Infrared Dim Target Detection Based on Sparse Enhanced Reweighting and Mask Patch-tensor
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摘要: 高度异构的复杂背景破坏了场景的低秩性，现有算法难以利用低秩稀疏恢复方法从背景中分离出小目标。为了解决上述问题，本文将小目标检测问题转化为张量模型的凸优化函数求解问题，提出基于稀疏增强重加权与掩码块张量的检测模型。首先，将掩码块图像以堆叠方式扩展至张量空间，并构建掩码块张量模型以筛选候选目标。在此基础上，利用结构张量构建稀疏增强重加权模型以抑制背景杂波，克服凸优化函数求解过程中设定加权参数的缺陷。实验表明本文检测算法在背景抑制因子及信杂比增益两方面都优于新近代表性算法，证明该算法的有效性。Abstract: The high heterogeneity of complex backgrounds destroys the low rank of a scene, and it is difficult for existing algorithms to use low-rank sparse recovery methods to separate dim targets from the background. To resolve this problem, this study transforms the dim target detection problem into a convex optimization function-solving problem for tensor models. It proposes a detection model based on sparsely enhanced reweighting and mask patch tensors. First, the stacked mask patch image was expanded into a tensor space, and a mask patch-tensor model was constructed to filter the candidate targets. Thus, a sparse enhanced reweighting model was constructed using structural tensors to suppress background clutter, and the limitation of setting the weighting parameters can be overcome by solving convex optimization functions. The experiments show that the proposed algorithm outperforms recent representative algorithms regarding the background suppression factor and signal-to-noise ratio gain, demonstrating its effectiveness.
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图 2 红外目标检测掩码图及三维结果显示图
(a)红外图像；(b)红外掩码图（红框内包含候选目标）；(c)掩码图的三维显示图；(d)检测结果图；(e)检测结果三维显示图
Figure 2. Infrared target detection mask diagram and three-dimensional result display diagram
(a) Infrared image; (b) Infrared mask image (candidate targets are included in the red box); (c) 3-D display of the mask image; (d) Detection result image; (e) 3-D display of the detection result
图 3 惩罚加权函数的检测结果对比。(a)红外图像；(b)原始图像的全局三维显示图；(c)指数型；(d)二次幂倒数型；(e)一次幂倒数型；(f)本文提出惩罚加权函数
Figure 3. Comparison of the detection results of the penalty weighting function. (a) Infrared image; (b) The global three -dimensional display of the original image; (c)Index; (d) Two -time dumplings; (e) Disposal type; (f)Proposed
表 1 本文算法流程
Table 1. Algorithm flow in this paper
1: Input an infrared image fF, and set relevant parameters λ, L＝1, h＝10, ε＝0.01, N, $ {W_{LS}} $; 2: Initialization: ${{\overset{\rightharpoonup }{\mathop{T}}} ^0}$＝y0＝0, ${{\overset{\rightharpoonup }{\mathop{B}}} ^0}$＝${\overset{\rightharpoonup }{\mathop{F}}} $, ${W_S}$＝1, k＝0, ${W^0} = {W_{{\text{LS}}}} \odot W_{\text{S}}^o$, μ＝5⋅std(vec(${\overset{\rightharpoonup }{\mathop{F}}} $)), i＝1, …, N; 3: Generate filtered image fDOG through DOG bandpass filter. 4: Obtain the mask image fmask according to cumulative distribution function of fDOG. 5: Building patch-tensor ${\overset{\rightharpoonup }{\mathop{F}}} $ according to 3-D stacking of patch images. 