CN113421279B - Infrared weak and small target detection method based on weighted nuclear norm minimization - Google Patents

Infrared weak and small target detection method based on weighted nuclear norm minimization Download PDF

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CN113421279B
CN113421279B CN202110777730.2A CN202110777730A CN113421279B CN 113421279 B CN113421279 B CN 113421279B CN 202110777730 A CN202110777730 A CN 202110777730A CN 113421279 B CN113421279 B CN 113421279B
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杨兰兰
严棚
李美惠
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Institute of Optics and Electronics of CAS
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Abstract

The invention relates to an infrared dim target detection method based on weighted nuclear norm minimization. Aiming at the condition that a weak and small target is easy to be missed or mistakenly detected in a complex environment, the method provides that the image to be processed is preliminarily detected by using a characteristic detection function, a weight related to the target is constructed based on the preliminary detection, a new target function is constructed by using the weight to solve to obtain a final target image, and finally threshold segmentation is carried out to remove partial interference; the method provided by the invention can effectively reduce the false alarm rate and has good detection effect on infrared weak and small targets.

Description

Infrared weak and small target detection method based on weighted kernel norm minimization
Technical Field
The invention relates to the field of infrared image processing and target detection, and particularly provides an infrared weak and small target detection method based on weighted nuclear norm minimization.
Background
Target detection technique has developed comparatively ripe now, in civilian field, is often used for intelligent monitoring, traffic management and control, medical feature identification etc. comparatively common have: SIFT, integral image characteristics and AdaBoost are used for detecting the human face, and the HOG and the SVM are combined and mainly used for detecting pedestrians; in the military field, the system is commonly used for reconnaissance, guidance, early warning and the like. Compared with visible light and radar imaging systems, the infrared imaging system has the advantages of small size, strong anti-interference capability, good concealment, full-day operation and the like, and is mostly used in the military field, so that the key technology of infrared weak and small target detection becomes a research hotspot. The difficulty of detecting the infrared weak and small target is mainly as follows: on one hand, the target is far away from the imaging system, is generally imaged between 2X2 to 9X9 pixels, lacks obvious shape and texture characteristics, and because of scattering of energy in long-distance imaging, the energy loss of a small target is serious, so that the contrast between the target and the background is low, and the final target presents weak and small characteristics; on the other hand, the background of the small target is variable and complex, and the strong edge features of some backgrounds are very similar to the features of the small target, which is very easy to cause the misjudgment of the target. Therefore, the detection of the visible infrared small and weak target is very challenging, and although a plurality of methods for detecting the infrared small and weak target have been proposed at present, the method cannot adapt to variable background environments and cannot maintain excellent detection performance under various environments. Based on these difficulties, infrared detection of small and weak targets has received attention from many researchers.
The major research institutions for weak and small target detection abroad comprise the naval laboratory and the air force laboratory in the United states, and the international conference on the weak and small target detection technology is held almost every year from 1989 by the international optical engineering institute (SPIE) to study the latest results of the weak and small target detection technology; in China, because the starting is late, the method has a certain gap with foreign countries, but the country has a great amount of investment in the aspect of weak and small target detection technology, and related research organizations in the aspect of weak and small target detection in China have the following characteristics: colleges and universities such as national defense science and technology university, huazhong science and technology university, and the 211 th research institute of the weapon industry group, 205 th research institute of the weapon industry group, 27 th research institute of the middle electric group, 717 th institute of the Chinese ship industry, and the like.
The infrared small and weak target detection methods can be roughly divided into two categories: tracking Before Detection (TBD) and tracking before Detection (DBT), the tracking method before detection usually needs to process according to information of multiple frames of pictures, and finally detects a target, which needs a large amount of calculation and storage, and cannot meet the real-time requirement in actual demand, so the method is rarely applied in practice; the detection method before tracking only needs to detect a single-frame picture, has higher processing speed but less available information amount, and can be roughly divided into three types according to research concerns:
(1) Background-based suppression methods. The method generally adopts various strategies to inhibit the background, generally considers that the background is positioned at the low-frequency part of an image signal, the target is positioned at the high-frequency part of the image signal, separates the low-frequency part and the high-frequency part of an infrared image through various transformations, then inhibits each low-frequency component, analyzes the high-frequency component, can detect the target, and can be divided into a spatial filtering method and a transform domain filtering method according to different background inhibition modes. The traditional spatial filtering-based method includes a maximum median/maximum mean (max-mean/max-mean) filter method, a two-dimensional least mean square (TDLMS) filter method, a mathematical morphology method, a median filtering method, a bilateral filter, a high-pass template filtering method and the like. The method of transform domain filtering firstly transforms the picture to obtain the information of the transform domain, which commonly has Fourier transform and wavelet transform, then processes the obtained information in the transform domain, finally carries out inverse transform to obtain the information of the spatial domain, and obtains the corresponding result. For the frequency domain, common weak and small target detection methods mainly include ideal high-pass filtering, butterworth high-pass filtering and the like. Since the wavelet transform has very excellent performance in multi-scale and multi-directional signal analysis, and can better detect singular portions in signals, the wavelet transform is also widely applied to infrared detection of weak and small targets on the sea surface, and common wavelet transform filtering methods mainly include a Countourlet transform-based method, a non-downsampling contourlet transform-based method, and the like.
