CN111160310B - Hyperspectral abnormal target detection method based on self-weight collaborative representation - Google Patents

Hyperspectral abnormal target detection method based on self-weight collaborative representation Download PDF

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CN111160310B
CN111160310B CN202010000282.0A CN202010000282A CN111160310B CN 111160310 B CN111160310 B CN 111160310B CN 202010000282 A CN202010000282 A CN 202010000282A CN 111160310 B CN111160310 B CN 111160310B
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王榕
胡豪杰
何芳
聂飞平
王震
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Northwestern Polytechnical University
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    • G06—COMPUTING; CALCULATING OR COUNTING
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    • G06V20/00—Scenes; Scene-specific elements
    • G06V20/10—Terrestrial scenes
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Abstract

The invention provides a hyperspectral abnormal target detection method based on self-weight collaborative representation. Firstly, setting the size of a double-window structure, and selecting all pixel points in the double-window structure to construct a dictionary by taking a pixel point to be detected as a center; then, constructing an abnormal detection target function represented by self-weight cooperation, substituting the dictionary into the abnormal detection target function, and solving the target function by adopting an iterative updating method to obtain an expected sparse vector; and finally, calculating the error between the pixel point to be detected and the reconstruction pixel by using the sparse vector, and judging whether the pixel point belongs to an abnormal target or not by comparing the error with a threshold value. According to the invention, the weight learning and the collaborative representation are combined to construct the target function, so that the abnormal target detection effect can be effectively improved.

