CN109215025B - Infrared weak and small target detection method based on non-convex rank approach minimization - Google Patents

Infrared weak and small target detection method based on non-convex rank approach minimization Download PDF

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CN109215025B
CN109215025B CN201811116093.9A CN201811116093A CN109215025B CN 109215025 B CN109215025 B CN 109215025B CN 201811116093 A CN201811116093 A CN 201811116093A CN 109215025 B CN109215025 B CN 109215025B
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target
image
infrared
block image
norm
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CN109215025A (en
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彭真明
张兰丹
张鹏飞
曹思颖
赵学功
刘雨菡
吕昱霄
张天放
于璐阳
彭闪
杨春平
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University of Electronic Science and Technology of China
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Abstract

The invention discloses an infrared weak and small target detection method based on non-convex rank approach minimization, belonging to the field of infrared image processing and target detection; which comprises the following steps of 1: traversing the original image by adopting a sliding window to construct an infrared block image; step 2: constructing a target function by utilizing non-convex rank approximation minimization, inputting the infrared block image into the target function, and solving the target function by utilizing an augmented Lagrange multiplier method and a differential convex programming method to obtain a background block image and a target block image; and step 3: reconstructing a background image and a target image according to the background block image and the target block image; and 4, step 4: performing threshold segmentation on the target image to determine the position of the target, and outputting a target detection result; the method solves the problem that the detection accuracy of the infrared weak and small target is low due to the fact that factors such as strong edges, partial noise, a false alarm source and the like have sparse characteristics in the existing IPI method, and achieves the effect of inhibiting the influence of sparse characteristics of other factors on the detection accuracy.

Description

Infrared weak and small target detection method based on non-convex rank approach minimization
Technical Field
The invention belongs to the field of infrared image processing and target detection, and particularly relates to an infrared weak and small target detection method based on non-convex rank approximation minimization.
Background
The infrared imaging technology has the characteristics of non-contact property, strong capability of capturing details and the like, and realizes the detection of continuous long-distance targets day and night without being influenced by obstacles such as smoke, fog and the like; the infrared search and tracking IRST (infrared search and tracking) system is widely applied to the fields of military, civil use and the like, wherein the infrared small and weak target detection technology is used as a basic function of the IRST system and has important significance in infrared search, infrared early warning and long-distance target detection. However, due to the lack of texture and structural information of the target in the infrared band, the influence of long distance, complex background and various clutter, the infrared target is often spotted or spotted and even submerged in the background, which makes the detection of the infrared weak and small target extremely difficult.
The infrared weak and small target detection technology is divided into two main categories: the technology for detecting the weak and small targets based on a single frame and the technology for detecting the weak and small targets based on multiple frames have the advantages that due to the fact that the technology for detecting the weak and small targets based on the multiple frames needs to be combined with the multiple frames to capture the motion tracks of the targets and eliminate noise interference, extremely large calculation amount and storage amount are needed, requirements on hardware are high, and application in practical engineering is few. Currently, the commonly used detection methods based on a single frame are classified into the following three categories:
(1) background suppression: the background suppression method is based on the assumption of background consistency in the infrared image, a filter is adopted to predict the background of the infrared image, then the background is subtracted from the original image, and finally threshold segmentation is carried out to detect the dim target. Maximum median filtering, maximum mean filtering, top-hat transformation, two-dimensional least mean square filtering, etc. all belong to the category of background suppression. Although this type of method is simple to implement, the background suppression method is very susceptible to noise clutter due to the assumption that noise does not conform to consistency, resulting in poor suppression of most infrared images with low signal-to-noise ratio.
(2) Visual saliency: the human visual system hvs (human visual system) involves three mechanisms, contrast, visual attention and eye movement, the most of which is the contrast mechanism, i.e. in the assumed infrared image, the most prominent object is targeted. For example, a gaussian difference filter calculates a saliency map using two different gaussian filters, and detects and identifies a target; the method based on local contrast utilizes the characteristics that the local contrast of a small neighborhood containing a target is high, but the local contrast of a background area of the target which is not contained is low, and achieves the aim of detection by computing a local contrast map, highlighting the target and restraining the background. When the infrared image conforms to the assumption of visual saliency, the method can obtain excellent effect, but in practical application scenes, the assumption is difficult to meet, for example, when a salient false alarm source exists, the false detection problem is difficult to overcome, and the accuracy is low.