(2) A method based on target enhancement. Because the weak and small target has no geometric shape or texture feature and available effective feature information is less, based on the target angle, only a detection operator can be designed according to the characteristic differences of gray scale, structure, contrast and the like of the target and the surrounding background in a single-frame infrared image, and the target is directly extracted. Inspired by the fact that small objects appear gaussian in image distribution, some methods based on local intensity and gradient are proposed. The small target can be simulated by using a two-dimensional Gaussian function, the two-dimensional Gaussian function forms a scalar field, the gradient field of the scalar field shows the characteristic that a gradient vector points to the center, and similarly, the small target has a gray scale scalar field, and the gradient field also shows the characteristic that the gradient vector points to the center of the target. These two properties are considered to be a local intensity property and a local gradient property, respectively. Based on the two attributes, target enhancement and clutter suppression can be achieved by calculating a Local Intensity and Gradient (LIG) map of the original infrared image. Inspired by biological vision, a weak and small target detection method based on a visual contrast mechanism is proposed, which is a novel weak and small target detection method appearing in recent years, and a local contrast measurement method (LCM) is mainly adopted according to the characteristic that the gray level of a small target is stronger than that of a neighborhood, but the method has the phenomenon of enhancing noise, so that a series of improved methods exist, such as: the method adopts an HVS size self-adaption process and an attention transfer mechanism, utilizes information such as image information entropy and local similarity, a local homogeneity measuring method, contrast measurement of multi-scale blocks, a local homogeneity measuring method, a relative local contrast measuring method, a local difference measuring method and the like. However, these methods have been proposed to blur the metric because strong edges and other interference can cause a high false alarm.
(3) Method based on object and background data structures. The method mainly comprises the step of displaying a data structure by searching a low-dimensional subspace structure or using a preset super-complete dictionary, so that the detection of small targets is realized. The target in the infrared image has sparsity, the background has low rank, the separation of the target image and the background image is realized based on the two characteristics, the target and the background are considered simultaneously by the method, and more attention is paid to the method based on the image data structure recently. Image data structure based methods typically detect small objects using two ways:
(1) the method for detecting the small targets comprises the steps of firstly presetting the overcomplete dictionary for an image by using a method for presetting the overcomplete dictionary, then displaying a data structure of the image by using the dictionary, and decomposing an image matrix by using a low-rank sparse representation model to obtain data components corresponding to the small targets, so that the small targets are detected. For the construction of the overcomplete dictionary, a two-dimensional Gaussian model, a generalized Gaussian model and a dictionary learning method can be used, a fractal theory is added in some researches, and background clutter can be eliminated through sparse representation on a fractal background overcomplete dictionary.
(2) The method is characterized in that a low-rank subspace structure is searched, typically, a detection problem of an infrared small target is described as an optimization problem for recovering a low-rank sparse matrix based on an infrared image block (IPI) model, a nuclear norm is usually used as an optimal convex approximation of a rank, unlike the matrix, a tensor is a multi-linear generation of a multi-dimensional matrix and usually directly acts on high-order data, so that a tensor method is generally adopted for processing, and then, some improved methods are also used for changing the nuclear norm into other norms on the basis of the model, which is more convenient for optimization, or some a priori knowledge is added, for example, weights are added in front of the target, or regular terms are added to constrain the target or the background, so as to solve the influence of strong edges and underutilized prior information on small target detection, and obtain a better background estimation effect, for example, a weighted infrared block image (WIPI) model, a weighted block tensor image (RIPT) model, a kernel tensor part based on image blocks and (IPT-tnn) model, and the like.
Disclosure of Invention
Although the weight proposed in the weighted block image tensor (RIPT) model can suppress the interference of a part of the background, but many strong edges in the complex background are not suppressed but enhanced, aiming at the problem, the invention provides an infrared weak and small target detection method based on weighted nuclear norm minimization, so as to solve the problem that the detection false alarm is enhanced due to the strong edge interference in the complex background in the existing model method.
The technical scheme provided by the invention is as follows:
a method for detecting infrared weak and small targets based on weighted kernel norm minimization comprises the following steps:
step 1: inputting an infrared image to be processed
Figure BDA0003151789460000031
Wherein +>
Figure BDA0003151789460000032
Representing a real space, m and n representing the number of pixel lines and the number of pixels of the image to be processed, respectivelyNumber of rows by using a length and width dimension of n 1 ×n 2 Traversing the infrared image D to be processed through a sliding window with the step length s to obtain the tensor of the infrared image block->
Figure BDA0003151789460000033
Wherein n is 1 ×n 2 Is equal to the size of the sliding window, n 3 The number of the sliding windows;
step 2: obtaining two maximum eigenvalues by calculating the structure tensor of the original infrared image to be processed, and preliminarily judging the positions of point features and line features in the original image according to the two eigenvalues to construct a feature description matrix W 0 And based on the matrix W 0 Obtaining a target weight matrix W p Then converted into tensor form;
and step 3: constructing a target function and a Lagrange function, and solving the target function and the Lagrange function to obtain a target image block tensor
Figure BDA0003151789460000041
And 4, step 4: tensor of the target image block
Figure BDA0003151789460000042
Reconstruct back to the target image->
Figure BDA0003151789460000043
And 5: the target image is processed
Figure BDA0003151789460000044
And performing threshold segmentation to obtain a detection result.