Description

Hyperspectral abnormal target detection method based on self-weight collaborative representation
Technical Field
The invention belongs to the technical field of hyperspectral abnormal target detection, and particularly relates to a hyperspectral abnormal target detection method based on self-weight collaborative representation.
Background
The hyperspectral abnormal target detection is one of the hot research fields of hyperspectral image processing in recent years, and has wide application in civil use and military use. The hyperspectral abnormal target detection belongs to a target detection problem without any prior information. The traditional hyperspectral abnormal target detection method assumes that the image background obeys the statistical characteristic of Gaussian distribution, however, due to the complexity of the image background and the interference of abnormal targets, the abnormal detection effect of an abnormal detection algorithm designed by the statistical assumption is not ideal.
In recent years, cooperative expression is introduced to target detection, and a good detection effect is obtained. The document "w.li and q.du, Collaborative representation for hyperspectral analog detection, IEEE trans. geosci. remote sens., vol.53, No.3, pp.1463-1474, and mar.2015." discloses a hyperspectral abnormal target detection method based on Collaborative representation. The method comprises the steps of constructing double windows by taking pixel points to be detected as centers, taking all pixel points between the double windows as dictionaries, solving sparse vectors through a sparse representation model, and finally judging whether the pixel points belong to abnormal targets or not through errors between the pixel points to be detected and reconstructed pixels. Although the hyperspectral abnormal target detection method based on collaborative representation achieves a certain detection effect, the method treats a plurality of wave bands of a hyperspectral image equally, and ignores the adverse effect of redundancy, even low-quality wave bands such as noise and the like on the detection effect.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a hyperspectral abnormal target detection method based on self-weight collaborative representation.
A hyperspectral abnormal target detection method based on self-weight collaborative representation is characterized by comprising the following steps:
step 1: to-be-detected pixel of hyperspectral image
Figure GDA0003379919280000011
i is 1, …, n is the total number of pixels in the hyperspectral image, d is the number of wave bands of the hyperspectral image, and y isiRespectively constructing the size w as the centerout×woutAnd win×winThe double windows, all pixels between the double windows form a dictionary YcI.e. by
Figure GDA0003379919280000012
c represents the number of pixels contained in the dictionary, and c is wout×wout-win×win，win＜woutMin { h, w }, h and w are the number of rows and columns of the hyperspectral image, respectively, n is h × w,
Figure GDA0003379919280000013
j is the jth pixel element in the dictionary, and j is 1, …, c;
step 2: constructing a hyperspectral anomaly detection target function as follows:
Figure GDA0003379919280000021
wherein alpha isiIs a pixel yiThe expectation sparse vector to be solved for anomaly detection is psi as a weight matrix, and is a self-weight vector
Figure GDA0003379919280000022
Is a diagonal matrix of diagonal elements, σkThe kth element representing the self-weight vector σ, λ being the regularization parameter, can take a value range of 10-6To 100；
And step 3: solving the objective function by adopting an iterative update solving algorithm, which specifically comprises the following steps:
step 3.1, initialization: according to
Figure GDA0003379919280000023
Initializing a weight matrix, wherein I is an identity matrix;
step 3.2, fix Ψ, update αi：
Figure GDA0003379919280000024
Fixed alphaiAnd updating psi:
Figure GDA0003379919280000025
Ψ＝diag(σ) (4)
wherein m iskThe kth element of a vector m, yi-Ycαiσ is the sum ofkThe vector of composition, k ═ 1, …, d;
step 3.3, use of the updated αiAnd Ψ calculating an objective function value, and repeating step 3.2 until the difference between the objective function value calculated this time and the last calculated objective function value is less than 10-6Then the iteration is terminated, at which time alpha is obtainediNamely the pixel yiSparse vectors of anomaly detection;
and 4, step 4: calculate Pixel y byiIs ofi：
δi＝||yi-Ycαi||. (5)
Then to deltaiNormalization, given a threshold A, if δiIf > A, the pixel y is judgediIs an abnormal pixel point, otherwise, the pixel y is judgediA background pixel point; the threshold value A is preferably in the range of 0 to 1.
The invention has the beneficial effects that: according to the invention, weight learning and collaborative representation are combined, a unified target function is designed, high-quality wave bands in a hyperspectral image can be automatically endowed with larger weights, low-quality wave bands are automatically endowed with smaller weights, so that the weighted wave band characteristics are more discriminative, and the effect of abnormal target detection is effectively improved.
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FIG. 1 is a flow chart of a hyperspectral abnormal target detection method based on self-weight collaborative representation according to the invention;
FIG. 2 is a diagram of results of hyperspectral anomalous target detection using a conventional method;
FIG. 3 is a diagram of the result of hyperspectral anomalous target detection by the method of the invention.
Detailed Description
The present invention will be further described with reference to the following drawings and examples, which include, but are not limited to, the following examples.
Hyperspectral anomalous target detectionThe method comprises the steps of calculating the value of each pixel point which is an abnormal target, judging that the pixel point belongs to the abnormal target pixel when the value of each pixel point is larger than a certain threshold value, and otherwise, judging that the pixel point belongs to a background pixel point. Assuming that the hyperspectral image to be processed is a three-dimensional matrix and comprises the number of rows, columns and wave bands of the image, the hyperspectral image can be converted into a two-dimensional matrix for convenient calculation
Figure GDA0003379919280000031
Wherein d represents the wave band number of the hyperspectral image, and n is the number of all pixel points of the hyperspectral image. As shown in fig. 1, the present invention provides a hyperspectral anomaly detection method based on self-weight collaborative representation, which is basically implemented as follows:
1. constructing a dictionary by a double-window structure
Assume that the pixel point to be measured is
Figure GDA0003379919280000032
With yiA double window structure is built up for the center. Let wout×woutDenotes the size of the outer window, win×winIndicating the size of the inner window. Dictionary construction by selecting all pixel points between double windows
Figure GDA0003379919280000033
Wherein c represents the number of pixels contained in the dictionary, and c is wout×wout-win×win，win＜woutMin { h, w }, where h and w are the number of rows and columns, respectively, of the hyperspectral image, and n is h × w,
Figure GDA0003379919280000034
j is the jth pixel in the dictionary, and j is 1, …, c.
2. Hyperspectral anomaly detection method based on self-weight collaborative representation
The traditional hyperspectral abnormal target detection method based on collaborative representation has the following objective functions:
Figure GDA0003379919280000035
where λ is the regularization parameter, αiFor the desired picture element yiSparse vectors for anomaly detection.
According to the hyperspectral anomaly detection method based on self-weight collaborative representation, based on the method, different influences of different quality wave bands on detection results are considered, and therefore appropriate weights need to be given to the different wave bands. However, the hyperspectral abnormal target detection is an unsupervised binary problem in practice, and no prior information is available for judging the quality of different wave bands. In order to solve the problem, the invention combines weight learning and collaborative representation to construct a uniform target function, the high-quality wave band in the hyperspectral image can be automatically endowed with larger weight, and the low-quality wave band is automatically endowed with smaller weight, so that the weighted features are more discriminative. The problem solved by the present invention can be represented by a mathematical model as:
Figure GDA0003379919280000041
the above equation has two unknown variables Ψ and αiWhere Ψ is a self-weight vector
Figure GDA0003379919280000042
Being a diagonal matrix of diagonal elements, the kth element σ of σkIndicating the weight corresponding to the k-th band. The range of possible values for the regularization parameter λ in the present invention is 10-6To 100。
3. Model solution
In order to solve the objective function (7), the invention designs an iterative update algorithm, and the weight matrix psi and the sparse vector alpha are updated continuously and iterativelyiUntil the objective function converges. The method specifically comprises the following steps:
(1) initialization: initialize the weight matrix, order
Figure GDA0003379919280000043
Where I is the identity matrix.
(2) Fix Ψ, update αi：
When Ψ is fixed, solving the problem (7) is equivalent to solving:
Figure GDA0003379919280000044
the above formula is aligned to alphaiTaking the derivative and then making it equal to 0, one can obtain:
Figure GDA0003379919280000045
(3) fixed alphaiAnd updating psi:
when alpha isiWhile fixed, the problem (7) can be expressed simply as:
Figure GDA0003379919280000046
defining a vector
Figure GDA0003379919280000047
The k-th element of which is denoted mkEquation (10) can be further converted to:
Figure GDA0003379919280000048
the above equation has two constraints on the unknown weight vector σ, since the constraint σT1＝1，0≤σk1 can be simplified to a non-negative constraint sigmakIs more than or equal to 0. First only the first constraint sigma is consideredTThe lagrangian function for the problem (11) can be expressed as 1:
Figure GDA0003379919280000049
wherein gamma is LagrangianAnd (4) adding the active ingredients. Will be the above formula to sigmakThe derivative is then made equal to 0, then:
Figure GDA0003379919280000051
due to constraint σT1-1, available:
Figure GDA0003379919280000052
combining equation (13) and equation (14), there is:
Figure GDA0003379919280000053
for arbitrary k, σkAll are non-negative, just in line with the non-negative constraint of the problem (11) on σ, so Ψ, which is obtained in equation (15), is the optimal solution for the problem (8).
(4) Repeating the step (2) and the step (3) to carry out alphaiIterative update calculation of Ψ until the objective function converges, i.e., each iteration utilizes an updated αiPsi calculating the objective function value according to the formula (7), and the variation of the objective function value obtained by two iterative calculations before and after being less than 10-6Then the iteration is terminated, at which time alpha is obtainediNamely the pixel yiSparse vectors for anomaly detection.
4. Extracting anomalous targets based on reconstruction errors
Calculating by solving the model to obtain yiCorresponding sparse vector alphai，YcαiI.e. reconstructed pixels using background pixels (dictionaries), if the original pixel yiCan be accurately represented by the reconstructed pixels, then y is indicatediIs a background pixel point, otherwise, yiThe abnormal pixel points are obtained. The reconstruction error is calculated as follows:
δi＝||yi-Ycαi||. (16)
then to deltaiNormalized if δiIs greater than a preset threshold value A, y is indicatediIs an abnormal pixel point, otherwise, yiAre background pixels. The threshold value A is preferably in the range of 0 to 1.
The above process is adopted for detecting each pixel point in the hyperspectral image, and the anomaly detection of the whole hyperspectral image is completed.
In order to verify the effectiveness and superiority of the method, the method is compared with the traditional hyperspectral abnormal target detection method based on collaborative representation. Fig. 2 and 3 are detection result diagrams obtained by normalizing the reconstruction error calculated by the conventional method and the method of the present invention, respectively, and although both methods have partial false alarms, the method of the present invention can basically detect an abnormal target point. Table 1 shows the AUC values of the detection results obtained by the traditional method and the AUC values of the detection results obtained by the method of the present invention when different double-window sizes are adopted, wherein CRD represents the traditional method, SWCRD represents the method of the present invention, and the larger the AUC value is, the better the detection performance of the method is. It can be seen that under different window sizes, the methods provided by the invention have higher AUC values, which proves that the methods have better detection performance.
TABLE 1
Figure GDA0003379919280000061