(3) Separating a target background: the method utilizes the non-local autocorrelation of the infrared image background and the sparsity of the target to convert the target detection problem into an optimization problem; the method can be further divided into a method based on an ultra-complete dictionary and low-rank representation and a method based on low-rank background and sparse target restoration. The first method needs to construct an ultra-complete dictionary with different target sizes and shapes in advance by a Gaussian intensity model, the process of constructing the target dictionary is complicated, the detection result is greatly influenced by the dictionary, and the Gaussian intensity model is not applicable any more if the target sizes and shapes are changed greatly; in the second method, a low-rank original block Image can be obtained by means of an IPI (acquired Path-Image) model, and then a background and a target Image are recovered by optimizing a target function by means of the characteristic of target sparsity, so that a detection result is finally obtained; the second method is excellent in effect, but has the following two problems: firstly, because strong edges, partial noise and false alarm sources are also sparse, the detection accuracy can be reduced; secondly, due to the fact that the process of objective function optimization needs iteration, real-time performance is difficult to achieve. Therefore, there is a need for an infrared small target detection method that overcomes the above problems.
Disclosure of Invention
The invention aims to: the invention provides an infrared small and weak target detection method based on non-convex rank approach minimization, and solves the problem that the existing IPI method has the sparse characteristic due to factors such as strong edges, partial noise, false alarm sources and the like, so that the infrared small and weak target detection accuracy is low.
The technical scheme adopted by the invention is as follows:
an infrared weak and small target detection method based on non-convex rank approximation minimization comprises the following steps:
step 1: traversing the original image by adopting a sliding window to construct an infrared block image;
step 2: based on non-convex rank approximation minimization thought, gamma norm combined with weighted l1Norm and l2,1The norm jointly constructs a target function, and after the infrared block images are input into the target function, the target function is solved by utilizing an augmented Lagrange multiplier method and a differential convex programming method to obtain a background block image and a target block image;
and step 3: reconstructing a background image and a target image according to the background block image and the target block image;
and 4, step 4: and performing threshold segmentation on the target image to determine the position of the target, and outputting a target detection result.
Preferably, the step 1 comprises the steps of:
step 1.1: obtaining the infrared image D epsilon R to be processedm×n；
Step 1.2: traversing an original image D according to the step length s by adopting a sliding window W with the size of p multiplied by p, and converting a matrix vector with the size of p multiplied by p in the sliding window W each time into p2A column vector of x 1;
step 1.3: repeating the step 1.2 according to the window sliding times q until the traversal is completed, and forming a new matrix, namely the infrared block image, by all the column vectors
Figure GDA0003060129010000021
Preferably, the step 2 comprises the steps of:
step 2.1: inputting an infrared block image
Figure GDA0003060129010000022
Step 2.2: weighted l in combination with rank minimization metric1Norm and l2,1Norm, constructing an objective function;
step 2.3: infrared block image
Figure GDA0003060129010000031
After the target function is input, the method of augmented Lagrange multiplier is adopted to solve the target function output background block image
Figure GDA0003060129010000032
And target block image
Figure GDA0003060129010000033
Preferably, said step 2.2 comprises the steps of:
step 2.2.1: suppose that an image X belongs to Rm×nThe method comprises the following steps of constructing an objective function to separate a low-rank component A and a sparse component E, wherein the objective function comprises the following formula:
min||A||γ+λ||E||w,1+β||N||2,1
s.t.X＝A+E+N
wherein λ and β represent balance coefficients, | | · | | non-calculationγNamely, it is
Figure GDA0003060129010000034
Representing a pseudo-norm, | · | | non-conducting phosphorw,1Namely, it is
Figure GDA0003060129010000035
Representing weighted l1Norm, | · | luminance2,1Namely, it is
Figure GDA0003060129010000036
Represents l2,1A norm;
step 2.2.2: and optimizing the objective function by adopting an augmented Lagrange equation, wherein the augmented Lagrange equation is as follows:
Figure GDA0003060129010000037
wherein Y represents a Lagrange multiplier, mu represents a nonnegative penalty factor, w represents a weight coefficient matrix, and w ═ 1 ∈ Rm ×n，<·>Represents inner product operation, | · | non-conducting phosphorFNamely, it is
Figure GDA0003060129010000038
Representing the Frobenius norm.
