An infrared small target detection method and device based on posterior information

Abstract

The application discloses an infrared small target detection method and device based on posterior information. The method comprises the following steps: (1) stacking a thermal infrared image sequence in time sequence to construct a three-dimensional space-time tensor D; (2) constructing a model based on low-rank sparse tensor decomposition; (3) defining a tensor kernel norm based on Framelet and Log to perform low-rank estimation on a background; (4) extracting posterior information based on morphology from a temporary target tensor obtained in the current iteration round to serve as significant weight information of the model based on low-rank sparse tensor decomposition in the next iteration round; (5) constructing an infrared small target detection model based on the tensor kernel norm based on Framelet and Log and the posterior information; (6) optimizing the model to obtain a target tensor component, reconstructing a target detection result image, obtaining a target detection result sequence T and realizing thermal infrared small target detection. The thermal infrared small target detection model and solving algorithm designed in the application can improve the comprehensive performance of thermal infrared small target detection.

Description

Technical Field

[0001] This invention relates to the field of image processing, and in particular to an infrared small target detection method and apparatus based on posterior information. Background Technology

[0002] Infrared small target detection technology plays a crucial role in military and civilian fields such as aerospace, maritime surveillance, and forest fire prevention. Due to the considerable distance between the imaging sensor and the target, infrared small targets typically lack specific shape and texture information. Furthermore, real infrared scenes often contain varying degrees of interference (e.g., suspected targets, man-made structures, clutter, etc.). Researchers focus on improving algorithm detection performance in complex scenes, neglecting background suppression and detection efficiency. Therefore, existing infrared small target detection technologies generally lack superior target detection capabilities, background suppression, and overall detection performance. With the development of modern military technology, it is necessary to utilize infrared imagery to conduct rapid and accurate small target detection tasks in different scenarios, improving the target detection and background suppression capabilities of infrared small target detection algorithms in complex environments.

[0003] Existing infrared small target detection algorithms can be broadly categorized into model-driven and data-driven methods. Data-driven methods primarily apply deep learning techniques to infrared small target detection and utilize a large number of labeled samples for training; examples include Generative Adversarial Networks (GANs) and attention-nested U-Net networks. However, most deep learning-based infrared small target detection methods exhibit poor generalization performance across different scenarios, limiting network performance and hindering practicality. Model-driven methods are typically divided into three categories: filter-based methods, human visual system (HVS)-based methods, and low-rank sparse decomposition-based methods.

[0004] Filter-based methods typically utilize local neighborhood information to predict the composition of the current pixel and remove the estimated background from the original image to obtain the target component. Most filter-based methods use relatively simple filters (such as the Top-hat filter), which are easily affected by complex backgrounds in complex scenes, resulting in low detection performance and a tendency to produce false alarms.

[0005] Methods based on the human visual system (HVS) detect small infrared targets by assessing the contrast between the target and the background. Many algorithms based on local contrast metrics have gained favor among researchers due to their efficient target detection capabilities, such as Local Contrast Metric (LCM), Weighted Local Contrast Metric, and Global Sparse Weighted Local Contrast Metric (GSWLCM). However, the detection capability of these methods depends on the contrast between the target and the background. Therefore, in complex scenes, HVS-based algorithms are susceptible to the effects of complex background textures and clutter, resulting in significant false alarms.

[0006] The low-rank sparse decomposition-based method is based on the fact that the original image signal D consists of a low-rank background signal B, a sparse target signal T, and a noise signal N, as shown below:

[0007] D = B + T + N

[0008] Low-rank sparse decomposition-based methods aim to transform infrared small target detection into extracting sparse target components from different forms of data, such as two-dimensional matrices, three-dimensional spatial tensors, three-dimensional spatiotemporal tensors, and four-dimensional spatiotemporal tensors. Existing low-rank sparse decomposition methods based on matrices or block tensors suffer from spatial information destruction due to image reconstruction, especially matrix-based methods, which affect subsequent low-rank sparse decomposition and thus reduce the overall performance of thermal infrared small target detection algorithms. Other low-rank sparse decomposition-based methods utilize complete image frames to construct three-dimensional spatiotemporal tensors and perform low-rank sparse decomposition to obtain target components. Although low-rank sparse tensor decomposition-based methods are gradually showing superiority, two key issues remain: accurate low-rank background estimation and target enhancement and background suppression. Therefore, it is necessary to conduct in-depth research on these two key issues. Summary of the Invention

[0009] To address the shortcomings of existing technologies, the present invention aims to provide a method and apparatus for detecting small targets in thermal infrared images based on posterior information. This method fully utilizes the spatiotemporal information of thermal infrared image sequences, the low-rank characteristics of background components, and the sparsity of targets. By defining tensor kernel norms based on Framelet and Log, the background is accurately estimated, thereby establishing an infrared small target detection model based on low-rank sparse tensor decomposition. This model can effectively characterize the features of different components in infrared image data. Furthermore, a feedback mechanism is introduced into the low-rank sparse tensor decomposition model. This feedback mechanism is based on posterior knowledge driven by three-dimensional morphology. The posterior information obtained in the current iteration can effectively guide the model to focus more on salient targets in the next iteration, contributing to improved detection performance and real-time performance. Comprehensive qualitative and quantitative analysis demonstrates that the infrared small target detection model based on tensor kernel norms of Framelet and Log and posterior information driven by three-dimensional morphology can efficiently achieve infrared small target detection, and both target detection capability and background suppression capability are effectively verified.

