompanying drawings.

[0033] The present invention provides an airborne hyperspectral image multi-scale relative total variation collaborative representation anomaly detection method, which uses a multi-scale relative total variation model to process a spatial neighborhood set to obtain structural information of the spatial neighborhood set, and specifically includes the following steps:

[0034] S1 sets the inner and outer window sizes, takes the pixel to be detected in the hyperspectral image as the central pixel, and obtains the surrounding spatial neighborhood pixel set through the double window; Figure 1 As shown;

[0035] S2 applies a multi-scale relative total variation model to the spatial neighborhood pixel set to solve the partial derivatives of the spatial neighborhood set in the x-direction and the y-direction, the weighted sum of the absolute values ​​of the gradients of the pixels in the spatial neighborhood set at all pixels, and the absolute value of the weighted sum of the gradients of the pixels in the spatial neighborhood set at all pixels;

[0036] S3 obtains structural information and texture information of different scales of the spatial neighborhood according to the solution value of step (2);

[0037] S4 changes different inner and outer window sizes, returns to step S1, and enters step S5 after a set number of times;

[0038] S5 fuses the obtained structural information of different scales to obtain the structural information of relative total variation at multiple scales;

[0039] S6 calculates a Tikhonov regularization matrix using a distance-weighted Tikhonov regularization method according to the spatial relationship between each pixel in the spatial neighborhood pixel set and the pixel to be tested;

[0040] S7 imposes constraints on the weight vector such that the sum is 1 and the bi-norm of the weight vector is minimized;

[0041] S8, according to the constraints of step S7 and the Tikhonov regularization matrix obtained in step S6, derives the weight vector in the anomaly detection objective function and makes the derivative equal to zero, thereby obtaining the weight vector;

[0042] S9 multiplies the weight vector of the pixel to be tested by the structural information obtained in step S5 to obtain a result represented by the spatial neighborhood set of the pixel to be tested;

[0043] S10 performs a difference operation between the result of step S9 and the original image to obtain a residual image, that is, to identify abnormal pixels in the image.

[0044] The multi-scale relative total variation model described is:

[0045]

[0046] Among them, Φ x (i) Φ y(i), θ x (i) and Θ y (i) are respectively expressed as:

[0047]

[0048]

[0049]

[0050]

[0051] g i,j It is expressed as:

[0052]

[0053] In the formula, Ω is the fusion parameter, N is the number of pixels in the spatial neighborhood set, S i is the structural information result image, I i is the spatial neighborhood set, λ is the weight parameter, ξ is a positive number, and Represent the partial derivatives in two directions, Φ x (i) and Φ y (i) is the weighted sum of the absolute values ​​of the gradients of all pixels in the neighborhood of pixel i, Θ x (i) and Θ y (i) is the absolute value of the weighted sum of the gradients of all pixels in the neighborhood of pixel i, j is the pixel in the spatial neighborhood R(i) of pixel i, x i and i Represents the x direction and y direction of pixel i, respectively. j and j represents the x and y directions of pixel j, g i,j It means that the Gaussian weight function is operated on pixel i and pixel j, and δ is the scale of the spatial window.

[0054] After obtaining the structural information of the spatial neighborhood, it can be used to collaboratively represent the pixels to be detected. The mathematical model of collaborative representation anomaly detection is:

[0055]

[0056] The weight vector mentioned is the solution of the above formula, which is expressed as follows:

[0057] α=(X lb T X lb +λΓ y T Γ y ) -1 X lbT y

[0058] The processed image is Figure 2 As shown, the final residual image is Figure 3 As shown, that is, the difference between the collaborative representation image and the original image is given by the following formula:

[0059] r1=||yX lb α||2

[0060] In the above formula, y is the pixel to be detected, X lb is the spatial neighborhood set after multi-scale relative total variation transformation, α is the weight vector, λ is the Lagrange multiplier, X lb T is the transpose of the spatial neighborhood set after multi-scale relative total variation transformation, Γ y is the regularization matrix, Γ y T is the transpose of the regularization matrix, and r1 is the residual matrix.

[0061] The above description of the disclosed embodiments enables one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

[0062] The present invention uses specific embodiments to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core idea. At the same time, for those skilled in the art, according to the idea of ​​the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as a limitation on the present invention.

Claims

1. A multi-scale relative total variation collaborative representation anomaly detection method for airborne hyperspectral images, characterized in that: The following steps are involved: S1 sets the size of the inner and outer windows, takes the pixel to be detected in the hyperspectral image as the central pixel, and obtains the surrounding spatial neighborhood pixel set through the double window; S2 applies a multi-scale relative total variation model to the spatial neighborhood pixel set to solve the partial derivatives of the spatial neighborhood pixel set in the x direction and the y direction, the weighted sum of the absolute values ​​of the gradients of the pixels in the spatial neighborhood set at all pixels, and the absolute value of the weighted sum of the gradients of the pixels in the spatial neighborhood set at all pixels; S3 obtains structural information and texture information of different scales of the spatial neighborhood according to the solution value of step (2); S4 changes different inner and outer window sizes, returns to step S1, and enters step S5 after a set number of times; S5 fuses the obtained structural information of different scales to obtain the structural information of relative total variation at multiple scales; S6 calculates a Tikhonov regularization matrix using a distance-weighted Tikhonov regularization method according to the spatial relationship between each pixel in the spatial neighborhood pixel set and the pixel to be tested; S7 imposes constraints on the weight vector such that the sum is 1 and the bi-norm of the weight vector is minimized; S8, according to the constraints of step S7 and the Tikhonov regularization matrix obtained in step S6, derives the weight vector in the anomaly detection objective function and makes the derivative equal to zero, thereby obtaining the weight vector; S9 multiplies the weight vector of the pixel to be tested by the structural information obtained in step S5 to obtain a result represented by the spatial neighborhood set of the pixel to be tested; S10 performs a difference operation between the result of step S9 and the original image to obtain a residual image, that is, to identify abnormal pixels in the image.

2. The method for anomaly detection based on multi-scale relative total variation collaborative representation of airborne hyperspectral images according to claim 1 is characterized in that: The multi-scale relative total variation model described in step S2 is: Among them, Φ x (i) Φ y (i), θ x (i) and Θ y (i) are respectively expressed as: g i,j It is expressed as: In the formula, Ω is the fusion parameter, N is the number of pixels in the spatial neighborhood set, S i is the structural information result image, I i is the spatial neighborhood set, λ is the weight parameter, ξ is a positive number, and Represent the partial derivatives in two directions, Φ x (i) and Φ y (i) is the weighted sum of the absolute values ​​of the gradients of all pixels in the neighborhood of pixel i, Θ x (i) and Θ y (i) is the absolute value of the weighted sum of the gradients of all pixels in the neighborhood of pixel i, j is the pixel in the spatial neighborhood R(i) of pixel i, x i and i Represents the x direction and y direction of pixel i, respectively. j and j represents the x and y directions of pixel j, g i,j It means that the Gaussian weight function is operated on pixel i and pixel j, and δ is the scale of the spatial window.

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