The method of the invention is based on a data structure, simultaneously considering the target and the background, using a weighted nuclear norm as a convex approximation of the background rank, while using a weighted L 1 Norm constrains sparsity of the target, and L is used to further suppress noise 21 The norm constrains noise, effectively reduces false alarm rate, improves algorithm robustness, and has good detection effect in complex environment.
On the basis, the step 1 comprises the following steps:
step 1.1: with the length and width dimension n 1 ×n 2 Traversing the infrared image D by a sliding window with the step length of s, and stacking pixels intercepted by the sliding window on a third dimension to construct a tensor;
step 1.2: repeating the step 1.1 until the whole infrared image is traversed, thereby finishing the tensor of the infrared image block
Figure BDA0003151789460000045
And (4) constructing.
Wherein the step 2 comprises the following steps:
step 2.1: constructing structure tensor by using infrared image D to be processed and solving eigenvalue lambda 1 And λ 2 The formula is as follows:
Figure BDA0003151789460000046
wherein J is the structure tensor, K ρ Is a gaussian kernel with variance p, representing a convolution,
Figure BDA0003151789460000047
represents a gradient,. Based on the presence of a marker>
Figure BDA0003151789460000048
Represents the Kronecker product, D σ The image to be processed is filtered by a gaussian smoothing filter with variance σ. />
Figure BDA0003151789460000049
Figure BDA00031517894600000410
Respectively represent D σ Gradient along x and y directions.
Obtaining the maximum two eigenvalues lambda according to the structure tensor 1 And λ 2 The formula is as follows:
Figure BDA00031517894600000411
/>
Figure BDA00031517894600000412
step 2.2: using lambda 1 And λ 2 Obtaining W rec And W 0 Further obtain the target weight matrix W p ；
Wherein the content of the first and second substances,
Figure BDA00031517894600000413
respectively constructing a point feature matrix W according to the feature point detection result of the original infrared image point Sum line feature matrix W line To thereby obtain a feature description matrix W 0 ＝W line +C*W point C is a constant and is finally based on W p ＝W rec .W sw .W 0 An objective weight matrix W can be obtained p Wherein->
Figure BDA00031517894600000414
Updating in subsequent iterative solution, wherein T represents a target matrix, eta is a nonzero constant, and | represents solving an absolute value;
step 2.3: using a sliding window to apply the target weight matrix W as described in step 1 p Stacked in tensor form
Figure BDA00031517894600000415
The described
Figure BDA00031517894600000416
The image block tensor is the target weight.
Wherein the step 2.2 comprises:
step 2.2.1: constructing a feature point detection function:
Figure BDA0003151789460000051
the function can alsoThe method is divided into two parts:
Figure BDA0003151789460000052
wherein e is a natural number;
step 2.2.2: constructing a point feature matrix according to a feature point detection function, defining a threshold value for val, and taking gamma of the maximum value except infinity 1 Multiplying by a threshold seg _ val, defining a threshold for val1, and taking the minimum value of gamma 2 Multiple threshold value seg _ val1 for simultaneous val satisfaction>The characteristic points of seg _ val and val1 which are less than or equal to seg _ val1 are regarded as point characteristics, the positions corresponding to the point characteristic matrix are set as 1, other positions are set as 0, and the point characteristic matrix is subjected to morphological expansion by adopting a circular structural element;
step 2.2.3: and constructing a line feature matrix according to the feature point detection function, considering feature points with val values being infinite and satisfying val1> seg _ val1 as line features, and setting the positions corresponding to the line feature matrix as 0 and setting other positions as 1.
In step 3, an objective function is constructed through the weighted nuclear norm and the target weight, an ADMM algorithm is used for constructing a Lagrangian function, and the Lagrangian function is solved to obtain a target image block tensor
Figure BDA0003151789460000053
The step 3 comprises the following steps:
step 3.1: inputting the infrared image block tensor
Figure BDA0003151789460000054
And a target weight image block tensor>
Figure BDA0003151789460000055
Step 3.2: constructing an objective function through the weighted kernel norm and the objective weight, and constructing a Lagrangian function by using an ADMM algorithm;
step 3.3: solving the Lagrange function to obtain the tensor of the target image block
Figure BDA0003151789460000056
Wherein said step 3.2 comprises:
step 3.2.1: constructing an objective function through the weighted kernel norm and the target weight, wherein the constructed objective function is as follows:
Figure BDA0003151789460000057
Figure BDA0003151789460000058
wherein
Figure BDA0003151789460000059
Tensor representative of noise->
Figure BDA00031517894600000510
Tensor representative of background,. Sup.>
Figure BDA00031517894600000511
Here | * Represents the nuclear norm by summing all the singular values of the matrix A>
Figure BDA00031517894600000512
L representing tensor A 1 Norm>
Figure BDA00031517894600000513
Figure BDA00031517894600000514
L being a noise component 21 Norm>
Figure BDA00031517894600000515
The status of the Hadamard product is indicated by the indicator, and the penalty coefficients are indicated by the indicator lambda and the beta; />
Step 3.2.2: constructing a Lagrangian function through an ADMM algorithm:
Figure BDA00031517894600000516
wherein |) F Represents the Frobenius norm,
Figure BDA00031517894600000517
representing the lagrange multiplier and μ the non-negative penalty factor.
