A method and device for detecting infrared small targets based on GoDec

Abstract

This invention discloses a method and apparatus for detecting small infrared targets based on GoDec. It includes: (1) constructing an infrared spatiotemporal tensor from a thermal infrared image sequence and expanding it along the time dimension to obtain a reconstructed matrix; (2) performing singular value decomposition to determine the low-rank constraint of the background component; (3) based on the assumption that the infrared image consists of low-rank background components and non-background components, establishing a GoDec-based decomposition model with the goal of minimizing the Welsch M estimate of the non-background components; (4) designing an optimization algorithm to obtain the non-background component matrix; and (5) designing an information filter to remove noise from the non-background components, obtaining a clean sparse target matrix, and reconstructing each row into an image matrix T with the same size as the original infrared image to obtain a target detection result sequence T, thus realizing the detection of small infrared targets. This invention can effectively suppress the background, enhance the target, and improve the detection performance of small infrared targets.

Description

Technical Field

[0001] This invention relates to the field of image processing, and in particular to a method and apparatus for detecting small infrared targets based on GoDec. Background Technology

[0002] Thermal infrared small target detection plays a crucial role in military reconnaissance, border patrol, security surveillance, and environmental monitoring. Typically, infrared small targets are characterized by their small size, lack of texture features, and weak signal strength. Furthermore, the poor quality and low signal-to-noise ratio of infrared images further complicate the task of small target detection. Therefore, research on infrared small target detection algorithms is of great significance.

[0003] Currently, methods for detecting small targets in thermal infrared mainly include traditional methods, visual saliency-based methods, low-rank sparse decomposition-based methods, and deep learning methods.

[0004] Classical methods include background-based modeling and wavelet transform-based methods. These methods can extract small target features from thermal infrared images, but the detection results are easily affected by noise and background, and they perform poorly in complex and variable scenes.

[0005] Inspired by the human visual system, and considering that small infrared targets often exhibit local features distinct from the background and noise, specific local descriptor operators can be designed to detect weak infrared targets. Common algorithms include the Local Contrast Metric (LCM) operator and its various variants, such as Multi-Scale Block Contrast Metric (MPCM), Weighted Local Contrast Metric (WLCM), and Multi-Lesson-Based Weighted Contrast Metric (MDWCM). However, these detectors are highly dependent on the contrast between the target and the background, and false detections are easily caused when the small target is similar to its surrounding neighborhood.

[0006] Low-rank sparse decomposition theory has injected new vitality into infrared small target detection. Because most regions in infrared images are occupied by locally autocorrelated background components, the background exhibits low-rank characteristics; while targets occupy only a few pixels, thus exhibiting sparse characteristics. Therefore, low-rank backgrounds and sparse targets can be modeled to separate target components from the original infrared image, achieving infrared small target detection. Common methods include GoDec, IPI, NRAM, LogTFNN, and RIPT, which show good performance in preserving target information and suppressing background and noise. However, many methods do not fully utilize or even destroy the spatiotemporal information of thermal infrared image sequences, potentially leading to background shrinkage or target loss.

[0007] With the development of deep learning technology, researchers have proposed many deep learning-based methods for detecting small thermal infrared targets, such as ALCNet, CBPNet, STDMANet, and APAFNet. However, these deep learning-based methods require a large amount of labeled data and high-performance hardware. In addition, during network training, issues such as feature loss, target misjudgment, and weak generalization ability can easily occur, which reduces the robustness of the algorithm when the background environment changes drastically. Therefore, deep learning-based methods still have certain limitations in practical applications. Summary of the Invention

[0008] To address the shortcomings of existing technologies, the present invention aims to provide a method and apparatus for detecting small thermal infrared targets based on GoDec. This method fully utilizes the spatiotemporal information of thermal infrared image sequences, the low-rank characteristics of background components, and the sparsity of targets. It organically combines the maximization of correlation entropy criterion with low-rank sparse decomposition theory, and incorporates adaptive low-rank background constraints and information filters to establish a component decomposition model based on "low-rank background part + non-background part." This model can effectively characterize the features of different components in infrared image data. Furthermore, based on semi-secondary optimization theory, an efficient optimization algorithm is proposed, which can quickly detect small thermal infrared targets, achieving infrared small target detection. The target detection capability and background suppression capability of this algorithm have been effectively verified.

