CN109325446B - Infrared weak and small target detection method based on weighted truncation nuclear norm - Google Patents

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

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CN109325446B
CN109325446B CN201811097652.6A CN201811097652A CN109325446B CN 109325446 B CN109325446 B CN 109325446B CN 201811097652 A CN201811097652 A CN 201811097652A CN 109325446 B CN109325446 B CN 109325446B
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CN109325446A (en
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彭真明
张兰丹
彭凌冰
张天放
刘雨菡
赵学功
张鹏飞
黄苏琦
王警予
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 dim target detection method based on weighted truncation nuclear norm, which comprises the following steps: obtaining an original infrared image D and constructing an infrared block image
Figure DDA0001805403470000011
In-built infrared block image
Figure DDA0001805403470000013
On the basis of the weighted truncated kernel norm and the weighted l1Norm, constructing an objective function, solving the objective function to obtain an optimal low-rank matrix and an optimal sparse matrix which are respectively corresponding to the background block images
Figure DDA0001805403470000016
And target block image
Figure DDA0001805403470000012
According to the obtained background block image
Figure DDA0001805403470000014
And target block image
Figure DDA0001805403470000015
Reconstructing a background image B and a target image T; and carrying out self-adaptive threshold segmentation on the obtained target image T, determining the position of the target and outputting a detection result. The method converts the infrared small and weak target detection problem into the target function solving problem, separates the target and the background in a self-adaptive manner, applies the weighted truncation kernel norm to the infrared small and weak target detection problem for the first time, and restrains the value of the truncation kernel norm through different weights, so that the small and weak target can be detected efficiently and accurately.

Description

Infrared weak and small target detection method based on weighted truncation nuclear norm
Technical Field
The invention belongs to the technical field of infrared image processing and target detection, and particularly relates to an infrared weak and small target detection method based on a weighted truncation nuclear norm.
Background
The infrared imaging technology has the characteristics of non-contact property, strong capability of capturing details and the like, can realize continuous detection day and night and detect a long-distance target, and is not influenced by obstacles such as smoke, fog and the like, so that the detection and the identification of the target can be realized by utilizing the infrared imaging technology. An Infrared search and track (IRST) system is widely applied to the fields of military, civil use and the like, and has extremely high military value, wherein an Infrared weak and small target detection technology is used as a basic function of the IRST system, and has important significance in Infrared search, Infrared early warning and remote target detection. However, due to the lack of texture and structure information of the target in the infrared band, the influence of long distance, complex background, various clutter and the like, the infrared target is often in a spot or a point shape and even is submerged in the background, so that the detection of the infrared weak and small target is extremely difficult, and the infrared weak and small target detection algorithm with high accuracy, high positioning accuracy and high robustness is designed, so that the effectiveness of an infrared target detection and tracking system can be facilitated.
The infrared weak and small target detection technology can be divided into two main categories on the whole: the technology for detecting the weak and small targets based on a single frame and multiple frames, however, the technology for detecting the weak and small targets based on the multiple frames needs to combine multiple frames to capture the motion trail of the target and eliminate the interference of noise, so that a large amount of calculation and storage are needed, the requirement on hardware is high, and the application in practical engineering is very little. Currently, the commonly used detection methods based on a single frame can be roughly classified into the following three categories:
(1) and (4) 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 (Max-Mean) filtering, maximum Mean (Max-Mean) filtering, Top-Hat (Top-Hat) transformation, two-dimensional least Mean square (TDLMS) filtering, etc., all fall into the category of background suppression. Although this type of method is simple to implement, the background suppression method is very susceptible to noise clutter since the noise does not conform to the assumption of consistency, and thus the effect is very poor for most infrared images with low signal-to-noise ratio;