Preferably, said step 2.3 comprises the steps of:
step 2.3.1: image of infrared block
Figure GDA0003060129010000039
Inputting an objective function, namely a known image X;
step 2.3.2: iterative solution of target function based on augmented Lagrange equation and difference convex programming method to obtain low-rank matrix, namely background block image
Figure GDA00030601290100000310
And sparse matrices, i.e. target block images
Figure GDA00030601290100000311
Preferably, said step 2.3.2 comprises the steps of:
step 2.3.2.1: initializing parameters of an augmented Lagrange equation, and enabling the iteration number k to be 0 and the maximum iteration number to be maxk;
step 2.3.2.2: fix A, N, Y, update Ek+1The calculation formula is as follows:
Figure GDA00030601290100000312
wherein S isτ(. represents a soft threshold shrink operator, Sτ(·)＝sgn(x)max(|x|-τ,0)；
Step 2.3.2.3: fixed E, N, Y, update A with the differential convex programming methodk+1The calculation formula is as follows:
Figure GDA0003060129010000041
let M be X-Ek+1-Nk+Yk/μkThe following can be obtained by using the differential convex programming method:
Ak+1＝Udiag{σ*}VT,
wherein U and V are left and right singular matrices of M, diag denotes a diagonal matrix,
Figure GDA0003060129010000042
Figure GDA0003060129010000043
denotes that f (-) is at σkGradient of (a)MRepresenting the singular value of M;
step 2.3.2.4: fix A, E, Y, update Nk+1The following were used:
Figure GDA0003060129010000044
let Q be X-Ak+1-Ek+1+Yk/μkThen, there are:
Figure GDA0003060129010000045
wherein [ N ]k+1]:,iRepresents Nk+1The ith column;
step 2.3.2.5: fix A, E, N, update Yk+1The following were used:
Yk+1＝Yk+μ(X-Ak+1-Ek+1-Nk+1)；
step 2.3.2.6: update the weight wk+1：
Figure GDA0003060129010000046
Wherein C and εTRepresents the update constant, C ≧ 1, εT＞0；
Step 2.3.2.7: updating muk+1＝ρμk
Wherein rho represents a growth coefficient, and rho is more than 1;
step 2.3.2.8: the number of iterations k is k + 1;
step 2.3.2.9: judging whether k is larger than maxk, if so, stopping iteration, and turning to step 2.3.2.10; if not, judging
Figure GDA0003060129010000051
If yes, stopping iteration, and going to step 2.3.2.10, and if not, going to step 2.3.2.2, wherein epsilon represents a loop termination threshold;
step 2.3.2.10: obtaining an optimal solution A*，E*，N*Outputting the final background block image
Figure GDA0003060129010000052
And target block image
Figure GDA0003060129010000053
In summary, due to the adoption of the technical scheme, the invention has the beneficial effects that:
1. the invention utilizes a non-convex rank approximation minimization method, restrains the low-rank component of the infrared block image by introducing a non-convex gamma norm, and introduces weighted l1Norm improvement for sparse component approximation2,1The norm is a structured sparse norm, so that the suppression of sparse high-frequency components (such as strong edges) is enhanced, and the optimal value of an objective function is solved by using an augmented Lagrange multiplier method and a differential convex programming method; solves the problem of the prior IPI method thatFactors such as strong edges, partial noise, false alarm sources and the like have sparse characteristics, so that the problem of low detection accuracy of the infrared weak and small target is solved, and the effect of inhibiting the influence of sparse characteristics of other factors on the detection accuracy is achieved;
2. the invention converts the infrared weak and small target detection problem into the solving problem of the target function, can self-adaptively separate the target and the background without calculating any characteristics, can efficiently and accurately detect the weak and small target, and simultaneously has the gamma norm, l1Norm sum l2,1The combination of the norm and the norm improves the anti-noise capability of the algorithm, and even if certain noise exists, the algorithm can still accurately detect the target, thereby further improving the accuracy of infrared weak and small target detection;
3. the invention reduces the times of singular value decomposition, has faster convergence speed, reduces the operation time of the algorithm and improves the real-time property.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the embodiments will be briefly described below, it should be understood that the following drawings only illustrate some embodiments of the present invention and therefore should not be considered as limiting the scope, and for those skilled in the art, other related drawings can be obtained according to the drawings without inventive efforts.