Wherein the step 3.3 comprises:
step 3.3.1: initializing ADMM equation parameters, iterating the times k =0,
Figure BDA00031517894600000518
μ 0 ＝0.007，/>
Figure BDA00031517894600000625
iteration end threshold epsilon =10 -7 ，/>
Figure BDA0003151789460000061
β＝0.1，η＝0.01；
Step 3.3.2: iterating until the Lagrangian function constructed by the ADMM algorithm converges;
wherein step 3.3.2 comprises:
step 3.3.2.1: updating parameters according to the following formula
Figure BDA0003151789460000062
Figure BDA0003151789460000063
Wherein
Figure BDA0003151789460000064
Is a singular value contraction operator>
Figure BDA0003151789460000065
In the formula, U and D X V is the moment of alignmentObtained by singular value decomposition of the array X, D X Representing a diagonal matrix composed of its eigenvalues;
step 3.3.2.2: updating the parameters according to the following formula
Figure BDA0003151789460000066
Figure BDA0003151789460000067
Wherein S is τ (X) is a soft threshold shrink operator, S τ (X)＝sign(X)×max(|X|-τ,0)；
Step 3.3.2.3: updating parameters according to the following formula
Figure BDA0003151789460000068
Figure BDA0003151789460000069
Wherein
Figure BDA00031517894600000610
Figure BDA00031517894600000611
Representing the ith matrix of image blocks truncated by a sliding window, | 2 A two-norm representing a matrix;
step 3.3.2.4: updating parameters according to the following formula
Figure BDA00031517894600000612
Figure BDA00031517894600000613
Wherein->
Figure BDA00031517894600000614
Is->
Figure BDA00031517894600000615
The portion of the data that needs to be updated;
step 3.3.2.5: updating the parameters according to the following formula
Figure BDA00031517894600000616
μ k+1 ：
Figure BDA00031517894600000617
μ k+1 ＝min(1.05μ k ,10 10 )；
Step 3.3.2.6: will be provided with
Figure BDA00031517894600000618
And &>
Figure BDA00031517894600000619
Both are attributed to the background section, namely: />
Figure BDA00031517894600000620
Step 3.3.2.7: update iteration number k = k +1;
step 3.3.2.8: respectively calculate
Figure BDA00031517894600000621
And &>
Figure BDA00031517894600000622
The number preT and currT of the medium nonzero elements;
step 3.3.2.9: judging whether preT and currT are equal and both greater than 0, if so, terminating iteration, and jumping to the step 3.3.2.10; if not, judging the formula
Figure BDA00031517894600000623
If the result is true, terminating iteration and jumping to the step 3.3.2.10, and if the result is false, jumping to the step 3.3.2.1;
step 3.3.2.10: obtaining an optimal solution
Figure BDA00031517894600000624
The infrared weak and small target detection method based on the weighted nuclear norm minimization has the beneficial effects that:
1. the model used is added with L 21 Norm constrained noise and using weighted L for the target image 1 Norm constraint and innovativeness provide a weight construction mode, and the problem that the result is interfered by edges, noise, false alarm sources and the like due to the fact that sparse constraint is not strict in the conventional algorithm is effectively solved;
2. the infrared small target detection problem is converted into an optimization problem, so that the target and the background are efficiently and accurately separated, and the small target detection accuracy is improved;
3. iterative solution is carried out by adopting an alternating direction multiplier method, and meanwhile, an improved iteration termination condition is used, so that the convergence speed is greatly improved, the calculation running time is greatly reduced, and the applicability is obviously improved.
Drawings
FIG. 1 is a flow chart of the infrared weak and small target detection method based on weighted nuclear norm minimization according to the present invention;
FIG. 2a is an infrared image containing a small target as employed in an embodiment of the present invention;
FIG. 2b is a three-dimensional representation of the original infrared image of FIG. 2a in an embodiment of the present invention;
FIG. 3a is a target image obtained by solving in FIG. 2a and subjected to threshold segmentation according to an embodiment of the present invention;
FIG. 3b is a three-dimensional representation of the target image shown in FIG. 3a according to an embodiment of the present invention;
FIG. 4a is a two-dimensional display of the processing results of FIG. 2a using a prior art intermediate infrared block image (IPI) model approach;
FIG. 4b is a three-dimensional display of the processing results of FIG. 2a using a prior art intermediate infrared block image (IPI) model approach;
FIG. 5a is a two-dimensional representation of the processing results of FIG. 2a using a prior art method of reweighted infrared block tensor (RIPT) model;
FIG. 5b is a three-dimensional representation of the processing results of FIG. 2a using a prior art method of reweighting infrared block tensor (RIPT) models.
Detailed Description
The following describes embodiments of the present invention in further detail with reference to the accompanying drawings. This should not be construed as limiting the scope of the invention to the following examples. Various substitutions and alterations according to the general knowledge and conventional practice in the art are intended to be included within the scope of the present invention without departing from the technical spirit of the present invention as described above.