[0009] To achieve the above objectives, the present invention provides the following technical solution:

[0010] This invention discloses an infrared small target detection method based on GoDec, characterized by comprising the following steps:

[0011] Step 1): In the original thermal infrared image sequence D, each frame of the image... Construct an infrared spatiotemporal tensor by stacking I3 consecutive image frames. and the spacetime tensor Expanding on the time dimension yields a new reconstruction matrix. I1 and I2 represent the length and width of the image frame, respectively, and I3 is the number of consecutive image frames acquired each time.

[0012] Step 2): Reconstruct the matrix Perform singular value decomposition, and adaptively obtain the rank r of the background component using the resulting singular value matrix;

[0013] Step 3): With the goal of minimizing the Welsch M estimate of non-background components, a matrix factorization model based on GoDec is established using the rank r from Step 2).

[0014] Step 4): Based on the theory of semi-secondary optimization, design a model optimization algorithm, and use the alternating solution method to solve the matrix factorization model based on GoDec to obtain the non-background component matrix.

[0015] Step 5): Design an information filter by removing non-background component matrices. By filtering out the noise components in the matrix, candidate target pixels are selected to obtain a clean target matrix. and the target matrix Each row is reconstructed into an image matrix T with the same size as the original infrared image, thus obtaining the infrared small target detection result sequence T, realizing thermal infrared small target detection.

[0016] The present invention also discloses a GoDec-based infrared small target detection device for implementing the method, comprising:

[0017] The infrared image module is reconstructed by constructing the original thermal infrared image sequence into a spatiotemporal tensor and expanding the spatiotemporal tensor into an image matrix in the time dimension.

[0018] The module for determining low-rank constraints of background components is used to determine the low-rank constraints of background components in the subsequent GoDec-based decomposition model.

[0019] The matrix factorization model building module based on GoDec establishes a matrix factorization model based on the assumption that infrared images consist of low-rank background components and non-background components, with the objective function being to minimize the Welsch M estimate of the non-background components.

[0020] The optimization model solving module, based on the theory of semi-secondary optimization, uses an alternating solution method to solve the matrix decomposition model to obtain the non-background component matrix;

[0021] An information filter is used to remove noise components from the non-background component matrix, select target candidate pixels, obtain a clean sparse target matrix, and reconstruct each row of the target matrix into an image matrix with the same size as the original infrared image to obtain a sequence of infrared small target detection results.

[0022] The target detection result output module is used to output infrared small target detection result images.

[0023] The beneficial effects of this invention are as follows:

[0024] 1) This invention makes full use of the rich temporal and spatial information carried by thermal infrared image sequences. Without destroying the spatial information of the images, the thermal infrared image sequences are constructed as spatiotemporal tensors. Then, the spatiotemporal tensors are expanded into image matrices from the time dimension, transforming the thermal infrared small target detection problem into a component decomposition-based problem. The constructed image matrix lays the data foundation for the establishment of the component decomposition-based optimization model.

[0025] 2) Inspired by the traditional GoDec algorithm, this invention fully utilizes the low-rank characteristics of the background in thermal infrared images and leverages the ability of the maximum correlation entropy criterion to effectively handle non-Gaussian signals at different levels. By designing adaptive low-rank constraints for background components and sparse constraints for target components, and based on the assumption that infrared images consist of low-rank background components and non-background components, a component decomposition model is established, and a robust optimization algorithm is designed. The background suppression capability, target detection capability, and overall effectiveness of the proposed infrared weak target detection method have all been verified. Attached Figure Description

[0026] Figure 1 This is a flowchart illustrating the GoDec-based thermal infrared small target detection process of this invention.

[0027] Figure 2 This is a schematic diagram of the infrared small target detection device of the present invention;

[0028] Figure 3 Example frame images of a thermal infrared image sequence used for experimental testing;

[0029] Figure 4 The thermal infrared small target detection results are shown in the example frames of the thermal infrared image sequence.

[0030] Figure 5 The images show the detection results and corresponding 3D grayscale visualizations of example frames of thermal infrared image sequences after being detected by the proposed method, WSLCM, GSWLCM, MDWCM and FAMSIS.