FIG. 1 is a flow chart of the present invention;
FIG. 2 is an infrared image of the present invention containing a small target;
FIG. 3 is a block image constructed from FIG. 2 according to the present invention;
FIG. 4 is a diagram of the background block image and the target block image separated from FIG. 3 according to the present invention;
FIG. 5 is a diagram of the target image and the background image recovered from FIG. 4 according to the present invention;
FIG. 6 is a gray scale three-dimensional distribution diagram of the target image of FIGS. 2 and 5 according to the present invention;
FIG. 7 is a diagram illustrating the adaptive threshold segmentation of the target image of FIG. 5 to obtain a detection result according to the present invention;
FIG. 8 is a graph of the result of the IPI method versus the FIG. 2 test and a three-dimensional gray scale;
FIG. 9 is a graph of the NIPPS method versus the test results of FIG. 2 and a three-dimensional gray scale;
FIG. 10 is a graph of the detection result of FIG. 2 by the Top-Hat method and a three-dimensional gray scale;
FIG. 11 is a diagram of the result of the detection of FIG. 2 by the MPCM method and a three-dimensional gray scale map;
FIG. 12 is a graph comparing the effects of the present invention;
fig. 13 is a sequence diagram of a comparative use of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the detailed description and specific examples, while indicating the preferred embodiment of the invention, are intended for purposes of illustration only and are not intended to limit the scope of the invention. The components of embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations.
Thus, the following detailed description of the embodiments of the present invention, presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments of the present invention without making any creative effort, shall fall within the protection scope of the present invention.
It is noted that relational terms such as "first" and "second," and the like, may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other identical elements in a process, method, article, or apparatus that comprises the element.
The technical problem is as follows: the problem that the existing IPI method has low accuracy of infrared weak and small target detection due to the fact that factors such as strong edges, partial noise, false alarm sources and the like have sparse characteristics is solved;
the technical means is as follows:
an infrared weak and small target detection method based on non-convex rank approximation minimization comprises the following steps:
step 1: traversing the original image by adopting a sliding window to construct an infrared block image;
step 2: based on non-convex rank approximation minimization thought, gamma norm combined with weighted l1Norm and l2,1The norm jointly constructs a target function, and after the infrared block images are input into the target function, the target function is solved by utilizing an augmented Lagrange multiplier method and a differential convex programming method to obtain a background block image and a target block image;
and step 3: reconstructing a background image and a target image according to the background block image and the target block image;
and 4, step 4: and performing threshold segmentation on the target image to determine the position of the target, and outputting a target detection result.
The step 1 comprises the following steps:
step 1.1: obtaining the infrared image D epsilon R to be processedm×n；
Step 1.2: traversing an original image D according to the step length s by adopting a sliding window W with the size of p multiplied by p, and converting a matrix vector with the size of p multiplied by p in the sliding window W each time into p2A column vector of x 1;
step 1.3: repeating the step 1.2 according to the window sliding times q until the traversal is completed, and forming a new matrix, namely the infrared block image, by all the column vectors
Figure GDA0003060129010000071
The step 2 comprises the following steps:
step 2.1: inputting an infrared block image
Figure GDA0003060129010000072
Step 2.2: weighted l in combination with rank minimization metric1Norm and l2,1Norm, constructing an objective function;
step 2.3: infrared block image
Figure GDA0003060129010000073
After the target function is input, the method of augmented Lagrange multiplier is adopted to solve the target function output background block image
Figure GDA0003060129010000074
And target block image
Figure GDA0003060129010000075
Step 2.2 comprises the following steps:
step 2.2.1: suppose that an image X belongs to Rm×nThe method comprises the following steps of constructing an objective function to separate a low-rank component A and a sparse component E, wherein the objective function comprises the following formula:
min||A||γ+λ||E||w,1+β||N||2,1
s.t.X＝A+E+N
wherein λ and β represent balance coefficients, | | · | | non-calculationγNamely, it is
Figure GDA0003060129010000076
Representing a pseudo-norm, | · | | non-conducting phosphorw,1Namely, it is
Figure GDA0003060129010000077
Representing weighted l1Norm, | · | luminance2,1Namely, it is
Figure GDA0003060129010000078
Represents l2,1A norm;
step 2.2.2: and optimizing the objective function by adopting an augmented Lagrange equation, wherein the augmented Lagrange equation is as follows:
Figure GDA0003060129010000079
wherein Y represents a Lagrange multiplier, mu represents a nonnegative penalty factor, w represents a weight coefficient matrix, and w ═ 1 ∈ Rm ×n，<·>Represents inner product operation, | · | non-conducting phosphorFNamely, it is
Figure GDA0003060129010000081
Representing the Frobenius norm.