(2) visual saliency. The Human Visual System (HVS) involves at least three mechanisms, contrast, Visual attention and eye movement, and this class of methods involves at most the contrast mechanism, i.e. assuming that the target is the most prominent object in the infrared image. For example, a difference of gaussian filter (DoG) calculates a saliency map using two different gaussian filters, and detects and identifies a target. The local contrast-based method (LCM) utilizes the characteristic 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 can highlight the target, inhibit the background and achieve the purpose of detection by calculating a local contrast map. Thereafter, many new methods are derived from DoG and LCM, and more features such as direction, entropy, etc. are introduced. When the infrared image conforms to the assumption of visual saliency, the method can obtain excellent effect, but in an actual application scene, the assumption is difficult to meet, the accuracy rate is low, and the false detection problem is difficult to overcome when a false alarm source with saliency exists;
(3) and separating the 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. Under the large category, the method can be subdivided into a method based on an over-complete dictionary and low-rank representation and a method based on low-rank background and sparse target restoration. Methods based on the overcomplete dictionary and the low-rank representation (including low-rank representation (LRR) based methods, low-rank and sparse representation (LRSR) based detection methods, and the like) need to construct overcomplete dictionaries 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. The method based on low-rank background and sparse target restoration can obtain a low-rank original block Image by means of a block-Image Model (PIM), and then recovers the background and the target Image by optimizing an objective function by means of the characteristic of target sparsity to finally obtain a detection result. The superiority of the method is verified by the emerging of a plurality of methods. However, strong edges, partial noise and false alarm sources are also sparse, and therefore, the detection accuracy is reduced. The invention provides an infrared small target detection method based on a weighted truncation nuclear norm on the research direction of improving the detection accuracy and the high efficiency based on a low-rank background and sparse target restoration method.
Disclosure of Invention
The invention aims to: the method solves the problems that in the prior art, under the conditions of complex infrared background, clutter interference, low signal-to-noise ratio and low contrast, an infrared dim target is difficult to be accurately detected, the detection accuracy is low and the efficiency is not high enough, and provides the infrared dim target detection method based on the weighted truncation nuclear norm.
The technical scheme adopted by the invention is as follows:
a method for detecting infrared weak and small targets based on weighted truncation nuclear norms comprises the following steps:
step 1, obtaining an original infrared image D and constructing an infrared block image
Figure BDA0001805403450000021
Step 2, constructing an infrared block image
Figure BDA0001805403450000022
On the basis of the weighted truncated kernel norm and the weighted l1Norm, constructing an objective function:
Figure BDA0001805403450000023
wherein λ and β represent equilibrium coefficients, L represents a low-rank component, S represents a sparse component, N represents a noise component, | · |. Yw，rRepresenting weighted truncated nuclear norms, i.e.
Figure BDA0001805403450000024
σi(L) denotes the ith singular value of L, r represents the rank of the matrix, w ═ w1，w2，...，wmin(m，n)]TRepresenting non-negative weighting coefficients, as used herein the element w of w1，w2，...，wrAre all 1, | · | | luminanceW，1Representing weighted l1Norm, i.e.
Figure BDA0001805403450000031
W∈Rm×nRepresenting a non-negative weighting coefficient, | · | | non-woven phosphorlRepresents any norm and can be changed according to actual needs;
solving the objective function to obtain an optimal low-rank matrix and an optimal sparse matrix which respectively correspond to the background block image
Figure BDA0001805403450000032
And target block image
Figure BDA0001805403450000033
Step 3, obtaining the background block image according to the step 2
Figure BDA0001805403450000034
And target block image
Figure BDA0001805403450000035
Reconstructing a background image B and a target image T;
and 4, performing self-adaptive threshold segmentation on the target image T obtained in the step 3, determining the position of the target, and outputting a detection result.
Further, constructing an infrared block image in the step 1
Figure BDA0001805403450000036
The method specifically comprises the following steps: traversing the original image D by the step length of s from left to right and from top to bottom by adopting a sliding window with the size of k multiplied by k, and quantizing the matrix vector with the size of k multiplied by k obtained in each sliding window into k2The X1 column vector, after traversing, all the obtained column vectors form a new matrix, and the infrared block image is obtained
Figure BDA0001805403450000037
Where t is the number of window slides.