[0031] Figure 6 The images show the detection results and corresponding 3D grayscale visualizations of example frames from thermal infrared image sequences after being detected by METTR, NIRPS, TCNN-NPSTT, WSNM-STIPT, and ECA-STT. Detailed Implementation

[0032] To make the objectives, technical solutions, and advantages of this invention clearer, the invention is described in detail below with reference to specific embodiments. Specific embodiments are described below to simplify the invention. However, it should be understood that the invention is not limited to the described embodiments, and various modifications are possible without departing from the basic principles; these equivalent forms also fall within the scope defined by the appended claims.

[0033] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0034] like Figure 1 The diagram shown is a flowchart illustrating the basic steps of the GoDec-based infrared small target detection method of the present invention in this embodiment, mainly including:

[0035] Step 1: In the original thermal infrared image sequence D, each frame of the image... Construct an infrared spatiotemporal tensor by stacking I3 consecutive image frames. and the spacetime tensor Expanding along the time dimension (i.e., mode-3), a new reconstruction matrix is ​​obtained. I1 and I2 represent the length and width of the image frame, respectively, and I3 is the number of consecutive image frames acquired each time.

[0036] Specifically, the original thermal infrared image sequence D, where each frame of the image... Each frame of an image can be modeled as consisting of a low-rank background matrix B, a sparse target matrix T, and a noise matrix N, expressed as follows:

[0037]

[0038] Where rank(·) denotes the rank operator, ||·||0 denotes the l0 norm, and ||·|| F Let λ denote the Frobenius norm, and λ1 and λ2 denote the positive tradeoff parameters.

[0039] From the original thermal infrared image sequence D, I3 image frames are acquired each time and stacked sequentially according to the frame order to construct the infrared spatiotemporal tensor. and The s-th frontal slice is the s-th complete image frame, thus the spatiotemporal tensor can be modeled as a low-rank sparse tensor decomposition model, expressed as:

[0040]

[0041] Represents the background tensor. Represents the target tensor. This represents the noise tensor; specifically, in this embodiment, s is set to 20.

[0042] spacetime tensor Each tube fiber in They all carry rich temporal information, which is the spacetime tensor. Expanding along the time dimension (i.e., mode-3), a new reconstruction matrix is ​​obtained. The first dimension of this matrix carries temporal information, the second dimension carries image spatial information, and each row vector of the reconstructed matrix... Let x represent an infrared image sample, where 1 ≤ x ≤ I3.

[0043] Step 2: Reconstruct the matrix Perform singular value decomposition, and adaptively obtain the rank r of the background component using the resulting singular value matrix;

[0044] Specifically, for the reconstructed matrix The singular value decomposition (SVD) is expressed as follows:

[0045]

[0046] Where "*" represents the matrix multiplication operator, U is a left singular matrix of size I3×I3, V is a right singular matrix of size I1I2×I1I2, Σ is a singular matrix of size I3×I1I2, and V T This represents the transpose of matrix V.

[0047] In infrared images, the vast majority of the region is occupied by low-rank background; therefore, in the reconstruction matrix... In this matrix, the vast majority of elements are background elements and still exhibit low-rank properties. For subsequent adaptive low-rank background decomposition, the rank r is determined as follows:

[0048]

[0049] Where H(·) is the unit step function, H(x) = 1 when x ≥ 0, otherwise H(x) = 0, Σ k,k This represents the element in the k-th row and k-th column of the singular value matrix Σ. max This represents the maximum element in Σ. Σ It is an adjustable positive constant, which can be adjusted by changing r. Σ The size of can be chosen to obtain a suitable rank r. Specifically, in the embodiment, r... Σ Set it to 0.1.

[0050] Step 3: With the goal of minimizing the Welsch M estimate of non-background components, a matrix factorization model based on GoDec is established using the rank r from step 2).

[0051] Specifically, the traditional Godec algorithm decomposes the image matrix based on the assumptions of "low-rank background + sparse target + Gaussian noise" to obtain the target matrix. Since maximizing the correlation entropy criterion is effective in handling non-Gaussian signals at different levels, and maximizing the correlation entropy criterion is equivalent to minimizing the Welsch M estimate, the Godec algorithm can be improved to reconstruct the matrix. As the object, based on the assumption of "low-rank background component + non-background component", with minimizing the Welsch M estimate of the non-background component as the objective function, the low-rank sparse tensor decomposition model (2) can be improved into the following matrix decomposition model:

[0052]

[0053] in, Represents the low-rank background component matrix. Let r represent the non-background component matrix, where r is the rank of the background component determined in step 2). Represents the non-background component matrix The Welsch M estimate (from R. He, W.-S. Zheng, and B.-G. Hu, “Maximum correntropy criterion for robust face recognition,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 33, no. 8, pp. 1561–1576, 2010.), g σ (·) represents a Gaussian kernel function with a standard deviation of σ. In this specific embodiment, σ is set to 10. 4 .