[0010] To achieve the above objectives, the present invention provides the following technical solution:

[0011] This invention discloses an infrared small target detection method based on posterior information, characterized by comprising the following steps:

[0012] Step 1): Utilizing the temporal and spatial information carried by the thermal infrared image sequence, stack the image frames in the thermal infrared image sequence in chronological order to construct a three-dimensional spatiotemporal tensor.

[0013] Step 2): Based on the features of the background, target, and noise components, establish a model based on low-rank sparse tensor decomposition;

[0014] Step 3): Define the tensor nuclear norm based on Framelet and Log to perform low-rank estimation of the background;

[0015] Step 4): During the iterative solution of the model based on low-rank sparse tensor decomposition, the posterior information based on three-dimensional morphological operations is extracted from the temporary target tensor obtained in the current iteration round and used as the saliency weight information of the model based on low-rank sparse tensor decomposition in the next iteration round.

[0016] Step 5): Using Framelet transform and Log operator, construct an infrared small target detection model based on tensor nuclear norm of Framelet and Log and posterior information driven by three-dimensional morphology.

[0017] Step 6): Based on the ADMM algorithm, optimize and solve the model in step 5), obtain the target tensor components, reconstruct the target detection result image, and obtain the target detection result sequence T to realize thermal infrared small target detection.

[0018] The present invention also discloses an infrared small target detection device based on posterior information for implementing the method, comprising:

[0019] The infrared image module is reconstructed by stacking the image frames in the original infrared image sequence in chronological order to construct a three-dimensional spatiotemporal tensor, which lays the data foundation for the subsequent establishment of a low-rank sparse tensor decomposition model.

[0020] The low-rank sparse decomposition framework building module establishes a model based on low-rank sparse tensor decomposition based on the features of background, target, and noise.

[0021] The low-rank background estimation module utilizes the Framelet transform and the Log operator to define a tensor nuclear norm based on Framelet and Log for accurate estimation of low-rank background.

[0022] The posterior information extraction module uses the temporary target tensor obtained in the current iteration to extract posterior information based on three-dimensional morphological operations, which is used as the saliency weight information of the model based on low-rank sparse tensor decomposition in the next iteration.

[0023] A small target detection model building module based on low-rank sparse tensor decomposition is used to construct an infrared small target detection model based on tensor nuclear norm of Framelet and Log and posterior information driven by three-dimensional morphology by using Framelet transformation and Log operator.

[0024] The optimization model solution module is used to solve the small target detection model based on low-rank sparse tensor decomposition, obtain the target tensor components, reconstruct the target detection result image, and obtain the target detection result sequence T.

[0025] The target detection result output module is used to output infrared small target detection result images.

[0026] The beneficial effects of this invention are as follows:

[0027] 1) This invention fully utilizes the spatiotemporal information carried by thermal infrared image sequences, the low-rank characteristics of background components, and the sparse characteristics of targets, and provides tensor kernel norms based on Framelet and Log that can achieve accurate background estimation. Based on this, an infrared small target detection model based on low-rank sparse tensor decomposition is established, which can effectively characterize the features of different components of infrared image data.

[0028] 2) This invention introduces a feedback mechanism in the low-rank sparse tensor decomposition model. This feedback mechanism is based on posterior knowledge driven by three-dimensional morphology. The posterior information obtained in the current iteration can effectively guide the model to pay more attention to salient targets in the next iteration, enhance the salientity of targets, and improve detection performance.

[0029] The background suppression capability, target detection capability, and overall effectiveness of the infrared small target detection method of the present invention have all been verified. Attached Figure Description

[0030] Figure 1 This is a schematic diagram of the construction of the three-dimensional spacetime tensor in this invention;

[0031] Figure 2 A schematic diagram of structural element s2 designed for this invention;

[0032] Figure 3 This is a schematic diagram of the infrared small target detection device based on posterior information according to the present invention;

[0033] Figure 4 An example frame image of a thermal infrared image sequence used for experimental testing;

[0034] Figure 5 The thermal infrared small target detection results are shown in the example frames of the thermal infrared image sequence.

[0035] Figure 6 The image shows the detection results of example frames of thermal infrared image sequences after being detected by the proposed methods: GCM, ELUM, MDWCM, METTR, IPCE, RCTVW, STT-TRNR, TSPK, and IAANet. Detailed Implementation

[0036] 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.

[0037] 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.

[0038] The basic steps of the infrared small target detection method based on posterior information of the present invention in this embodiment mainly include:

[0039] Step 1: As Figure 1 As shown, by utilizing the temporal and spatial information carried by the thermal infrared image sequence, the image frames in the thermal infrared image sequence are stacked in chronological order to construct a three-dimensional spatiotemporal tensor.