As shown in fig. 1, the method for detecting infrared weak and small targets based on weighted nuclear norm minimization of the present invention includes the following steps:
step 1: inputting a 256X 256 infrared image to be processed
Figure BDA0003151789460000071
Wherein->
Figure BDA0003151789460000072
Representing a real number space, wherein m and n respectively represent the number of lines and the number of columns of the image to be processed, and traversing the infrared image D to be processed through a sliding window to obtain the tensor (greater or lesser) of the infrared image block>
Figure BDA0003151789460000073
Wherein n is 1 ×n 2 Is equal to the size of the sliding window, n 3 The number of the sliding windows;
specifically, the step 1 comprises:
step 1.1: traversing the infrared image D by adopting a sliding window with the length and width of 40 multiplied by 40 and the step length of 40, and stacking pixels intercepted by the sliding window on a third dimension to construct a tensor;
step 1.2: repeating the step 1.1 until the whole infrared image is traversed, thereby finishing the tensor of the infrared image block
Figure BDA0003151789460000074
In which n is 1 ＝n 2 ＝n 3 ＝40。
And 2, step: by calculating the originalObtaining two maximum eigenvalues by the structure tensor of the infrared image, and preliminarily judging the positions of the point characteristic and the line characteristic in the original image according to the two eigenvalues to construct W in the target weight matrix 0 Thereby obtaining a target weight W p Then converted into tensor form;
specifically, the step 2 includes:
step 2.1: a structure tensor J is constructed according to the infrared image D to be processed, and the formula is as follows:
Figure BDA0003151789460000081
wherein, K ρ Is a gaussian kernel with variance p, representing a convolution,
Figure BDA0003151789460000082
represents a gradient,. Based on the presence of a marker>
Figure BDA0003151789460000083
Represents the Kronecker product, D σ The image to be processed is filtered by a gaussian smoothing filter with variance σ. />
Figure BDA0003151789460000084
Respectively represent D σ Gradient along x and y directions.
Obtaining the maximum two eigenvalues lambda according to the structure tensor 1 And λ 2 The formula is as follows:
Figure BDA0003151789460000085
Figure BDA0003151789460000086
step 2.2: using lambda 1 And λ 2 Obtaining W rec And W 0 Further obtain the target weight matrix W p ，
Wherein the content of the first and second substances,
Figure BDA0003151789460000087
respectively constructing point characteristic moments W according to characteristic point detection results of original infrared images point Array sum line feature matrix W line Thereby obtaining a matrix W 0 ＝W line +C*W point (ii) a A better result can be obtained when the initial test C =2, and finally a target weight matrix can be obtained: w p ＝W rec .W sw .W 0 Wherein->
Figure BDA0003151789460000088
η =0.01, updated in subsequent iterative solutions.
Wherein, step 2.2 includes:
step 2.2.1: constructing a feature point detection function:
Figure BDA0003151789460000089
the function can be divided into two parts: />
Figure BDA00031517894600000810
Figure BDA00031517894600000811
Step 2.2.2: constructing a point feature matrix according to a feature point detection function, defining a threshold value for val, and taking gamma of the maximum value except infinity 1 (in this example, 0.5 times) the threshold seg _ val, the threshold is defined for val1, and γ is the minimum value of the threshold seg _ val 2 (100 times in this embodiment) the threshold seg _ val1, for the simultaneous satisfaction of val>The characteristic points of seg _ val and val1 which are less than or equal to seg _ val1 are regarded as point characteristics, so that the corresponding positions of the point characteristic matrix are set as 1, other positions are set as 0, as the point characteristics are more easily presented by a remote weak and small target, in order to keep the shape characteristics of the weak and small target, the point characteristic matrix needs to be subjected to morphological expansion, and a circular structural element with the radius of 5 is adopted in the example;
step 2.2.3: constructing a line feature matrix according to the feature point detection function, regarding feature points with val values being infinite and satisfying val1> seg _ val1 as line features, and setting the positions corresponding to the line feature matrix as 0 and setting other positions as 1;
step 2.3: using sliding window to obtain the target weight matrix W according to the step 1 p Stacked in tensor form
Figure BDA0003151789460000091
And 3, step 3: constructing an objective function through the weighted nuclear norm and the target weight, constructing a Lagrangian function by using an ADMM algorithm, and solving the Lagrangian function to obtain a target image block tensor
Figure BDA0003151789460000092
Wherein, step 3 includes:
step 3.1: inputting the infrared image block tensor
Figure BDA0003151789460000093
And a target weight image block tensor; />
Step 3.2: constructing an objective function through the weighted kernel norm and the target weight, and constructing a Lagrangian function by using an ADMM algorithm;
wherein, step 3.2 includes:
step 3.2.1: the infrared weak and small target image is composed of a background with low-rank components, a target with sparse components and noise, a weighted nuclear norm is adopted because the nuclear norm cannot approach the rank well, the weight added to the target part is used for better inhibiting the background, and the constructed target function is as follows:
Figure BDA0003151789460000094
Figure BDA0003151789460000095
wherein
Figure BDA0003151789460000096
Tensor representative of noise->
Figure BDA0003151789460000097
Tensor representative of background,. Sup.>
Figure BDA0003151789460000098
Here |) * Represents the nuclear norm by summing all the singular values of the matrix A>
Figure BDA0003151789460000099
L representing tensor A 1 Norm>
Figure BDA00031517894600000910
Figure BDA00031517894600000911
L being a noise component 21 Norm>
Figure BDA00031517894600000912
As indicates Hadamard product, λ and β indicate penalty coefficients;
step 3.2.2: constructing a Lagrangian function through an ADMM algorithm:
Figure BDA00031517894600000913
wherein |) F Represents the Frobenius norm,
Figure BDA00031517894600000914
representing a lagrange multiplier, mu representing a non-negative penalty factor;
step 3.3: solving the Lagrange function to obtain the tensor of the target image block
Figure BDA00031517894600000915
Wherein, step 3.3 includes:
step 3.3.1: initializing ADMM equation parameters, iterating the times k =0,
Figure BDA00031517894600000916
μ 0 ＝0.007，/>
Figure BDA00031517894600000917
iteration termination threshold epsilon =10 -7 ，/>
Figure BDA00031517894600000918
β＝0.1；
Step 3.3.2: and iterating until the Lagrangian function constructed by the ADMM algorithm converges.