[0054] Step 4: Based on the theory of semi-secondary optimization, design a model optimization algorithm, and use the alternating solution method to solve the matrix factorization model based on GoDec to obtain the non-background component matrix.

[0055] Specifically, based on the theory of half-quadratic optimization (from M. Nikolova and MKNg, “Analysis of half-quadratic minimization methods for signal and image recovery,” SIAM J. Sci. Comput., vol. 27, no. 3, pp. 937–966, 2005), by introducing... The auxiliary variable E, which makes the matrix decomposition model (5) in step 3) equivalent to:

[0056]

[0057] Where φ(·) is the Gaussian kernel function g σ The dual function of (·). Furthermore, the optimization model (6) can be solved by the alternating solution method, and the resulting alternating solution model is:

[0058]

[0059] The specific solution algorithm for the alternating solution model (7) is as follows:

[0060] 1) Input the reconstruction matrix Error ε, rank r determined in step 2), iteration number t = 1;

[0061] 2) Randomly initialize the standard Gaussian matrix

[0062] 3) Calculation when Then execute steps 4)-9); otherwise, execute step 10).

[0063] 4)

[0064] 5) for i = 1, 2, ..., p

[0065]

[0066] end

[0067] 6) Perform qr-decomposition on matrix Y2, Y2 = QR, and K = Q;

[0068] 7) Among them, ⊙ represents the Hadamarda accumulation;

[0069] 8) The number of iterations t = t + 1;

[0070] 9) Return to step 3);

[0071] 10) Output the background component matrix

[0072] In the specific implementation example, p is set to 1, and the error ε is set to 10. -7 .

[0073] Finally, the low-rank background component matrix can be obtained by the alternating solution model (7). Non-background component matrix

[0074] Step 5: Design an information filter by removing non-background components from the matrix. By analyzing the noise components in the data, candidate target pixels are selected to obtain a clean sparse target matrix. Each row of the sparse target matrix is ​​then reconstructed into an image matrix with the same size as the original infrared image, thereby obtaining the infrared small target detection result sequence T, realizing infrared small target detection;

[0075] The non-background component matrix obtained from step 4) In the middle, each line This represents the non-background portion of each infrared image, containing both noise and target components. Since the pixel grayscale values ​​of the target components are greater than those of the noise components, an information filter is constructed to select candidate target pixels, remove the noise components, and obtain a clean sparse target matrix. The information filter is designed as follows:

[0076]

[0077] in, This indicates that the row vector The index value belongs to the set Ω x An operator that projects an element to itself and projects all other elements to zero. This indicates retrieving the x-th row vector. Middle anterior κ x The set of indices Ω corresponding to the largest element x The operator, and κ x Let η be ηI1I2, where η is an adjustable positive constant, η∈(0,1). Specifically, in this embodiment, η is taken as 2×102 -5 .

[0078] Furthermore, the sparse target matrix Each row vector The image is reconstructed into an image matrix T with the same size as the original infrared image, where 1≤x≤I3, resulting in I3 images. This yields the infrared small target detection result sequence T, thus realizing the detection of thermal infrared small targets.

[0079] Corresponding to the aforementioned embodiment of an infrared small target detection method based on GoDec, the present invention also provides an embodiment of an infrared small target detection device based on GoDec.

[0080] Figure 2 This is a block diagram illustrating a GoDec-based infrared small target detection device according to an exemplary embodiment, such as... Figure 2 As shown, the device includes:

[0081] The infrared image module is reconstructed, the original infrared image sequence is constructed into a spatiotemporal tensor, and the spatiotemporal tensor is expanded into an image matrix in the time dimension, laying the data foundation for the subsequent decomposition model.

[0082] The module for determining low-rank constraints of background components is used to determine the low-rank constraints of background components in the subsequent GoDec-based decomposition model, thereby improving the ability of the decomposition model to accurately extract background components.