[0040] Specifically, considering that thermal infrared images carry both temporal and spatial information, a sequence containing n3 thermal infrared image frames is stacked sequentially in chronological order. t , t = 1, 2, ..., n3, are constructed into a three-dimensional spacetime tensor The size is n1×n2×n3; n1 represents The width of the front slice, n2 represents The height of the front slice, n3 represents The thickness;

[0041] In the specific embodiment, n1 and n2 are both 6, and n3 is 6;

[0042] Step 2: Based on the features of background, target, and noise components, establish a low-rank sparse tensor decomposition model;

[0043] Specifically, the three-dimensional spacetime tensor constructed in step 1) It can be viewed as a background tensor Target Tensor and noise tensor The linear combination of is shown in formula (1):

[0044]

[0045] Considering the low-rank characteristics of the background tensor and the sparse characteristics of the target tensor, the detection of small targets in thermal infrared is transformed into an optimization problem based on low-rank sparse tensor decomposition. A framework based on low-rank sparse tensor decomposition is established, as shown in Equation (2):

[0046]

[0047] Where rank(·) denotes the rank estimator, and ||·||0 represents Norm, λ represents the square of the Frobenius norm, and λ1 and λ2 represent the tradeoff coefficients;

[0048] Step 3: Define tensor nuclear norms based on Framelet and Log to perform low-rank estimation of the background;

[0049] Specifically, the background tensor Perform a Framelet transform along the third dimension (time dimension) to obtain the Framelet transform tensor. As shown in formula (3):

[0050]

[0051] Among them, the Framelet transform tensor The size is n1×n2×ωn3, where ω represents the parameters of the Framelet transform. This represents the Framelet transformation operator. Let F represent the framelet transform matrix, with size ωn³×n³. If F contains n filters and has l levels, then ω is of size 1 + l(n-1). B (3) Represents the background tensor The expansion matrix obtained by expanding in mode-3 is as follows: unfold3(·) is the pattern-3 unfold operator for tensors, resulting in the unfolded matrix B. (3) The size is n1n2×n3, B (3) Height n3 and background tensor The thickness of the third dimension is the same, B (3) The width is n1n2, which is numerically equivalent to the background tensor. The product of the first dimension length n1 and the second dimension height n2; fold3(·) is the matrix FB of size n1n2×ωn3. (3) Convert to a three-dimensional matrix of size n1×n2×ωn3 according to mode -3. Operators;

[0052] For Framelet Transform Tensors For each frontal slice, a Log operator transformation is performed on the singular values, thereby defining the tensor nuclear norm ||·|| based on Framelet and Log. FL-ITNN As shown in formula (4):

[0053]

[0054] in, express The p-th singular value of the k-th front slice, 1≤k≤ωn3, 1≤p≤P, ε0 represents a positive constant, and log(·) represents the log operator;

[0055] Step 4: Extract posterior information based on 3D morphological operations from the temporary target tensor obtained in the current iteration round, and feed it back to the target tensor in the next iteration round with weights.

[0056] Specifically, the solution process based on the low-rank sparse tensor decomposition model is an iterative process, considering the temporary target tensor obtained in the current iteration t. It is a three-dimensional spatiotemporal tensor, which extends morphological operations to the three-dimensional tensor domain to extract posterior information:

[0057] First, the top-hat transformation operation is extended from two-dimensional images to three-dimensional space to process three-dimensional tensors. By defining three-dimensional structuring elements, the three-dimensional tensor is opened, and then the difference between the three-dimensional tensor and the result after the opening operation is calculated to realize the three-dimensional top-hat transformation operation.

[0058] Design a three-dimensional unit sphere as the structuring element s1, and... Perform a 3D top-hat transformation to obtain the 3D top-hat transformation tensor for the current iteration t. As shown in formula (5):

[0059]

[0060] in, Indicates the opening operator. This represents the erosion operation operator. Indicates the dilation operator;

[0061] 3D top-hat transformation tensor Each frontal slice contains rich spatial information, such as Figure 2 As shown, design a structural element s2 with a "3×3" grid, specifically in the form of... right Perform a closing operation on each front slice to obtain the posterior information of the current iteration t. As shown in formula (6):

[0062]

[0063] Where ★ denotes the closing operator, The three-dimensional top-hat transformation tensor representing the current iteration round t The i-th frontal slice;

[0064] For posterior information For each element, calculate its reciprocal, which serves as the target weight for the low-rank sparse tensor decomposition framework (2) in step 2) at the next iteration t+1. As shown in formula (7):

[0065]

[0066] Where "←" represents the variable iteration update symbol, (·) -1 The operator represents the inverse operator for elements of a tensor, and |·| represents the absolute value operator.