Wherein step 3.3.2 comprises:
step 3.3.2.1: updating the parameters according to the following formula
Figure BDA00031517894600000919
Figure BDA00031517894600000920
Wherein
Figure BDA00031517894600000921
Is a singular value contraction operator, in conjunction with a value selection function>
Figure BDA00031517894600000922
In the formula, U and D X V is obtained by singular value decomposition of X, D X Representing a diagonal matrix composed of its eigenvalues.
Step 3.3.2.2: updating the parameters according to the following formula
Figure BDA0003151789460000101
Figure BDA0003151789460000102
Wherein S is τ (X) is a soft threshold shrink operator, S τ (X)＝sign(X)×max(|X|-τ,0)；
Step 3.3.2.3: updating the parameters according to the following formula
Figure BDA0003151789460000103
Figure BDA0003151789460000104
/>
Wherein
Figure BDA0003151789460000105
Figure BDA0003151789460000106
Representing the ith matrix of image blocks truncated by a sliding window, | 2 A two-norm representing a matrix;
step 3.3.2.4: updating the parameters according to the following formula
Figure BDA0003151789460000107
Figure BDA0003151789460000108
Wherein->
Figure BDA0003151789460000109
Is/>
Figure BDA00031517894600001010
The part of the system that needs to be updated.
Step 3.3.2.5: updating parameters according to the following formula
Figure BDA00031517894600001011
μ k+1 ：
Figure BDA00031517894600001012
μ k+1 ＝min(1.05μ k ,10 10 )
Step 3.3.2.6: will be provided with
Figure BDA00031517894600001013
And &>
Figure BDA00031517894600001014
Both are attributed to the background part, i.e.: />
Figure BDA00031517894600001015
Step 3.3.2.7: update iteration number k = k +1;
step 3.3.2.8: respectively calculate
Figure BDA00031517894600001016
And &>
Figure BDA00031517894600001017
The number preT and currT of the medium nonzero elements;
step 3.3.2.9: judging whether preT and currT are equal and both greater than 0, if so, terminating iteration, and skipping to the step 3.3.2.10; if not, judging the formula
Figure BDA00031517894600001018
If yes, terminating iteration and skipping to the step 3.3.2.10; if not, jumping to step 3.3.2.1.
Step 3.3.2.10: obtaining an optimal solution
Figure BDA00031517894600001019
And 4, step 4: tensor of the target image block
Figure BDA00031517894600001020
Reconstruct back to the target image->
Figure BDA00031517894600001021
Reconstructing each frontal slice in the infrared image block tensor sequentially into a 256 × 256 target image->
Figure BDA00031517894600001022
And determining the pixel value of the position by adopting a mean filtering mode for the overlapped part.
And 5: the target image is processed
Figure BDA00031517894600001023
Performing threshold segmentation to obtain a detection result: based on the reconstructed target image->
Figure BDA00031517894600001024
Adaptive threshold segmentation is performed, where Th = μ + c σ, where μ denotes a mean value of the input infrared image, σ is a standard deviation of the input infrared image, and c denotes a constant, in this example c =3, and the detection result is obtained after the segmentation is completed.
Effect analysis was performed according to the attached figures: fig. 2a is an infrared image, a small target is located at the edge of a road, the background is complex, some small stones are located on the roadside besides the small target, the edge of the road is obvious, the small stones greatly interfere the target detection, and fig. 2b is a three-dimensional display of an original image, so that the interference is particularly large; FIG. 3a is a thresholded target image obtained by the method of the present invention, and FIG. 3b is a three-dimensional display showing that the responses are all 0 except for the target region; fig. 4 to 5 are a two-dimensional display and a three-dimensional display of results obtained after processing and threshold segmentation of the infrared block image (IPI) model and the heavily weighted infrared block tensor (RIPT) model in the prior art for fig. 2a, respectively, where the IPI method has a lot of clutter interference to cause a lot of false alarms, the RIPT method has false detections, and the presence of clutter interference part weakens the target; by comparison, the processing results of the two existing methods have clutter interference, but the method only has response in the target area, so that the false alarm rate can be reduced, and the accuracy of target detection can be improved.
The above description is only for the specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto, and these examples are only for illustrative purpose and are not intended to limit the scope of the present invention. The scope of the invention is defined by the appended claims and equivalents thereof. Various alternatives and modifications can be devised by those skilled in the art without departing from the scope of the invention, and these alternatives and modifications are intended to fall within the scope of the invention.