Further, the step 2 further comprises the steps of carrying out Lagrange equation conversion on the target function, solving according to the optimized equation to obtain an optimal low-rank matrix and an optimal sparse matrix, and respectively and correspondingly obtaining the background block image
Figure BDA0001805403450000038
And target block image
Figure BDA0001805403450000039
The method comprises the following specific steps:
step 2.1, the augmented Lagrange equation of the constructed objective function is obtained as follows:
Figure BDA00018054034500000310
wherein Y represents a Lagrangian multiplier, μ represents a non-negative penalty factor,<·>representing inner product operations，||·||FRepresenting the Frobenius norm, i.e.
Figure BDA00018054034500000311
Step 2.2, in the formula of step 2.1,
Figure BDA00018054034500000312
A∈Rr×m，B∈Rn ×ri is a unit matrix, | L | | non-woven phosphorw，*Representing weighted nuclear norms of the matrix, i.e.
Figure BDA00018054034500000313
σi(L) denotes the ith singular value of L, r represents the rank of the matrix, w ═ w1，w2，...，wmin(m，n)]TRepresenting non-negative weight values, as used herein the element w of w1，w2，...，wrAll are 1, tr represents the trace of the matrix, and the augmented lagrange equation obtained in step 2.1 is rewritten as follows:
Figure BDA0001805403450000041
step 2.3, image of infrared block
Figure BDA0001805403450000042
Inputting the Lagrange equation obtained in the step 2.2, solving the Lagrange equation, and outputting a background block image
Figure BDA0001805403450000043
And target block image
Figure BDA0001805403450000044
Further, the lagrangian equation solved in the step 2.3 adopts an overlapping direction multiplier method, and the specific solving process is as follows:
step 2.3.1, initialize L, S, N, Y to 0, the iteration number k is 0, the maximum iteration number is maxk, and the initial iteration number isThe initialization mu is more than 0, rho is more than 1,
Figure BDA0001805403450000045
β＞0，w＝1，W＝1×1T，εB≥1，εT＞0；
step 2.3.2, fix L, N, Y, update Sk+1The following were used:
Figure BDA0001805403450000046
wherein S isτ(x) Is a soft threshold shrink operator, Sτ(x)＝sgn(x)max(|x|-τ，0)；
Step 2.3.3, on LkSingular value decomposition is carried out: [ U ]k，∑k，Vk]＝svd(Lk) To obtain
Figure BDA0001805403450000047
Figure BDA0001805403450000048
Thereby obtaining
Figure BDA0001805403450000049
Step 2.3.4, let w1＝w2＝...＝w r1, let tem be X-Sk+1-Nk+(Yk-(Ak)TBkMu), singular value decomposition of tem, i.e. [ U ]t，∑t，Vt]＝svd(tem)；
Step 2.3.5, fix S, N, Y, update Lk+1The following were used:
Figure BDA00018054034500000410
wherein diag denotes that the diagonal is max (Σ)ii-wiA diagonal matrix of/[ mu ]);
step 2.3.6, fix L, S, Y, update Nk+1The following were used:
Figure BDA0001805403450000051
step 2.3.7, fix L, S, N, update Yk+1The following were used:
Yk+1＝Yk+μ(X-Lk+1-Sk+1-Nk+1)；
step 2.3.8, update the weight wk+1，Wk+1：
Figure BDA0001805403450000052
Figure BDA0001805403450000053
Wherein epsilonB，εTRepresents a positive constant;
step 2.3.9, updating the iteration number k to k + 1;
step 2.3.10, judging whether k is larger than maxk, if so, stopping iteration, and turning to step (2.3.11); if not, judging
Figure BDA0001805403450000054
If so, stopping iteration and going to step (2.3.11), otherwise, going to step (2.3.2);
step 2.3.11, outputting the final optimal low rank matrix L*And a sparse matrix S*Respectively correspond to background block images
Figure BDA0001805403450000055
And target block image
Figure BDA0001805403450000056
Further, the step 3 is based on the background block image
Figure BDA0001805403450000057
To know
Figure BDA0001805403450000058
In a manner opposite to the method for constructing the infrared block image in the step 1
Figure BDA0001805403450000059
And
Figure BDA00018054034500000510
reconstructing the image into small blocks of images, sequentially reconstructing a background image B according to the sequence, and determining the gray value of the position by adopting a median filtering mode for the overlapped position in each small block.