[0083] Based on the improved GoDoec decomposition model building module, and based on the assumption of "low-rank background components + non-background components", a matrix decomposition model is established with the goal of minimizing the Welsch M estimate of non-background components.

[0084] The optimization model solving module, based on the theory of semi-secondary optimization, uses an alternating solution method to solve the model and obtain the non-background component matrix;

[0085] An information filter is used to remove noise components from the non-background component matrix, select target candidate pixels, obtain a clean sparse target matrix, and reconstruct each row of the target matrix into an image matrix with the same size as the original infrared image to obtain a sequence of infrared small target detection results.

[0086] The target detection result output module is used to output infrared small target detection result images.

[0087] Regarding the apparatus in the above embodiments, the specific manner in which each module performs its operation has been described in detail in the embodiments related to the method, and will not be elaborated upon here.

[0088] For the device embodiments, since they basically correspond to the method embodiments, the relevant parts can be referred to the description of the method embodiments. The device embodiments described above are merely illustrative; the various modules in the device represent a logical functional division, and in actual implementation, there may be other division methods. For example, multiple modules may be combined or integrated into another unit. Furthermore, the connections between the displayed or discussed modules may be communication connections through some interfaces, which may be electrical or other forms. Some or all of the modules can be selected to achieve the purpose of this application according to actual needs. Those skilled in the art can understand and implement this without creative effort. The following uses a publicly available real thermal infrared image sequence as an example to illustrate specific implementation methods to demonstrate the technical effects of the present invention; specific steps in the embodiments will not be repeated.

[0089] Example

[0090] The accompanying drawings illustrating the embodiments of the present invention will make the objectives, technical solutions, and advantages of the present invention clearer. It should be noted that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the scope of the invention. All equivalent substitutions and improvements made within the framework of the methods and principles provided by the present invention should be included within the protection scope of the present invention.

[0091] In this embodiment, the effectiveness of the thermal infrared small target detection method will be verified using a publicly available thermal infrared image sequence. Qualitatively, the method is evaluated using an example frame of the thermal infrared image sequence, along with its corresponding 3D visualization grayscale image. Quantitatively, the detection performance is assessed using the 3D-ROC evaluation index system. The 3D-ROC evaluation index system includes target detection capability (TD), background suppression capability (BS), and overall detector effectiveness evaluation index, detailed in the table below:

[0092] Table 1 3D-ROC Evaluation Index System

[0093]

[0094] For a publicly available, real thermal infrared image sequence containing 200 frames, with each frame being 256×256 pixels, the image shows a complex air-to-ground background containing bright buildings and strong noise clutter, and the aircraft moving slowly. Figure 3 Here is an example frame from this thermal infrared image sequence. Figure 4 The corresponding target detection result image obtained using the method of this invention is shown. The detection result image shows that the background (including bright buildings and noise) is completely suppressed, and the salience of small targets is enhanced. To quantitatively evaluate the effectiveness of the proposed method, Table 2 presents the 3D-ROC evaluation system indicators for small target detection results of the thermal infrared image sequence using WSLCM, GSWLCM, MDWCM, FAMSIS, METTR, NIRPS, TCNN-NPSTT, WSNM-STIPT, ECA-STT, and the method proposed in this invention. The bold and underlined values ​​represent the corresponding optimal and second-best AUC values, respectively. Among them, WSLCM, GSWLCM, MDWCM, and FAMSIS are small target detection methods based on local contrast measurement; METTR and NIRPS are small target detection methods based on low-rank sparse matrix factorization; and TCNN-NPSTT, WSNM-STIPT, and ECA-STT are small target detection methods based on low-rank sparse tensor factorization.

[0095] The sources for each comparison method are as follows:

[0096] WSLCM is from J. Han, S. Moradi, I. Faramarzi, H. Zhang, Q. Zhao, X. Zhang, and N. Li, “Infrared small target detection based on the weighted strengthened local contrast measure,” IEEE Geosci. Remote Sens. Lett., vol. 18, no. 9, pp. 1670–1674, 2020.

[0097] GSWLCM is from Z. Qiu, Y. Ma, F. Fan, J. Huang, and L. Wu, “Global sparsity-weighted local contrast measure for infrared small target detection,” IEEE Geosci. Remote Sens. Lett., vol. 19, pp. 1–5, 2022.