[0067] To accelerate the convergence speed of the iteration, a sparse reweighting strategy is designed. The reweighted tensor of the next iteration t+1 is... The temporary target tensor obtained from the current iteration round t The result is shown in formula (8):

[0068]

[0069] Where k is a positive constant and ε2 is a positive constant;

[0070] From formulas (7) and (8), we obtain the weighted tensor of the target tensor in the next iteration t+1. As shown in formula (9):

[0071]

[0072] Where ⊙ represents the Hadamarda complex;

[0073] Step 5: Construct an infrared small target detection model based on tensor nuclear norm of Framelet and Log and posterior information driven by 3D morphology using Framelet and Log transformation and Log operator.

[0074] Specifically, combining steps 1) to 4), an infrared small target detection model based on the tensor nuclear norm of Framelet and Log and posterior information is constructed, as shown in formula (10):

[0075]

[0076] in, The weighted weight tensor represents the target tensor, and ||·||1 represents... Norm;

[0077] Step 6: Optimize the solution model based on the ADMM algorithm, obtain the target tensor components, and reconstruct the target detection result image to obtain the target detection result sequence T, thereby realizing the detection of small thermal infrared targets;

[0078] Specifically, the alternating direction multiplier method is used to solve the infrared small target detection model (10) based on the nuclear norm and posterior information in step 5). To make model (10) solvable, the Framelet transformation tensor is introduced. Auxiliary variables Therefore, formula (11) is obtained as follows:

[0079]

[0080] Formula (11) corresponds to the variable augmented Lagrange function for

[0081]

[0082] Where μ represents the penalty coefficient. and Represents the Lagrange multipliers.

[0083] The solution process of formula (12) is decomposed into several sub-problems, and the variables are updated alternately:

[0084] 1) - Subproblem

[0085] By fixing the other parameters in the t-th iteration, the variables in the (t+1)-th iteration are updated iteratively. The calculation formula is

[0086]

[0087] Here, argmin represents the parameter value at which the function achieves its minimum value in its domain. Represents the (t+1)th iteration

[0088]

[0089] Where "←" represents the variable iteration update symbol. Tensor The transpose of , * denotes the tensor product operator, Tensor Let D denote the singular value tensor of the singular value contraction operator; let Tensor The element at index (i, j, k) is given, where ε represents a positive constant. If a² > 0, then... If a2 < 0, then Indicates according to tensor Perform a Fast Fourier Transform on the third dimension. Indicates according to tensor If we perform an inverse fast Fourier transform on the third dimension, then we have

[0090]

[0091] 2) - Subproblem

[0092] With other parameters fixed during the t-th iteration, the iteration updates yield the result for the (t+1)-th iteration. The calculation formula is

[0093]

[0094] in, Represents the (t+1)th iteration

[0095]

[0096] in, Represent tensors respectively According to the corresponding matrix after expansion in Mode-3, F represents the Framelet transformation matrix.

[0097] The solution formula for formula (16) is as follows:

[0098]

[0099] According to the properties of UEP, Then we have:

[0100]

[0101] Here, fold3(·) represents the operator that converts a matrix into a three-dimensional matrix according to pattern -3;

[0102] 3) - Subproblem

[0103] With other parameters fixed during the t-th iteration, the iteration updates are used to obtain the parameters for the (t+1)-th iteration. The calculation formula is:

[0104]

[0105] in, Represents the (t+1)th iteration Th (·) (·) represents the soft threshold shrinkage operator, Th (τ) (x) = sign(x)·max(|x|-τ,0), where sign(·) is the sign function and τ is the soft threshold;

[0106] 4) - Subproblem

[0107] With other parameters fixed during the t-th iteration, the iteration updates are used to obtain the parameters for the (t+1)-th iteration. The calculation formula is:

[0108]

[0109] in, Represents the (t+1)th iteration

[0110] 5) - Subproblem

[0111] The iterative formula is

[0112]

[0113]

[0114]

[0115] in, They represent the (t+1)th iteration.

[0116] 6) Lagrange multiplier-subproblem

[0117] Lagrange multipliers and The iterative formula is

[0118]

[0119]

[0120] in, They represent the (t+1)th iteration.

[0121] 7) Penalty Item - Subproblem

[0122] The iterative formula for the penalty term μ is:

[0123] μ (t+1) ←min(γμ (t) μ max (26)

[0124] Where, μ (t+1) Let μ and γ represent the update coefficients in the (t+1)th iteration, respectively. max This represents the maximum value of μ;

[0125] In the specific implementation, k is set to 1, and λ2 = 20λ1. λ L =3, μ max =100, γ=1.2, μ (0) =0.01,

[0126] During the iteration process, when the relative error The iteration terminates when the error δ = 0.0001 is less than the target tensor. When the norm stops changing, stop iterating.

[0127] Furthermore, the target tensor is extracted sequentially. For each frontal slice, n3 target detection result images T are obtained, realizing thermal infrared small target detection.

[0128] Corresponding to the aforementioned embodiment of an infrared small target detection method based on posterior information, the present invention also provides an embodiment of an infrared small target detection device based on posterior information.