Step 2.3 comprises the following steps:
step 2.3.1: image of infrared block
Figure GDA0003060129010000082
Inputting an objective function, namely a known image X;
step 2.3.2: iterative solution of target function based on augmented Lagrange equation and difference convex programming method to obtain low-rank matrix, namely background block image
Figure GDA0003060129010000083
And sparse matrices, i.e. target block images
Figure GDA0003060129010000084
Step 2.3.2 comprises the following steps:
step 2.3.2.1: initializing parameters of an augmented Lagrange equation, and enabling the iteration number k to be 0 and the maximum iteration number to be maxk;
step 2.3.2.2: fix A, N, Y, update Ek+1The calculation formula is as follows:
Figure GDA0003060129010000085
wherein S isτ(. represents a soft threshold shrink operator, Sτ(·)＝sgn(x)max(|x|-τ,0)；
Step 2.3.2.3: fixed E, N, Y, update A with the differential convex programming methodk+1The calculation formula is as follows:
Figure GDA0003060129010000086
let M be X-Ek+1-Nk+Yk/μkThe following can be obtained by using the differential convex programming method:
Ak+1＝Udiag{σ*}VT,
wherein U and V are left and right singular matrices of M, diag denotes a diagonal matrix,
Figure GDA0003060129010000087
Figure GDA0003060129010000088
denotes that f (-) is at σkGradient of (a)MRepresenting the singular value of M;
step 2.3.2.4: fix A, E, Y, update Nk+1The following were used:
Figure GDA0003060129010000089
let Q be X-Ak+1-Ek+1+Yk/μkThen, there are:
Figure GDA0003060129010000091
wherein [ N ]k+1]:,iRepresents Nk+1The ith column;
step 2.3.2.5: fix A, E, N, update Yk+1The following were used:
Yk+1＝Yk+μ(X-Ak+1-Ek+1-Nk+1)；
step 2.3.2.6: update the weight wk+1：
Figure GDA0003060129010000092
Wherein C and εTRepresents the update constant, C ≧ 1, εT＞0；
Step 2.3.2.7: updating muk+1＝ρμk
Wherein rho represents a growth coefficient, and rho is more than 1;
step 2.3.2.8: the number of iterations k is k + 1;
step 2.3.2.9: judging whether k is larger than maxk, if so, stopping iteration, and turning to step 2.3.2.10; if not, judging | D0-Ak+1-Ek+1-Nk+1||2/||D0||2If yes, stopping iteration, and going to step 2.3.2.10, if not, going to step 2.3.2.2, wherein epsilon represents a loop termination threshold value;
step 2.3.2.10: obtaining an optimal solution A*，E*，N*Outputting the final background block image
Figure GDA0003060129010000093
And target block image
Figure GDA0003060129010000094
The technical effects are as follows: the invention utilizes a non-convex rank approximation minimization method, restrains the low-rank component of the infrared block image by introducing a non-convex gamma norm, and introduces weighted l1Norm improvement for sparse component approximation2,1The norm is a structured sparse norm, so that the suppression of sparse high-frequency components (such as strong edges) is enhanced, and the optimal value of an objective function is solved by using an augmented Lagrange multiplier method and a differential convex programming method; the problem that the detection accuracy of the infrared weak and small target is low due to the fact that factors such as strong edges, partial noise and a virtual alarm source are sparse in the existing IPI method is solved, and the effect of inhibiting the influence of the sparse characteristics of other factors on the detection accuracy is achieved.
The features and properties of the present invention are described in further detail below with reference to examples.
Example 1
As shown in fig. 1 to 13, a method for detecting an infrared weak and small target based on non-convex rank approach minimization includes the following steps:
step 1: traversing the original image by adopting a sliding window to construct an infrared block image;
step 2: based on non-convex rank approximation minimization thought, gamma norm combined with weighted l1Norm and l2,1The norm jointly constructs a target function, and after the infrared block images are input into the target function, the target function is solved by utilizing an augmented Lagrange multiplier method and a differential convex programming method to obtain a background block image and a target block image;
and step 3: reconstructing a background image and a target image according to the background block image and the target block image;
and 4, step 4: and performing self-adaptive threshold segmentation on the target image to determine the position of the target and outputting a target detection result.