[0098] MDWCM is from R. Lu, X. Yang, W. Li, J. Fan, D. Li, and X. Jing, “Robust infrared small target detection via multidirectional derivative-based weighted contrast measure,” IEEE Geosci. Remote Sens. Lett., vol. 19, pp. 1–5, 2020.

[0099] FAMSIS is from Y. Chen, G. Zhang, Y. Ma, J. U. Kang, and C. Kwan, “Small infrared target detection based on fast adaptive masking and scaling with iterative segmentation,” IEEE Geosci. Remote Sens. Lett., vol. 19, pp. 1–5, 2021.

[0100] METTR is from Z. Cao, X. Kong, Q. Zhu, S. Cao, and Z. Peng, “Infrared dim target detection via mode-k1k2 extension tensor tubal rank under complex ocean environment,” ISPRS-J. Photogramm. Remote Sens., vol. 181, pp. 167–190, 2021.

[0101] NIRPS is from Y. Liu and Z. Peng, “Infrared small target detection based on resampling-guided image model,” IEEE Geosci. Remote Sens. Lett., vol. 19, pp. 1–5, 2021.

[0102] TCNN-NPSTT is from G. Wang, B. Tao, X. Kong, and Z. Peng, “Infrared small target detection using nonoverlapping patch spatial–temporal tensor factorization with capped nuclear norm regularization,” IEEE Trans. Geosci. Remote Sens., vol. 60, pp. 1–17, 2021.

[0103] WSNM-STIPT is from Y. Sun, J. Yang, M. Li, and W. An, “Infrared small target detection via spatial–temporal infrared patch-tensor model and weighted schatten pnorm minimization,” Infrared Phys. Technol., vol. 102, p. 103050, 2019.

[0104] ECA-STT comes from P.Zhang, L.Zhang, X.Wang, F.Shen, T.Pu, and C.Fei, "Edge and corner awareness-based spatial–temporal tensor model for infrared small-target detection," IEEE Trans.Geosci.Remote Sens., vol.59, no.12, pp.10 708–10724, 2020.

[0105] Table 2. Quantitative indicators of the detection results of thermal infrared image example sequences using WSLCM, GSWLCM, MDWCM, FAMSIS, METTR, NIRPS, TCNN-NPSTT, WSNM-STIPT, ECA-STT, and the proposed method.

[0106] method <![CDATA[AUC (D，F) ]]> <![CDATA[AUC (D，τ) ]]> <![CDATA[AUC (F，τ) ]]> <![CDATA[AUC TD ]]> <![CDATA[AUC BS ]]> <![CDATA[AUC SNPR ]]> <![CDATA[AUC TDBS ]]> <![CDATA[AUC ODP ]]> This invention 1.0000 <![CDATA[ 0.9960 ]]> 0.0000 <![CDATA[ 1.9960 ]]> 1.0000 Inf <![CDATA[ 0.9960 ]]> <![CDATA[ 1.9960 ]]> WSLCM 1.0000 0.9944 4.7191e-5 1.9944 1.0000 <![CDATA[ 2.1071e4 ]]> 0.9943 1.9943 GSWLCM 1.0000 0.5439 <![CDATA[ 3.5092e-5 ]]> 1.5438 <![CDATA[ 0.9999 ]]> 1.5498e4 0.5438 1.5438 MDWCM 0.6446 0.0146 8.9593e-5 0.6591 0.6445 1.6274e2 0.0145 0.6590 FAMSIS <![CDATA[ 0.9999 ]]> <![CDATA[ 0.9960 ]]> 1.2999e-4 1.9959 0.9997 7.6621e3 0.9959 1.9957 METTR 1.0000 0.9956 1.7947e-1 1.9956 0.8205 5.5475 0.8161 1.8161 NIRPS 1.0000 0.8704 4.8391e-4 1.8703 0.9995 1.7986e3 0.8699 1.8698 TCNN-NPSTT 1.0000 0.9027 9.8142e-5 1.9027 <![CDATA[ 0.9999 ]]> 9.1977e3 0.9026 1.9026 WSNM-STIPT 0.9600 0.9264 1.1617e-4 1.8864 0.9599 7.9744e3 0.9262 1.8862 ECA-STT 1.0000 0.9993 1.0066e-3 1.9993 0.9990 9.9273e2 0.9983 1.9983