Claims (1)

1. A hyperspectral abnormal target detection method based on self-weight collaborative representation is characterized by comprising the following steps:
step 1: to-be-detected pixel of hyperspectral image
Figure FDA0003379919270000011
n is the total number of pixels in the hyperspectral image, d is the number of wave bands of the hyperspectral image, and yiRespectively constructing the size w as the centerout×woutAnd win×winDouble window, doubleAll pixels between windows constitute a dictionary YcI.e. by
Figure FDA0003379919270000012
c represents the number of pixels contained in the dictionary, and c is wout×wout-win×win，win＜woutMin { h, w }, h and w are the number of rows and columns of the hyperspectral image, respectively, n is h × w,
Figure FDA0003379919270000013
j is the jth pixel element in the dictionary, and j is 1, …, c;
step 2: constructing a hyperspectral anomaly detection target function as follows:
Figure FDA0003379919270000014
wherein alpha isiIs a pixel yiThe expectation sparse vector to be solved for anomaly detection is psi as a weight matrix, and is a self-weight vector
Figure FDA0003379919270000015
Is a diagonal matrix of diagonal elements, σkThe kth element representing the self-weight vector σ, λ being the regularization parameter, can take a value range of 10-6To 10 °;
and step 3: solving the objective function by adopting an iterative update solving algorithm, which specifically comprises the following steps:
step 3.1, initialization: according to
Figure FDA0003379919270000016
Initializing a weight matrix, wherein I is an identity matrix;
step 3.2, fix Ψ, update αi：
Figure FDA0003379919270000017
Fixed alphaiAnd updating psi:
Figure FDA0003379919270000018
Ψ＝diag(σ) (4)
wherein m iskThe kth element of a vector m, yi-Ycαiσ is the sum ofkThe vector of composition, k ═ 1, …, d;
step 3.3, use of the updated αiAnd Ψ calculating an objective function value, and repeating step 3.2 until the difference between the objective function value calculated this time and the last calculated objective function value is less than 10-6Then the iteration is terminated, at which time alpha is obtainediNamely the pixel yiSparse vectors of anomaly detection;
and 4, step 4: calculate Pixel y byiIs ofi：
δi＝||yi-Ycαi||. (5)
Then to deltaiNormalization, given a threshold A, if δi>A, then judging the pixel yiIs an abnormal pixel point, otherwise, the pixel y is judgediA background pixel point; the threshold value A is preferably in the range of 0 to 1.
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