[0129] Figure 3 This is a block diagram illustrating an infrared small target detection device based on posterior information according to an exemplary embodiment, such as... Figure 3 As shown, the device includes:

[0130] The infrared image module is reconstructed by stacking the image frames in the original infrared image sequence in chronological order to construct a three-dimensional spatiotemporal tensor, which lays the data foundation for the subsequent establishment of a low-rank sparse tensor decomposition model.

[0131] The low-rank sparse decomposition framework building module establishes a model based on low-rank sparse tensor decomposition based on the features of background, target, and noise.

[0132] The low-rank background estimation module utilizes the Framelet transform and the Log operator to define a tensor nuclear norm based on Framelet and Log for accurate estimation of low-rank background.

[0133] The posterior information extraction module uses the temporary target tensor obtained in the current iteration to extract posterior information based on three-dimensional morphological operations, which is used as the saliency weight information of the model based on low-rank sparse tensor decomposition in the next iteration.

[0134] A small target detection model building module based on low-rank sparse tensor decomposition is used to construct an infrared small target detection model based on tensor nuclear norm of Framelet and Log and posterior information driven by three-dimensional morphology by using Framelet transformation and Log operator.

[0135] The optimization model solution module is used to solve the small target detection model based on low-rank sparse tensor decomposition, obtain the target tensor components, reconstruct the target detection result image, and obtain the target detection result sequence T.

[0136] The target detection result output module is used to output infrared small target detection result images.

[0137] 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.

[0138] 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.

[0139] Example

[0140] 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.

[0141] In this embodiment, the effectiveness of the thermal infrared small target detection algorithm will be verified using a publicly available infrared image sequence. Qualitatively, the target detection result of an instance frame from the infrared image sequence will be evaluated; quantitatively, the performance of the infrared small target detection method will be evaluated 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, which are described in detail below:

[0142] 1) Target detection capability (TD):

[0143] AUC (D,τ) For (P) D The AUC value of the curve (τ) characterizes the target detection capability of the detector:

[0144] 0≤AUC (D,τ) ≤1

[0145] AUC TD Joint detection capability of detectors:

[0146] 0≤AUC TD =AUC (D,F) +AUC (D,τ) )≤2

[0147] 2) Background suppression ability (BS)

[0148] AUC (F,τ) Indicates (P) D The AUC value of the (τ) curve is used to characterize the background suppression capability of the detector.

[0149] 0≤AUC (F,τ) ≤1

[0150] AUC BS Used to characterize the joint background suppression capability of the detector

[0151] -1≤AUC BS =AUC (D,F) -AUC (F,τ) )≤1

[0152] AUC SNPR Used to characterize the signal-to-noise ratio of the detector

[0153]

[0154] 3) Overall effectiveness of the detector

[0155] AUC TDBS Integrated target detection and background suppression capabilities for detectors

[0156] -1≤AUC TDBS =AUC (D,τ) -AUC (F,τ) )≤1

[0157] AUC (D,F) Used to characterize (P) D ,P F The AUC value of the curve characterizes the effectiveness of the detector.

[0158] 0≤AUC (D,F) ≤1

[0159] AUC ODP Used to characterize the total detection probability of the detector

[0160] -1≤AUC ODP =AUC (D,F) +AUC (D,τ) -AUC (F,τ) ≤2

[0161] For a publicly available online sequence of 110 real thermal infrared images, with each frame measuring 256×256, the image presents a complex air-to-ground background containing bright route structures, blocky ground structures, and distinct forest structures. Small targets move slowly and are easily obscured by background clutter and noise. Figure 4 Here is an example frame from this infrared image sequence. Figure 5 The product obtained by the method of this invention Figure 4 The example frame corresponds to the target detection result image. The detection result image shows that the method proposed in this invention can completely suppress background and noise components and significantly enhance small targets. To quantitatively evaluate the effectiveness of the proposed algorithm, Table 1 presents the 3D-ROC evaluation system metrics for small target detection results using GCM, ELUM, MDWCM, METTR, IPCE, RCTVW, STT-TRNR, TSPK, IAANet, and the method proposed in this invention, respectively. Bold and underlined values ​​represent the corresponding optimal and second-best AUC values, respectively. GCM, ELUM, and MDWCM are small target detection algorithms based on local contrast measurement; METTR, IPCE, RCTVW, STT-TRNR, and TSPK are small target detection algorithms based on low-rank sparse decomposition; and IAANet is a deep learning-based small target detection algorithm.

[0162] The source of the above comparison algorithm is as follows:

[0163] GCM comes from Y.Tang, K.Xiong and C.Wang, "Fast Infrared Small TargetDetection Based on Global Contrast Measure Using Dilate Operation," in IEEEGeoscience and Remote Sensing Letters, vol.20, pp.1-5, 2023, Art no.8000105, doi:10.1109 / LGRS.2023.3233958.

[0164] ELUM comes from E.Zhao, W.Zheng, M.Li, H.Sun and J.Wang, "Infrared Small TargetDetection Using Local Component Uncertainty Measure With ConsistencyAssessment," in IEEE Geoscience and Remote Sensing Letters, vol.19, pp.1-5, 2022, Art no.6518205,doi:10.1109 / LGRS.2022.3221088.