Further, in step 4, when the adaptive threshold segmentation is performed on the target image T, the threshold Th is m + c σ, where m represents a mean value of all the grays in T, σ represents a standard deviation of all the grays in T, and c represents a constant between 1 and 15.
In summary, due to the adoption of the technical scheme, the invention has the beneficial effects that:
1. in the invention, the infrared small and weak target detection problem is converted into the solving problem of the target function, the target and the background are separated in a self-adaptive manner, the weighted truncation nuclear norm is applied to the infrared small and weak target detection problem for the first time, and the value of the truncation nuclear norm is constrained by different weights, so that the small and weak target can be detected efficiently and accurately;
2. in the invention, the optimal value of the objective function is solved by adopting the multiplier method in the overlapping direction, so that the method is more efficient;
3. in the invention, the target function introduces noise components, the influence of background clutter, strong edges and the like on the detection of weak and small targets is fully considered, the accuracy is improved, and the robustness of the algorithm is enhanced.
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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 method of the present invention;
FIG. 2 is an exemplary infrared image of a target containing small and weak objects in accordance with the present invention;
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 diagram illustrating the detection result obtained by adaptive threshold segmentation of the target image in FIG. 5 according to 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.
In this context, the matrix is represented by capital letters such as X, and the elements thereof are subscripted by XijWith prime symbol indicating optimum, e.g. L*。
A method for detecting infrared weak and small targets based on weighted truncated nuclear norm, as shown in fig. 1, includes the following steps:
step 1: obtaining an original infrared image D epsilon R to be processedm×nAs shown in fig. 2.
Step 2: traversing the original infrared image D by the step length of s from left to right and from top to bottom by adopting a sliding window with the size of k multiplied by k, and quantizing the matrix vector with the size of k multiplied by k obtained in each sliding window into k2The X1 column vector, after traversing, all the obtained column vectors form a new matrix, and the infrared block image is obtained
Figure BDA0001805403450000071
Where t is the number of window slides and the infrared block image is shown in fig. 3.
And step 3: infrared block image constructed at step 2
Figure BDA0001805403450000072
Based on combining the weighted truncated nuclear norm and the weighted l1Norm, constructing an objective function, solving an optimal low-rank matrix and an optimal sparse matrix according to the objective function, and respectively corresponding to the background block images
Figure BDA0001805403450000073
And target block image
Figure BDA0001805403450000074
As shown in fig. 4, the specific steps are as follows:
step 3.1, inputting the infrared block image
Figure BDA0001805403450000075
Step 3.2, combine weighted truncated Kernel norm and weighted l1Norm, constructing an objective function, and specifically comprising the following steps:
step 3.2.1, suppose image X ∈ Rm×nThe low rank component L, the sparse component S, and the noise component N form a low rank component L and a sparse component S, and in order to recover the low rank component L and the sparse component S, an objective function may be constructed as follows:
Figure BDA0001805403450000076
wherein λ and β represent equilibrium coefficients, L represents a low-rank component, S represents a sparse component, N represents a noise component, | · |. Yw，rRepresenting weighted truncated nuclear norms, i.e.
Figure BDA0001805403450000077
σi(L) denotes the ith singular value of L, r represents the rank of the matrix, w ═ w1，w2，...，wmin(m，n)]TRepresenting non-negative weighting coefficients, as used herein the element w of w1，w2，...，wrAre all 1, | · | | luminanceW，1Representing weighted l1Norm, i.e.