Claims (2)

1. A method for detecting infrared weak and small targets based on weighted nuclear norm minimization is characterized by comprising the following steps:
step 1: inputting an infrared image to be processed
Figure FDA0003879301670000011
Wherein->
Figure FDA0003879301670000012
Representing real number space, m and n respectively representing the pixel row number and the pixel column number of the image to be processed, and adopting the length and width dimension as n 1 ×n 2 Traversing the infrared image D to be processed by the sliding window with the step length of s to obtain the tensor of the infrared image block>
Figure FDA0003879301670000013
Wherein n is 1 ×n 2 Is equal to the size of the sliding window, n 3 The number of the sliding windows;
and 2, step: obtaining two maximum eigenvalues by calculating the structure tensor of the original infrared image to be processed, and initially judging the positions of the point characteristic and the line characteristic in the original image according to the two eigenvalues to construct an eigen description matrix W 0 And is based on W 0 Obtaining a target weight matrix W p Then it is converted into tensor form;
and step 3: constructing a target function and a Lagrange function, and solving the target function and the Lagrange function to obtain a target image block tensor
Figure FDA0003879301670000014
And 4, step 4: tensor of the target image block
Figure FDA0003879301670000015
Reconstructed back to the target image>
Figure FDA0003879301670000016
And 5: the target image is processed
Figure FDA0003879301670000017
Performing threshold segmentation to obtain a detection result;
wherein the step 2 comprises the following steps:
step 2.1: constructing structure tensor by using infrared image D to be processed and solving eigenvalue lambda 1 And λ 2 ；
Step 2.2: using lambda 1 And λ 2 Obtaining W rec And W 0 Further obtain the target weight matrix W p ；
Wherein the content of the first and second substances,
Figure FDA0003879301670000018
respectively constructing a point feature matrix W according to the feature point detection result of the original infrared image point Sum line feature matrix W line To thereby obtain a feature description matrix W 0 ＝W line +C*W point C is a constant and is finally based on W p ＝W rec .W sw .W 0 Obtaining a target weight matrix W p (ii) a Wherein->
Figure FDA0003879301670000019
Updating in subsequent iterative solution, wherein T represents a target matrix, eta is a nonzero constant, and | represents an absolute value;
step 2.3: using sliding window to obtain the target weight matrix W according to the step 1 p Stacked in tensor form
Figure FDA00038793016700000110
Is/are>
Figure FDA00038793016700000111
A tensor of the target weight image block;
wherein the step 2.2 comprises:
step 2.2.1: constructing a feature point detection function:
Figure FDA00038793016700000112
the function can in turn be divided into two parts:
Figure FDA00038793016700000113
wherein e is a natural number;
step 2.2.2: constructing a point feature matrix according to a feature point detection function, defining a threshold value for val, and taking gamma of the maximum value except infinity 1 Multiplying by a threshold seg _ val, defining a threshold for val1, and taking the minimum value of the threshold value gamma 2 The multiple is a threshold value seg _ val1, feature points which simultaneously satisfy val > seg _ val and val1 is less than or equal to seg _ val1 are regarded as point features, the positions corresponding to the point feature matrix are set as 1, other positions are set as 0, and the point feature matrix is morphologically expanded by adopting circular structural elements;
step 2.2.3: constructing a line feature matrix according to the feature point detection function, regarding feature points with val values being infinite and satisfying val1> seg _ val1 as line features, and setting the positions corresponding to the line feature matrix as 0 and setting other positions as 1;
in the step 3, a target function is constructed through the weighted nuclear norm and the target weight, an ADMM algorithm is used for constructing a Lagrangian function, and the Lagrangian function is solved to obtain a target image block tensor
Figure FDA0003879301670000021
The step 3 comprises the following steps: />
Step 3.1: inputting the infrared image block tensor
Figure FDA0003879301670000022
And a target weight image block tensor>
Figure FDA0003879301670000023
Step 3.2: constructing an objective function through the weighted kernel norm and the target weight, and constructing a Lagrangian function by using an ADMM algorithm;
step 3.3: solving the Lagrange function to obtain the target image block tensor
Figure FDA0003879301670000024
Said step 3.2 comprises:
step 3.2.1: constructing an objective function through the weighted kernel norm and the target weight, wherein the constructed objective function is as follows:
Figure FDA0003879301670000025
Figure FDA0003879301670000026
wherein the content of the first and second substances,
Figure FDA0003879301670000027
tensor representative of noise->
Figure FDA0003879301670000028
A representative background tensor; />
Figure FDA0003879301670000029
Here | | | charging * Represents a nuclear norm,>
Figure FDA00038793016700000210
representing a tensor>
Figure FDA00038793016700000211
L of 1 Norm, specifically expressed as: />
Figure FDA00038793016700000212
Figure FDA00038793016700000213
L being a noise component 21 Norm>
Figure FDA00038793016700000214
The status of the Hadamard product is indicated by the indicator, and the penalty coefficients are indicated by the indicator lambda and the beta;
step 3.2.2: constructing a Lagrangian function through an ADMM algorithm:
Figure FDA00038793016700000215
wherein | | | calving F Represents the norm of Frobenius,
Figure FDA00038793016700000216
representing the lagrange multiplier and μ the non-negative penalty factor.