[0165] 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," in IEEE Geoscience and Remote Sensing Letters, vol. 19, pp. 1 - 5, 2022, Art no. 7000105, doi: 10.1109 / LGRS.2020.3026546.

[0166] METTR is from Cao, Zhaoyang, et al. "Infrared dim target detection via mode-k1k2 extension tensor tubal rank under complex ocean environment." ISPRS Journal of Photogrammetry and Remote Sensing, vol. 181, pp. 167 - 190, 2021, doi: 10.1016 / j.isprsjprs.2021.09.007.

[0167] IPCE is from C. Zhang, Y. He, Q. Tang, Z. Chen and T. Mu, "Infrared Small Target Detection via Interpatch Correlation Enhancement and Joint Local Visual Saliency Prior," in IEEE Transactions on Geoscience and Remote Sensing, vol. 60, pp. 1 - 14, 2022, Art no. 5001314, doi: 10.1109 / TGRS.2021.3128189.

[0168] RCTVW is from T. Liu, J. Yang, B. Li, Y. Wang and W. An, "Representative Coefficient Total Variation for Efficient Infrared Small Target Detection," in IEEE Transactions on Geoscience and Remote Sensing, vol. 61, pp. 1 - 18, 2023, Art no. 5622918, doi: 10.1109 / TGRS.2023.3324821.

[0169] STT - TRNR is from H. Yi et al., "Spatial - Temporal Tensor Ring Norm Regularization for Infrared Small Target Detection," in IEEE Geoscience and Remote Sensing Letters, vol. 20, pp. 1 - 5, 2023, Art no. 7000205, doi: 10.1109 / LGRS.2023.3236030.

[0170] TSPK is from D. Pang, P. Ma, Y. Feng, T. Shan, R. Tao and Q. Jin, "Tensor Spectral k - Support Norm Minimization for Detecting Infrared Dim and Small Target Against Urban Backgrounds," in IEEE Transactions on Geoscience and Remote Sensing, vol. 61, pp. 1 - 13, 2023, Art no. 5002513, doi: 10.1109 / TGRS.2023.3277848.

[0171] IAANet comes from K.Wang, S.Du, C.Liu and Z.Cao, "Interior Attention-AwareNetwork for Infrared Small Target Detection," in IEEE Transactions onGeoscience and Remote Sensing, vol.60, pp.1-13, 2022, Art no.5002013, doi:10.1109 / TGRS.2022.3163410.

[0172] Table 1. Quantitative indicators of the detection results of thermal infrared image example sequences using GCM, ELUM, MDWCM, METTR, IPCE, RCTVW, STT-TRNR, TSPK, IAANet, and the proposed method.

[0173] This invention 1.0000 0.9960 3.3099e-6 1.9960 1.0000 3.0091e5 0.9960 1.9960 GCM 1.0000 0.9849 1.1589e-3 1.9849 <![CDATA[ 0.9988 ]]> 8.4992e2 0.9838 1.9838 ELUM 1.0000 0.9887 1.8582e-3 <![CDATA[ 1.9887 ]]> 0.9981 5.3204e2 0.9868 <![CDATA[ 1.9868 ]]> MDWCM 0.6269 0.0368 9.3947e-5 0.6637 0.6268 3.9132e2 0.0367 0.6636 METTR 1.0000 0.9873 1.7057e-1 1.9873 0.8294 5.7882 0.8167 1.8167 IPCE 0.4000 0.3412 5.7503e-5 0.7412 0.3999 5.9336e3 0.3411 0.7411 RCTVW <![CDATA[ 0.9909 ]]> <![CDATA[ 0.9905 ]]> <![CDATA[ 1.0128e-5 ]]> 1.9815 0.9909 <![CDATA[ 9.7803e4 ]]> <![CDATA[ 0.9905 ]]> 1.9814 STT-TRNR 0.9264 0.9188 7.5529e-2 1.8452 0.8508 1.2165e1 0.8433 1.7697 TSPK 0.9727 0.9727 1.4248e-3 1.9455 0.9713 6.8269e2 0.9713 1.9440 IAANet 0.9632 0.9482 2.1999e-3 1.9114 0.9610 4.3100e2 0.9460 1.9092

[0174] Figure 6 The image shows the small target detection results of a thermal infrared image example frame after being processed by the present invention, GCM, ELUM, MDWCM, METTR, IPCE, RCTVW, STT-TRNR, TSPK, and IAANet. The small target detection results qualitatively reflect that the contrastive methods have weak background suppression capabilities, and residual background components still exist, especially with IAANet, TSPK, and METTR. Figure 6 It has been found that GCM and RCTVW are susceptible to background clutter; furthermore, IPCE has insufficient target detection capability, easily leading to target loss. In contrast, the method proposed in this invention exhibits superior target detection and background suppression capabilities. Qualitative comparative analysis shows that the proposed method achieves optimal values ​​on eight 3D-ROC evaluation systems, reflecting that its background suppression capability, target enhancement capability, and overall performance are superior to the latest existing infrared small target detection methods. Combining qualitative and quantitative analysis, the thermal infrared small target detection method proposed in this invention demonstrates excellent target detection capability, background suppression capability, and overall effectiveness.