Figure BDA0001805403450000078
W∈Rm×nRepresenting a non-negative weighting coefficient which is,
Figure BDA0001805403450000079
representing any norm, which can be changed according to actual needs, since in most cases the noise, especially strong edge components, is sparse for the whole image, it is used herel1N is constrained by a norm, i.e., l is 1;
step 3.2.2, the augmented Lagrange equation of the constructed objective function is obtained as follows:
Figure BDA00018054034500000710
wherein Y represents a Lagrangian multiplier, μ represents a non-negative penalty factor,<·>represents inner product operation, | · | non-conducting phosphorFRepresenting the Frobenius norm, i.e.
Figure BDA0001805403450000081
Step 3.2.3, in the equation of step 3.2.2,
Figure BDA0001805403450000082
A∈Rr×m，B∈Rn×ri is a unit matrix, | L | | non-woven phosphorw，*Representing weighted nuclear norms of the matrix, i.e.
Figure BDA0001805403450000083
σi(L) denotes the ith singular value of L, r represents the rank of the matrix, w ═ w1，w2，...，wmin(m，n)]TRepresenting non-negative weight values, as used herein the element w of w1，w2，...，wrAll are 1, tr represents the trace of the matrix, and the augmented lagrange equation obtained in step 2.1 is rewritten as follows:
Figure BDA0001805403450000084
step 3.3, image of infrared block
Figure BDA0001805403450000085
Inputting the Lagrange equation obtained in the step 3.2.3, solving the Lagrange equation by adopting a cross-over direction multiplier method, and outputting a background block image
Figure BDA0001805403450000086
And target block image
Figure BDA0001805403450000087
The specific solving process is as follows:
step 3.3.1, initializing L, S, N, Y to 0, the number of iterations k to 0, the maximum number of iterations maxk, μ > 0 for initialization, ρ > 1,
Figure BDA0001805403450000088
β＞0，w＝1，W＝1×1T，εB≥1，εT＞0，ρ，εB，εTall are variables used by the algorithm when the equation is solved;
step 3.3.2, fix L, N, Y, update Sk+1The following were used:
Figure BDA0001805403450000089
wherein S isτ(x) Is a soft threshold shrink operator, Sτ(x)＝sgn(x)max(|x|-τ，0)；
Step 3.3.3, to LkSingular value decomposition is carried out: [ U ]k，∑k，Vk]＝svd(Lk) To obtain
Figure BDA00018054034500000810
Figure BDA00018054034500000811
Thereby obtaining
Figure BDA00018054034500000812
Step 3.3.4, let w1＝w2＝...＝w r1, let tem be X-Sk+1-Nk+(Yk-(Ak)TBkMu), singular value decomposition of tem, i.e. [ U ]t，∑t，Vt]＝svd(tem)；
Step 3.3.5, fix S, N, Y, update Lk+1The following were used:
Figure BDA0001805403450000091
wherein diag denotes that the diagonal is max (Σ)ii-wiA diagonal matrix of/[ mu ]);
step 3.3.6, fix L, S, Y, update Nk+1The following were used:
Figure BDA0001805403450000092
step 3.3.7, fix L, S, N, update Yk+1The following were used:
Yk+1＝Yk+μ(X-Lk+1-Sk+1-Nk+1)；
step 3.3.8, update the weight wk+1，Wk+1：
Figure BDA0001805403450000093
Figure BDA0001805403450000094
Wherein epsilonB，εTRepresents a positive constant;
step 3.3.9, updating the iteration number k to k + 1;
step 3.3.10, judging whether k is larger than maxk, if so, stopping iteration, and turning to step (2.3.11); if not, judging
Figure BDA0001805403450000095
If so, stopping iteration and going to step (2.3.11), otherwise, going to step (2.3.2);
step 3.3.11, outputting the final optimal low rank matrix L*And a sparse matrix S*Respectively correspond to background block images
Figure BDA0001805403450000096
And target block image
Figure BDA0001805403450000097
And 4, step 4: obtaining the background block image according to the step 3
Figure BDA0001805403450000098
And target block image
Figure BDA0001805403450000099
Reconstructing the background image B e Rm×nAnd the target image T epsilon Rm×nAs shown in fig. 5, the specific steps are as follows: for input background block image
Figure BDA00018054034500000910
In a reverse manner to step 2, the
Figure BDA00018054034500000911
The T column vectors in the image are reconstructed into T small block images with the size of k multiplied by k, then the background image B is sequentially reconstructed according to the sequence, the gray value of the position is determined by adopting a median filtering mode for the overlapped position in each small block, and the target image T adopts the same mode
Figure BDA0001805403450000101
And (6) reconstructing.