The step 1 comprises the following steps:
step 1.1: obtaining the infrared image D epsilon R to be processedm×nSize 240 × 320;
step 1.2: traversing an original image D according to the step length of 10 by adopting a sliding window W with the size of 50 multiplied by 50, and converting a matrix vector with the size of 50 multiplied by 50 in the sliding window W each time into a column vector with the size of 2500 multiplied by 1;
step 1.3: repeating the step 1.2 according to the window sliding times 560 until the traversal is completed, and forming a new matrix, namely 2500 x 560 infrared block images by all the column vectors
Figure GDA0003060129010000101
The step 2 comprises the following steps:
step 2.1: input 2500 x 560 infrared block image
Figure GDA0003060129010000102
Step (ii) of2.2: weighted l in combination with rank minimization metric1Norm and l2,1Norm, constructing an objective function;
step 2.3: infrared block image
Figure GDA0003060129010000103
After the target function is input, the method of augmented Lagrange multiplier is adopted to solve the target function output background block image
Figure GDA0003060129010000104
And target block image
Figure GDA0003060129010000105
Step 2.2 comprises the following steps:
step 2.2.1: suppose that an image X belongs to Rm×nThe method comprises the following steps of constructing an objective function to separate a low-rank component A and a sparse component E, wherein the objective function comprises the following formula:
min||A||γ+λ||E||w,1+β||N||2,1
s.t.X＝A+E+N
wherein, λ and β represent equilibrium coefficients,
Figure GDA0003060129010000106
β＝1.8，γ＝0.002，||·||γnamely, it is
Figure GDA0003060129010000107
Representing a pseudo-norm, | · | | non-conducting phosphorw,1Namely, it is
Figure GDA0003060129010000108
Representing weighted l1Norm, | · | luminance2,1Namely, it is
Figure GDA0003060129010000111
Represents l2,1A norm;
step 2.2.2: and optimizing the objective function by adopting an augmented Lagrange equation, wherein the augmented Lagrange equation is as follows:
Figure GDA0003060129010000112
wherein Y represents a lagrange multiplier, μ represents a non-negative penalty factor, μ is 90, w represents a weight coefficient matrix, w is 1 ∈ Rm×n，<·>Represents inner product operation, | · | non-conducting phosphorFNamely, it is
Figure GDA0003060129010000113
Representing the Frobenius norm.
Step 2.3 comprises the following steps:
step 2.3.1: image of infrared block
Figure GDA0003060129010000114
Inputting an objective function, namely a known image X;
step 2.3.2: iterative solution of target function based on augmented Lagrange equation and difference convex programming method to obtain low-rank matrix, namely background block image
Figure GDA0003060129010000115
And sparse matrices, i.e. target block images
Figure GDA0003060129010000116
Step 2.3.2 comprises the following steps:
step 2.3.2.1: initializing parameters of the augmented Lagrange equation, setting the iteration number k to be 0, setting the maximum iteration number to be maxk, setting A, E, N and Y to be 0,
Figure GDA0003060129010000117
w＝1，μ＝90；
step 2.3.2.2: fix A, N, Y, update Ek+1The calculation formula is as follows:
Figure GDA0003060129010000118
wherein S isτ(. represents a soft threshold shrink operator, Sτ(·)＝sgn(x)max(|x|-τ,0)；
Step 2.3.2.3: fixed E, N, Y, update A with the differential convex programming methodk+1The calculation formula is as follows:
Figure GDA0003060129010000119
let M be X-Ek+1-Nk+Yk/μkThe following can be obtained by using the differential convex programming method:
Ak+1＝Udiag{σ*}VT,
wherein U and V are left and right singular matrices of M, diag denotes a diagonal matrix,
Figure GDA00030601290100001110
Figure GDA0003060129010000121
denotes that f (-) is at σkGradient of (a)MRepresenting the singular value of M;
step 2.3.2.4: fix A, E, Y, update Nk+1The following were used:
Figure GDA0003060129010000122
let Q be X-Ak+1-Ek+1+Yk/μkThen, there are:
Figure GDA0003060129010000123
wherein [ N ]k+1]:,iRepresents Nk+1The ith column;
step 2.3.2.5: fix A, E, N, update Yk+1The following were used:
Yk+1＝Yk+μ(X-Ak+1-Ek+1-Nk+1)；
step 2.3.2.6: update the weight wk+1：
Figure GDA0003060129010000124
Wherein C and εTDenotes the update constant, C ≧ 1, C ═ 1.2, εT＞0，εT＝0.4；