[0175] 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 posterior information, characterized in that, Includes the following steps: Step 1): Utilizing the temporal and spatial information carried by the thermal infrared image sequence, stack the image frames in the thermal infrared image sequence in chronological order to construct a three-dimensional spatiotemporal tensor. Step 2): Based on the features of the background, target, and noise components, establish a model based on low-rank sparse tensor decomposition; Step 3): Define the tensor nuclear norm based on Framelet and Log to perform low-rank estimation of the background; Step 4): During the iterative solution of the model based on low-rank sparse tensor decomposition, the posterior information based on three-dimensional morphological operations is extracted from the temporary target tensor obtained in the current iteration round and used as the saliency weight information of the model based on low-rank sparse tensor decomposition in the next iteration round. Step 5): Using Framelet transform and Log operator, construct an infrared small target detection model based on tensor nuclear norm of Framelet and Log and posterior information driven by three-dimensional morphology. Step 6): Based on the ADMM algorithm, optimize and solve the model in step 5), obtain the target tensor components, reconstruct the target detection result image, and obtain the target detection result sequence T to realize thermal infrared small target detection.

2. The infrared small target detection method based on posterior information according to claim 1, characterized in that, Step 1) specifically refers to: Considering that thermal infrared images carry both temporal and spatial information, a sequence containing n3 thermal infrared image frames is stacked sequentially in chronological order. t For t = 1, 2, ..., n3, construct a three-dimensional spacetime tensor. The size is n1×n2×n3, where n1 represents The width of the front slice, n2 represents The height of the front slice.

3. The infrared small target detection method based on posterior information according to claim 1, characterized in that, Step 2) specifically refers to: The three-dimensional spacetime tensor constructed in step 1) Treat as background tensor Target Tensor and noise tensor The linear combination of is shown in formula (1): Considering the low-rank characteristics of the background tensor and the sparse characteristics of the target tensor, the detection of small targets in thermal infrared is transformed into an optimization problem based on low-rank sparse tensor decomposition. A model based on low-rank sparse tensor decomposition is established, as shown in Equation (2): Where rank(·) denotes the rank estimator, and ||·||0 represents Norm, Let λF denote the square of the Frobenius norm, and λ1 and λ2 denote the weighting coefficients.

4. The infrared small target detection method based on posterior information according to claim 1, characterized in that, Step 3) specifically refers to: background tensor Perform a Framelet transform along the time dimension to obtain the Framelet transform tensor. As shown in formula (3): Among them, the Framelet transform tensor The size is n1×n2×ωn3, where ω represents the parameters of the Framelet transform. This represents the Framelet transformation operator. Let F represent the framelet transform matrix, with size ωn³×n³. If F contains n filters and has l levels, then ω is of size 1 + l(n-1). (3) This represents the expanded matrix obtained by expanding the background tensor in mode-3, and fold3(·) represents the operator that converts the matrix into a three-dimensional matrix in mode-3. For Framelet Transform Tensors For each frontal slice, a Log operator transformation is performed on the singular values, thereby defining the tensor nuclear norm ||·|| based on Framelet and Log. FL-ITNN As shown in formula (4): in, express The p-th singular value of the k-th front slice, 1≤k≤ωn3, 1≤p≤P, where P represents the total number of singular values, ε0 represents a positive constant, and log(·) represents the log operator.

5. The infrared small target detection method based on posterior information according to claim 1, characterized in that, Step 4) specifically refers to: The solution process based on the low-rank sparse tensor decomposition model is an iterative process, considering the temporary target tensor obtained in the current iteration t. It is a three-dimensional spatiotemporal tensor, which extends morphological operations to the three-dimensional tensor domain to extract posterior information: First, design a three-dimensional unit sphere as the structuring element s1, and then... Perform a 3D top-hat transformation to obtain the 3D top-hat transformation tensor for the current iteration t. As shown in formula (5): in, Indicates the opening operator. This represents the erosion operation operator. Indicates the dilation operator; 3D top-hat transformation tensor Each frontal slice contains rich spatial information. A structural element s2 with a "3×3" grid is designed, specifically in the form of... right Perform a closing operation on each front slice to obtain the posterior information of the current iteration t. As shown in formula (6): Where ★ denotes the closing operator. The three-dimensional top-hat transformation tensor representing the current iteration round t The i-th frontal slice; For posterior information For each element, calculate its reciprocal, which serves as the target weight for model (2) based on low-rank sparse tensor decomposition in step 2) in the next iteration round t+1. As shown in formula (7): Where "←" represents the variable iteration update symbol, (·) -1 The operator represents the inverse operator for elements of a tensor, and |·| represents the absolute value operator. To accelerate the convergence speed of the iteration, a sparse reweighting strategy is designed. The reweighted tensor of the next iteration t+1 is... The temporary target tensor obtained from the current iteration round t The result is shown in formula (8): Where k is a positive constant and ε2 is a positive constant; From formulas (7) and (8), we obtain the weighted tensor of the target tensor in the next iteration t+1. As shown in formula (9): Where ⊙ represents the Hadamarda.