2. The infrared weak and small target detection method based on weighted nuclear norm minimization as claimed in claim 1, characterized in that:
said step 3.3 comprises:
step 3.3.1: initializing ADMM equation parameters, iterating the times k =0,
Figure FDA00038793016700000217
μ 0 ＝0.007，
Figure FDA00038793016700000218
iteration end threshold epsilon =10 -7 ，/>
Figure FDA00038793016700000219
β＝0.1，η＝0.01；
Step 3.3.2: iterating until the Lagrangian function constructed by the ADMM algorithm converges;
wherein step 3.3.2 comprises:
step 3.3.2.1: updating parameters according to the following formula
Figure FDA00038793016700000220
Figure FDA00038793016700000221
Wherein
Figure FDA0003879301670000031
Is a singular value contraction operator>
Figure FDA0003879301670000032
In the formula, U and D X V is obtained by singular value decomposition of matrix X, D X Representing a diagonal matrix composed of its eigenvalues;
step 3.3.2.2: updating the parameters according to the following formula
Figure FDA0003879301670000033
Figure FDA0003879301670000034
Wherein S is τ (x) Is a soft threshold shrink operator, S τ (X)＝sign(X)×max(|X|-τ，0)；
Step 3.3.2.3: updating parameters according to the following formula
Figure FDA0003879301670000035
/>
Figure FDA0003879301670000036
Wherein
Figure FDA0003879301670000037
Figure FDA0003879301670000038
Representing the ith image block matrix intercepted by a sliding window, | | | calting 2 A two-norm representing a matrix;
step 3.3.2.4: updating parameters according to the following formula
Figure FDA0003879301670000039
Figure FDA00038793016700000310
Wherein +>
Figure FDA00038793016700000311
Is W T k+1 The portion of the data that needs to be updated;
step 3.3.2.5: updating parameters according to the following formula
Figure FDA00038793016700000312
μ k+1 ：
Figure FDA00038793016700000313
μ k+1 ＝min(1.05μ k ，10 10 )；
Step 3.3.2.6: will be provided with
Figure FDA00038793016700000314
And &>
Figure FDA00038793016700000315
Both are attributed to the background part, i.e.: />
Figure FDA00038793016700000316
Step 3.3.2.7: update iteration number k = k +1;
step 3.3.2.8: respectively calculate
Figure FDA00038793016700000317
And &>
Figure FDA00038793016700000320
The number of the non-zero elements is preT and currT;
step 3.3.2.9: judging whether preT and currT are equal and both greater than 0, if so, terminating iteration, and skipping to the step 3.3.2.10; if not, judging the formula
Figure FDA00038793016700000318
If the result is true, terminating iteration and jumping to the step 3.3.2.10, and if the result is false, jumping to the step 3.3.2.1;
step 3.3.2.10: obtaining an optimal solution
Figure FDA00038793016700000319
/>
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Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US6282301B1 (en) * 1999-04-08 2001-08-28 The United States Of America As Represented By The Secretary Of The Army Ares method of sub-pixel target detection
CN109215025A (en) * 2018-09-25 2019-01-15 电子科技大学 A kind of method for detecting infrared puniness target approaching minimization based on non-convex order
CN109934815A (en) * 2019-03-18 2019-06-25 电子科技大学 A kind of tensor recovery method for detecting infrared puniness target of combination ATV constraint
CN110135344A (en) * 2019-05-16 2019-08-16 电子科技大学 Based on the method for detecting infrared puniness target for weighting fixed order expression
CN111160181A (en) * 2019-12-20 2020-05-15 西北工业大学 Small target detection method based on infrared video image
CN112329764A (en) * 2020-09-28 2021-02-05 中国空气动力研究与发展中心计算空气动力研究所 Infrared dim target detection method based on TV-L1 model

Patent Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US6282301B1 (en) * 1999-04-08 2001-08-28 The United States Of America As Represented By The Secretary Of The Army Ares method of sub-pixel target detection
CN109215025A (en) * 2018-09-25 2019-01-15 电子科技大学 A kind of method for detecting infrared puniness target approaching minimization based on non-convex order
CN109934815A (en) * 2019-03-18 2019-06-25 电子科技大学 A kind of tensor recovery method for detecting infrared puniness target of combination ATV constraint
CN110135344A (en) * 2019-05-16 2019-08-16 电子科技大学 Based on the method for detecting infrared puniness target for weighting fixed order expression
CN111160181A (en) * 2019-12-20 2020-05-15 西北工业大学 Small target detection method based on infrared video image
CN112329764A (en) * 2020-09-28 2021-02-05 中国空气动力研究与发展中心计算空气动力研究所 Infrared dim target detection method based on TV-L1 model

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
Infrared small target detection based on partial sum of the tensor nuclear norm;Landan Zhang et.al;《Remote Sensing》;20190213;全文 *
Infrared small target detection via spatial-temporal infrared patch-tensor model and weighted Schatten p-norm minimization;Yang Sun et.al;《INFRARED PHSICS & TECHNOLOGY》;20190930;全文 *
红外弱小目标检测算法综述;李俊宏等;《中国图象图形学报》;20200916(第09期);全文 *

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