Step 2.3.2.7: updating muk+1＝ρμk，
Wherein ρ represents a growth coefficient, ρ > 1, and ρ is 1.1;
step 2.3.2.8: the number of iterations k is k + 1;
step 2.3.2.9: judging whether k is larger than maxk, if so, stopping iteration, and turning to step 2.3.2.10; if not, judging | D0-Ak+1-Ek+1-Nk+1||2/||D0||2If ≦ ε is true, stop iteration, go to step 2.3.2.10, if false, go to step 2.3.2.2, where ε represents the threshold for loop termination, ε is 10-7；
Step 2.3.2.10: obtaining an optimal solution A*，E*，N*Outputting the final background block image
Figure GDA0003060129010000125
And target block image
Figure GDA0003060129010000126
The specific steps of the step 3 are as follows: for input background block image
Figure GDA0003060129010000127
Take out B0Each column in the image is reconstructed into a small matrix with the size of 50 multiplied by 50, and then a background image B epsilon R of 240 multiplied by 320 is sequentially formed according to the sequencem×nFor the position contained by a plurality of small blocks, the gray value of the position is determined by adopting a median filtering mode, and the target image T is formed by adopting the same modeT0Reconstructing;
the specific steps of the step 4 are as follows: and performing adaptive threshold segmentation on the target image T, wherein a threshold Th is m + c sigma, m represents the mean value of all gray scales in the target image T, sigma represents the standard deviation of all gray scales in the target image T, c represents a constant between 1 and 10, and the segmentation is completed to obtain a target detection result.
Effect analysis was performed according to the attached figures: FIG. 2 shows an infrared image with a complex background, with a very bright white false alarm source in addition to a small target; FIG. 3 is a block image D constructed from an original image through step 10(ii) a FIG. 4 shows the result of step 2 from step D0Recovered B0And T0(ii) a Fig. 5 is the background B and the target map T reconstructed through step 3; fig. 6 is a three-dimensional gray scale diagram of the original image D and the target image T, and it can be seen that the separated target image suppresses the background well, and the gray scales of the background at the positions other than the small target are 0; FIG. 7 is the final test result; 8-11 are several other methods (IPI, NIPPS, Top-Hat, MPCM in sequence) for detecting the small target in FIG. 2 (for ease of illustration, the result has been binarized), and corresponding three-dimensional distribution of gray scale, it can be seen that the rest four methods do not completely suppress the background, and have different degrees of noise, which will affect the subsequent positioning detection, FIG. 13 is an original diagram of one of the sequences selected for comparison, which has been gray-scale processed, and thus is gray-green; fig. 12 is a comparison of the performance of the present invention with that of the other four methods, and it is obvious that the signal-to-noise ratio gain SCRG and the background suppression factor BSF are the largest, and the target detection accuracy of the present invention is far better than that of the other methods.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.

Claims (6)

1. An infrared weak and small target detection method based on non-convex rank approximation minimization is characterized in that: the method comprises the following steps:
step 1: traversing the original image by adopting a sliding window to construct an infrared block image;
step 2: based on non-convex rank approximation minimization thought, gamma norm combined with weighted l1Norm and l2,1The norm jointly constructs a target function, and after the infrared block images are input into the target function, the target function is solved by utilizing an augmented Lagrange multiplier method and a differential convex programming method to obtain a background block image and a target block image;
and step 3: reconstructing a background image and a target image according to the background block image and the target block image;
and 4, step 4: and performing threshold segmentation on the target image to determine the position of the target, and outputting a target detection result.