And 5: and (3) performing adaptive threshold segmentation on the target image T obtained in the step (4), determining the position of the target, and outputting a detection result, wherein when the target image T is subjected to the adaptive threshold segmentation, as shown in FIG. 6, a threshold value Th is m + c σ, wherein m represents the mean value of all gray scales in T, σ represents the standard deviation of all gray scales in T, and c represents a constant between 1 and 15.
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. A method for detecting infrared weak and small targets based on weighted truncation nuclear norms is characterized by comprising the following steps: the method comprises the following steps:
step 1, obtaining an original infrared image D and constructing an infrared block image
Figure FDA0001805403440000011
Step 2, constructing an infrared block image
Figure FDA0001805403440000012
On the basis of the weighted truncated kernel norm and the weighted l1Norm, constructing an objective function:
Figure FDA0001805403440000013
wherein λ and β represent equilibrium coefficients, L represents a low-rank component, S represents a sparse component, N represents a noise component, | · |. Yw，rRepresenting weighted truncated nuclear norms, i.e.
Figure FDA0001805403440000014
σi(L) denotes the ith singular value of L, r represents the rank of the matrix, w ═ w1，w2，...，wmin(m，n)]TRepresenting non-negative weighting coefficients, as used herein the element w of w1，w2，...，wrAre all 1, | · | | luminanceW，1Representing weighted l1Norm, i.e.
Figure FDA0001805403440000015
W∈Rm×nRepresenting a non-negative weighting coefficient, | · | | non-woven phosphorlRepresents any norm and can be changed according to actual needs;
solving the objective function to obtain the optimal low-rank matrixL*And a sparse matrix S*Respectively correspond to background block images
Figure FDA0001805403440000016
And target block image
Figure FDA0001805403440000017
Step 3, obtaining the background block image according to the step 2
Figure FDA00018054034400000113
And target block image
Figure FDA0001805403440000018
Reconstructing the background image B and the target image T:
and 4, performing self-adaptive threshold segmentation on the target image T obtained in the step 3, determining the position of the target, and outputting a detection result.
2. The infrared weak and small target detection method based on the weighted truncation nuclear norm as claimed in claim 1, characterized in that: constructing an infrared block image in the step 1
Figure FDA0001805403440000019
The method specifically comprises the following steps: traversing the original image D by the step length of s from left to right and from top to bottom by adopting a sliding window with the size of k multiplied by k, and quantizing the matrix vector with the size of k multiplied by k obtained in each sliding window into k2The X1 column vector, after traversing, all the obtained column vectors form a new matrix, and the infrared block image is obtained
Figure FDA00018054034400000110
Where t is the number of window slides.
3. The infrared weak and small target detection method based on the weighted truncation nuclear norm as claimed in claim 1, characterized in that: in the step 2The method comprises the steps of carrying out Lagrange equation conversion on an objective function, solving according to the optimized equation to obtain an optimal low-rank matrix and an optimal sparse matrix, and respectively and correspondingly obtaining a background block image
Figure FDA00018054034400000111
And target block image
Figure FDA00018054034400000112
The method comprises the following specific steps:
step 2.1, the augmented Lagrange equation of the constructed objective function is obtained as follows:
Figure FDA0001805403440000021
wherein Y represents a Lagrangian multiplier, μ represents a non-negative penalty factor,<·>represents inner product operation, | · | non-conducting phosphorFRepresenting the Frobenius norm, i.e.
Figure FDA0001805403440000022
Step 2.2, in the formula of step 2.1,
Figure FDA0001805403440000023
A∈Rr×m，B∈Rn×ri is a unit matrix, | L | | non-woven phosphorw，*Representing weighted nuclear norms of the matrix, i.e.