6: Compute the local structural weight $ {W_{LS}} $ of infrared image fF according to equation (7). 7: Update : $ {{\overset{\rightharpoonup }{\mathop{B}}} ^{k + 1}} = {{\overset{\rightharpoonup }{\mathop{T}}} _\mu }({\overset{\rightharpoonup }{\mathop{F}}} + \mu {y^k} - {\varepsilon ^k}) $. 8: Update: $ {{\overset{\rightharpoonup }{\mathop{T}}} ^{k + 1}} = {S_{\mu \lambda {W^k}}}({\overset{\rightharpoonup }{\mathop{F}}} + \mu {y^k} - {{\overset{\rightharpoonup }{\mathop{B}}} ^{k + 1}}) $. 9: Update: $ {y^{k + 1}} = {y^k} + ({\overset{\rightharpoonup }{\mathop{F}}} - {{\overset{\rightharpoonup }{\mathop{B}}} ^{k + 1}} - {{\overset{\rightharpoonup }{\mathop{T}}} ^{k + 1}})\mu _{_k}^{ - 1} $. 10: Calculate the sparse enhancement weight $ {W_{LS}} $ of the infrared image fF according to equation (8). 11: Update: $ {W^{k + 1}} = {W_{{\text{LS}}}} \odot {W_{\text{S}}}^{k + 1} $. 12: Separate targets ${{\overset{\rightharpoonup }{\mathop{T}}} ^k}$ and background $ {{\overset{\rightharpoonup }{\mathop{B}}} ^k} $ according to equation (10). 13: Restore target patch-tensor ${{\overset{\rightharpoonup }{\mathop{T}}} ^k}$ and background patch-tensor $ {{\overset{\rightharpoonup }{\mathop{B}}} ^k} $ to target image fT and background image fB. 14: Segment the target by the adaptive threshold method. 
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表 3 1~10组检测结果的定量比较
Table 3. Quantitative comparison of detection results of 1-10 groups
Methods IPI NIPPS NRAM PSTNN SMSL TV-PCP Tophat MLCM IAANet Ours Group 1 SCRG Inf Inf Inf Inf 84.88 89.61 121.78 Inf Inf Inf BSF Inf Inf Inf Inf 0.99 4.89 8.28 Inf Inf Inf Group 2 SCRG 0.08 0.10 Inf Inf 1.28 1.26 0.96 Inf 0.18 Inf BSF 2.10 13.95 Inf Inf 2.41 3.52 6.78 Inf 0.90 Inf Group 3 SCRG 7.87 0.11 Inf Inf 1.24 1.24 0.56 0.25 10.05 Inf BSF 1.36 25.26 Inf Inf 1.13 0.34 13.10 0.49 0.78 Inf Group 4 SCRG 0.21 Inf 0.52 0.46 1.11 0.62 1.13 0.45 0.34 Inf BSF 0.56 Inf 0.22 0.23 0.96 0.24 8.59 0.23 0.32 Inf Group 5 SCRG 1.14 0.26 Inf Inf 1.08 1.14 2.15 Inf Inf Inf BSF 2.78 22.11 Inf Inf 1.37 1.49 28.48 Inf Inf Inf Group 6 SCRG 0.90 0.13 0.17 0.76 0.47 2.39 3.23 0.85 0.89 Inf BSF 0.85 181.59 3.70 0.85 3.94 52.92 32.28 2.76 0.70 Inf Group 7 SCRG 0.78 Inf Inf Inf 0.78 0.52 0.37 Inf Inf Inf BSF 2.03 Inf Inf Inf 1.67 1.40 10.99 Inf Inf Inf Group 8 SCRG 1.81 0.13 4.26 2.00 1.09 0.39 1.26 Inf 2.08 0.02 BSF 1.36 2.57 2.73 1.33 1.53 7.64 15.56 Inf 0.72 6.79 Group 9 SCRG 1.11 Inf Inf Inf 1.12 1.12 1.28 1.30 Inf Inf BSF 6.71 Inf Inf Inf 5.10 9.11 0.30 0.30 Inf Inf Group 10 SCRG 0.52 0.03 3.20 Inf 1.02 1.03 0.12 0.09 Inf Inf BSF 2.77 730.01 729.98 Inf 8.64 40.57 114.37 1.04 Inf Inf Note: Inf represents infinity.
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