2. The infrared weak and small target detection method based on non-convex rank approach minimization as claimed in claim 1, characterized in that: the step 1 comprises the following steps:
step 1.1: obtaining an original image to be processed, namely an infrared image D epsilon Rm×n；
Step 1.2: traversing the infrared image D according to the step length s by adopting a sliding window W with the size of p multiplied by p, and converting a matrix vector with the size of p multiplied by p in the sliding window W each time into p2A column vector of x 1;
step 1.3: repeating the step 1.2 according to the window sliding times q until the traversal is completed, and forming a new matrix, namely the infrared block image, by all the column vectors
Figure FDA0003060128000000011
3. The method for detecting the infrared weak and small target based on the non-convex rank approximation minimization according to claim 1 or 2, characterized in that: the step 2 comprises the following steps:
step 2.1: inputting an infrared block image
Figure FDA0003060128000000012
Step 2.2: weighted l in combination with rank minimization metric1Norm and l2,1Norm, constructing an objective function;
step 2.3: infrared block image
Figure FDA0003060128000000013
After the target function is input, the method of augmented Lagrange multiplier is adopted to solve the target function output background block image
Figure FDA0003060128000000014
And target block image
Figure FDA0003060128000000015
4. The infrared weak and small target detection method based on non-convex rank approximation minimization according to claim 3, characterized in that: the step 2.2 comprises the following steps:
step 2.2.1: suppose that an image X belongs to Rm×nThe method comprises the following steps of constructing an objective function to separate a low-rank component A and a sparse component E, wherein the objective function comprises the following formula:
min||A||γ+λ||E||w,1+β||N||2,1
s.t.X＝A+E+N
wherein λ and β represent balance coefficients, | | · | | non-calculationγNamely, it is
Figure FDA0003060128000000016
Representing a pseudo-norm, | · | | non-conducting phosphorw,1Namely, it is
Figure FDA0003060128000000021
Representing weighted l1Norm, | · | luminance2,1Namely, it is
Figure FDA0003060128000000022
Represents l2,1A norm;
step 2.2.2: and optimizing the objective function by adopting an augmented Lagrange equation, wherein the augmented Lagrange equation is as follows:
Figure FDA0003060128000000023
wherein Y represents a Lagrange multiplier, mu represents a nonnegative penalty factor, w represents a weight coefficient matrix, and w ═ 1 ∈ Rm×n，<Represents inner product operation, | | | non-conducting phosphorFNamely, it is
Figure FDA0003060128000000024
Representing the Frobenius norm.
5. The infrared weak and small target detection method based on non-convex rank approximation minimization according to claim 4, characterized in that: the step 2.3 comprises the following steps:
step 2.3.1: image of infrared block
Figure FDA0003060128000000025
Inputting an objective function, namely a known image X;
step 2.3.2: iterative solution of target function based on augmented Lagrange equation and difference convex programming method to obtain low-rank matrix, namely background block image
Figure FDA0003060128000000026
And sparse matrices, i.e. target block images
Figure FDA0003060128000000027
6. The infrared weak and small target detection method based on non-convex rank approximation minimization according to claim 5, characterized in that: the step 2.3.2 comprises the following steps:
step 2.3.2.1: initializing parameters of an augmented Lagrange equation, and enabling the iteration number k to be 0 and the maximum iteration number to be maxk;
step 2.3.2.2: fix A, N, Y, update Ek+1The calculation formula is as follows:
Figure FDA0003060128000000028
wherein S isτ(. represents a soft threshold shrink operator, Sτ(·)＝sgn(x)max(|x|-τ,0)；
Step 2.3.2.3: fixed E, N, Y, update A with the differential convex programming methodk+1The calculation formula is as follows:
Figure FDA0003060128000000029
let M be X-Ek+1-Nk+Yk/μkThe following can be obtained by using the differential convex programming method:
Ak+1＝Udiag{σ*}VT,
wherein U and V are left and right singular matrices of M, diag denotes a diagonal matrix,
Figure FDA00030601280000000210
Figure FDA0003060128000000031
Figure FDA0003060128000000032
denotes that f (-) is at σkGradient of (a)MRepresenting the singular value of M;
step 2.3.2.4: fix A, E, Y, update Nk+1The following were used:
Figure FDA0003060128000000033
let Q be X-Ak+1-Ek+1+Yk/μkThen, there are:
Figure FDA0003060128000000034
wherein [ N ]k+1]:,iRepresents Nk+1The ith column;
step 2.3.2.5: fix A, E, N, update Yk+1The following were used:
Yk+1＝Yk+μ(X-Ak+1-Ek+1-Nk+1)；
step 2.3.2.6: update the weight wk+1：
Figure FDA0003060128000000035
Wherein C and εTRepresents the update constant, C ≧ 1, εT＞0；
Step 2.3.2.7: updating muk+1＝ρμk
Wherein rho represents a growth coefficient, and rho is more than 1;
step 2.3.2.8: the number of iterations k is k + 1;
step 2.3.2.9: judging whether k is larger than maxk, if so, stopping iteration, and turning to step 2.3.2.10; if not, judging | D0-Ak+1-Ek+1-Nk+1||2/||D0||2If yes, stopping iteration, and going to step 2.3.2.10, if not, going to step 2.3.2.2, wherein epsilon represents a loop termination threshold value;
step 2.3.2.10: obtaining an optimal solution A*，E*，N*Outputting the final background block image
Figure FDA0003060128000000036
And target block image
Figure FDA0003060128000000037
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