[0107] Figure 5 The following are examples of small target detection results and corresponding 3D grayscale visualization images of a thermal infrared image frame obtained by the present invention, WSLCM, GSWLCM, MDWCM and FAMSIS respectively; Figure 6 Example frames of thermal infrared images are provided, showing the small target detection results and corresponding 3D grayscale visualizations obtained using METTR, NIRPS, TCNN-NPSTT, WSNM-STIPT, and ECA-STT methods, respectively. Qualitative results show that the selected contrast methods can detect small targets, but their background suppression capabilities are weak, leaving residual background components, especially in METTR. The detection method proposed in this invention, however, can completely suppress the background and enhance target saliency. The quantitative results shown in Table 2 also reflect that the background suppression capability of the proposed method is superior to all contrast methods. Specifically, the AUC of the proposed method is significantly higher than that of all other methods. (F，τ) Reaching 0, AUC BS Reaching 1, AUC SNPR Reaching infinity indicates excellent background suppression capability; although the target detection capability-related indicators are lower than ECA-STT, they are still superior to most comparative methods. Based on comprehensive qualitative and quantitative analysis, the thermal infrared small target detection method proposed in this invention possesses superior target detection capability, background suppression capability, and overall effectiveness.

[0108] The accompanying drawings illustrating the embodiments of the present invention will make the objectives, technical solutions, and advantages of the present invention clearer. It should be noted that the specific embodiments described herein are merely illustrative and not intended to limit the scope of the invention. All equivalent substitutions and improvements made within the framework of the methods and principles provided by the present invention should be included within the protection scope of the present invention.

Claims

1. A method for detecting small infrared targets based on GoDec, characterized in that, Includes the following steps: Step 1): For the original thermal infrared image sequence, stack consecutive image frames to construct an infrared spatiotemporal tensor. and the spacetime tensor Expanding on the time dimension yields a new reconstruction matrix. Step 2): Reconstruct the matrix Perform singular value decomposition, and adaptively obtain the rank r of the background component using the resulting singular value matrix; Step 3): With the goal of minimizing the Welsch M estimate of non-background components, a matrix factorization model based on GoDec is established using the rank r from Step 2). Step 3) specifically refers to: Improvements to the GoDec algorithm for matrix reconstruction As an object, based on the reconstruction matrix Assuming that the low-rank sparse tensor decomposition model consists of low-rank background components and non-background components, and taking minimizing the Welsch M estimate of the non-background components as the objective function, the low-rank sparse tensor decomposition model is improved to the following matrix decomposition model: in, Represents the low-rank background component matrix. Let r represent the non-background component matrix, where r is the rank of the background component determined in step 2). Represents the non-background component matrix Welsch M estimates that g σ (·) represents the Gaussian kernel function with standard deviation σ, and rank() represents the rank calculation operator; Step 4): Based on the theory of semi-secondary optimization, design a model optimization algorithm, and use the alternating solution method to solve the matrix factorization model based on GoDec to obtain the non-background component matrix. Step 5): Design an information filter by removing non-background component matrices. By filtering out the noise components in the matrix, candidate target pixels are selected to obtain a clean target matrix. and the target matrix Each row is reconstructed into an image matrix T with the same size as the original infrared image, thereby obtaining the infrared small target detection result sequence and realizing thermal infrared small target detection.

2. The infrared small target detection method based on GoDec according to claim 1, characterized in that, Step 1) specifically refers to: For each frame of the original thermal infrared image sequence I1 and I2 represent the length and width of the image frame, respectively. Each frame is modeled as consisting of a low-rank background matrix B, a sparse target matrix T, and a noise matrix N, expressed as follows: Where rank(·) denotes the rank operator, ||·||0 denotes the l0 norm, and ||·|| F λ represents the Frobenius norm, and λ1 and λ2 represent the positive trade-off parameters; From the original thermal infrared image sequence, I3 consecutive image frames are acquired at each time. These frames are then stacked sequentially according to their frame order to construct a spatiotemporal tensor. and The s-th frontal slice is the s-th complete image frame, thus the spatiotemporal tensor is modeled as a low-rank sparse tensor decomposition model, expressed as: in, Represents the background tensor. Represents the target tensor. Represents the noise tensor; spacetime tensor Each tube fiber in All carry time information, where 1≤i≤I1, 1≤j≤I2; this spacetime tensor Expanding on the time dimension yields a new reconstruction matrix. The reconstruction matrix The first dimension carries temporal information, the second dimension carries image spatial information, and each row vector of the reconstruction matrix... Let x represent an infrared image sample, where 1 ≤ x ≤ I3.