Figure FDA0001805403440000024
σi(L) denotes the ith singular value of L, r represents the rank of the matrix, w ═ w1，w2，...，wmin(m，n)]TRepresenting non-negative weight values, as used herein the element w of w1，w2，...，wrAll are 1, tr represents the trace of the matrix, and the augmented lagrange equation obtained in step 2.1 is rewritten as follows:
Figure FDA0001805403440000025
step 2.3, image of infrared block
Figure FDA00018054034400000211
Inputting the Lagrange equation obtained in the step 2.2, solving the Lagrange equation, and outputting a background block image
Figure FDA0001805403440000026
And target block image
Figure FDA0001805403440000027
4. The infrared weak and small target detection method based on the weighted truncation nuclear norm as claimed in claim 3, characterized in that: the lagrangian equation in the step 2.3 is solved by adopting an overlapping direction multiplier method, and the specific solving process is as follows:
step 2.3.1, initializing L, S, N, Y to 0, the number of iterations k to 0, the maximum number of iterations maxk, μ > 0 for initialization, ρ > 1,
Figure FDA0001805403440000028
β＞0，w＝1，W＝1×1T，εB≥1，εT＞0；
step 2.3.2, fix L, N, Y, update Sk+1The following were used:
Figure FDA0001805403440000029
wherein S isτ(x) Is a soft threshold shrink operator, Sτ(x)＝sgn(x)max(|x|-τ，0)；
Step 2.3.3, on LkSingular value decomposition is carried out: [ U ]k，∑k，Vk]＝svd(Lk) To obtain
Figure FDA00018054034400000210
Figure FDA0001805403440000031
Thereby obtaining
Figure FDA0001805403440000032
Step 2.3.4, let w1＝w2＝...＝wr1, let tem be X-Sk+1-Nk+(Yk-(Ak)TBkMu), singular value decomposition of tem, i.e. [ U ]t，∑t，Vt]＝svd(tem)；
Step 2.3.5, fix S, N, Y, update Lk+1The following were used:
Figure FDA0001805403440000033
wherein diag denotes that the diagonal is max (Σ)ii-wiA diagonal matrix of/[ mu ]);
step 2.3.6, fix L, S, Y, update Nk+1The following were used:
Figure FDA0001805403440000034
step 2.3.7, fix L, S, N, update Yk+1The following were used:
Yk+1＝Yk+μ(X-Lk+1-Sk+1-Nk+1)；
step 2.3.8, update the weight wk+1，Wk+1：
Figure FDA0001805403440000035
Figure FDA0001805403440000036
Wherein epsilonB，εTRepresents a positive constant;
step 2.3.9, update λk+1＝ρλkUpdating the iteration times k to k + 1;
step 2.3.10, judging whether k is larger than maxk, if so, stopping iteration, and turning to step (2.3.11); if not, judging
Figure FDA0001805403440000037
If so, stopping iteration and going to step (2.3.11), and if not, going to step (2.3.2):
step 2.3.11, outputting the final optimal low rank matrix L*And a sparse matrix S*Respectively correspond to background block images
Figure FDA0001805403440000038
And target block image
Figure FDA0001805403440000041
5. The infrared weak and small target detection method based on the weighted truncation nuclear norm as claimed in claim 1, characterized in that: in the step 3, the image is obtained according to the background block
Figure FDA0001805403440000042
And
Figure FDA0001805403440000043
in a manner opposite to the method for constructing the infrared block image in the step 1
Figure FDA0001805403440000044
To know
Figure FDA0001805403440000045
Reconstructing the image into small blocks of images, sequentially reconstructing a background image B according to the sequence, and determining the gray value of the position by adopting a median filtering mode for the overlapped position in each small block.
6. The infrared weak and small target detection method based on the weighted truncation nuclear norm as claimed in claim 1, characterized in that: in the step 4, when the target image T is subjected to adaptive threshold segmentation, the threshold Th is m + c σ, where m represents a mean value of all the grays in T, σ represents a standard deviation of all the grays in T, and c represents a constant between 1 and 15.
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