6. The infrared small target detection method based on posterior information according to claim 1, characterized in that, Step 5) specifically refers to: Combining steps 1) to 4), an infrared small target detection model based on the tensor nuclear norm of Framelet and Log and posterior information is constructed, as shown in formula (10): in, The weighted weight tensor represents the target tensor, and ||·||1 represents... Norm.

7. The infrared small target detection method based on posterior information according to claim 6, characterized in that, Step 6) is specifically as follows: The infrared small target detection model (10) based on the nuclear norm and posterior information in step 5) is solved using the alternating direction multiplier method. To make model (10) solvable, the Framelet transform tensor is introduced. Auxiliary variables Therefore, formula (11) is obtained as follows: Formula (11) corresponds to the variable augmented Lagrange function for Where μ represents the penalty coefficient. and Represents the Lagrange multipliers. The solution process of formula (12) is decomposed into several sub-problems, and the variables are updated alternately: 1) - Subproblem By fixing the other parameters in the t-th iteration, the variables in the (t+1)-th iteration are updated iteratively. The calculation formula is: Here, argmin represents the parameter value at which the function achieves its minimum value in its domain. Represents the (t+1)th iteration Where "←" represents the variable iteration update symbol, Tensor The transpose of , * denotes the tensor product operator, Tensor Let D denote the singular value tensor of the singular value contraction operator; let Tensor The element at index (i, j, k) is given, where ε represents a positive constant. If a2 > 0, then... If a2 < 0, then Indicates according to tensor Perform a Fast Fourier Transform on the third dimension. Indicates according to tensor If we perform an inverse fast Fourier transform on the third dimension, then we have 2) - Subproblem With other parameters fixed during the t-th iteration, the iteration updates are used to obtain the parameters for the (t+1)-th iteration. The calculation formula is: in, Represents the (t+1)th iteration in, Represent tensors respectively According to the corresponding matrix after expansion in Mode-3, F represents the Framelet transformation matrix. The solution formula for formula (16) is as follows: According to the properties of UEP, Then we have: Here, fold3(·) represents the operator that converts a matrix into a three-dimensional matrix according to pattern -3; 3) - Subproblem With other parameters fixed during the t-th iteration, the iteration updates are used to obtain the parameters for the (t+1)-th iteration. The calculation formula is: in, Represents the (t+1)th iteration Th (.) (·) denotes the soft threshold shrinkage operator, Th (τ) (x) = sign(x)·max(|x|-τ,0), where sign(·) is the sign function and τ is the soft threshold; 4) - Subproblem With other parameters fixed during the t-th iteration, the iteration updates are used to obtain the parameters for the (t+1)-th iteration. The calculation formula is: in, Represents the (t+1)th iteration 5) - Subproblem The iterative formula is in, They represent the (t+1)th iteration. 6) Lagrange multiplier-subproblem Lagrange multipliers and The iterative formula is in, They represent the (t+1)th iteration. 7) Penalty Item - Subproblem The iterative formula for the penalty term μ is: m (t+1) ←min(gm (t) ,m max ) (26) Where, μ (t+1) Let μ and γ represent the update coefficients in the (t+1)th iteration, respectively. max This represents the maximum value of μ; During the iteration process, when the relative error The iteration terminates when the error is less than δ; when the target tensor When the norm stops changing, stop iterating. Furthermore, the target tensor is extracted sequentially. For each frontal slice, n3 target detection result images T are obtained, realizing thermal infrared small target detection.

8. An infrared small target detection device based on posterior information implementing the method of claim 1, characterized in that, include: The infrared image module is reconstructed by stacking the image frames in the original infrared image sequence in chronological order to construct a three-dimensional spatiotemporal tensor, which lays the data foundation for the subsequent establishment of a low-rank sparse tensor decomposition model. The low-rank sparse decomposition framework building module establishes a model based on low-rank sparse tensor decomposition based on the features of background, target, and noise. The low-rank background estimation module utilizes the Framelet transform and the Log operator to define a tensor nuclear norm based on Framelet and Log for accurate estimation of low-rank background. The posterior information extraction module uses the temporary target tensor obtained in the current iteration to extract posterior information based on three-dimensional morphological operations, which is used as the saliency weight information of the model based on low-rank sparse tensor decomposition in the next iteration. A small target detection model building module based on low-rank sparse tensor decomposition is used to construct an infrared small target detection model based on tensor nuclear norm of Framelet and Log and posterior information driven by three-dimensional morphology by using Framelet transformation and Log operator. The optimization model solution module is used to solve the small target detection model based on low-rank sparse tensor decomposition, obtain the target tensor components, reconstruct the target detection result image, and obtain the target detection result sequence T. The target detection result output module is used to output infrared small target detection result images.

Images