3. The infrared small target detection method based on GoDec according to claim 1, characterized in that, Step 2) specifically refers to: For the reconstruction matrix Singular value decomposition is performed, and its expression is: Where "*" represents the matrix multiplication operator, U is a left singular matrix of size I3×I3, V is a right singular matrix of size I1I2×I1I2, Σ is a singular value matrix of size I3×I1I2, and V T I1 represents the transpose of matrix V; I2 and I3 represent the length and width of the image frame, respectively; I3 is the number of consecutive image frames acquired each time. The method for determining the rank r of the background component is as follows: Where H(·) is the unit step function, H(x) = 1 when x ≥ 0, otherwise H(x) = 0, Σ k,k This represents the element in the k-th row and k-th column of the singular value matrix Σ. max r represents the maximum element in Σ. Σ This represents an adjustable positive constant.

4. The infrared small target detection method based on GoDec according to claim 1, characterized in that, Step 4) specifically refers to: Based on the theory of semi-secondary optimization, by introducing The auxiliary variable E, which makes the matrix decomposition model in step 3) equivalent to Where φ(·) is the Gaussian kernel function g σ The dual function of (·); furthermore, by solving equation (6) using the alternating solution method, the resulting alternating solution model is: Where t is the number of the t-th iteration; Finally, the low-rank background component matrix is ​​obtained by the alternating solution model. Non-background component matrix 5. The infrared small target detection method based on GoDec according to claim 4, characterized in that, The specific solution algorithm for the alternating solution model is as follows: 1) Input the reconstruction matrix Error ε, rank r of the background component determined in step 2), iteration number t = 1; 2) Randomly initialize the standard Gaussian matrix 3) Calculation when Then execute steps 4)-9); otherwise, execute step 10). 4) 5) 6) Perform qr-decomposition on matrix Y2, Y2 = QR, and K = Q; 7) Among them, ⊙ represents the Hadamarda accumulation; 8) The number of iterations t = t + 1; 9) Return to step 3); 10) Output the background component matrix 6. The infrared small target detection method based on GoDec according to claim 1, characterized in that, Step 5) specifically refers to: The non-background component matrix obtained from step 4) In the middle, each line This represents the non-background portion of each infrared image, containing both noise and target components. Since the pixel grayscale values ​​of the target components are greater than those of the noise components, an information filter is constructed to select candidate target pixels, remove the noise components, and obtain a clean sparse target matrix. The information filter is designed as follows: in, This indicates that the row vector The index value belongs to the set Ω x An operator that projects an element to itself and projects all other elements to zero. This indicates retrieving the x-th row vector. Middle anterior κ x The set of indices Ω corresponding to the largest element x The operator, and κ x Let η be the length and width of the image frame, where η is an adjustable positive constant, η∈(0,1); I1 and I2 are the length and width of the image frame, respectively, and I3 is the number of consecutive image frames acquired each time. Furthermore, the pure target matrix Each row vector The image is reconstructed into an image matrix T with the same size as the original thermal infrared image, where 1≤x≤I3, resulting in I3 images. This yields a sequence of infrared small target detection results, thus achieving infrared small target detection.

7. A GoDec-based infrared small target detection device implementing the method of claim 1, characterized in that, include: The infrared image module is reconstructed by constructing the original thermal infrared image sequence into a spatiotemporal tensor and expanding the spatiotemporal tensor into an image matrix in the time dimension. The module for determining low-rank constraints of background components is used to determine the low-rank constraints of background components in the subsequent GoDec-based decomposition model. The matrix factorization model building module based on GoDec establishes a matrix factorization model based on the assumption that infrared images consist of low-rank background components and non-background components, with the objective function being to minimize the Welsch M estimate of the non-background components. The optimization model solving module, based on the theory of semi-secondary optimization, uses an alternating solution method to solve the matrix decomposition model to obtain the non-background component matrix; An information filter is used to remove noise components from the non-background component matrix, select target candidate pixels, obtain a clean sparse target matrix, and reconstruct each row of the target matrix into an image matrix with the same size as the original infrared image to obtain a sequence of infrared small target detection results. The target detection result output module is used to output infrared small target detection result images.

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