The Multi-domain Union Clutter Suppression Algorithm Based on Robust Principal Component Analysis
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摘要: 奇异值分解等传统算法在处理穿墙成像中的杂波抑制问题时，杂波消除不够彻底，目标成像质量不高，严重影响后续的目标检测与识别。为解决这一问题，该文基于鲁棒主成分分析理论，在回波域和图像域分别建立联合低秩稀疏模型，以光滑化快速交替线性化(SFAL)方法来求解模型，并对目标图像进行指数加权联乘多域图像融合处理，从而得到最终成像结果。仿真结果表明，该算法速度快、精度高，可有效改善目标成像质量，并能较好地满足穿墙成像的实时性和准确性要求。Abstract: In through-the-wall imaging, the clutter can not be eliminated completely through traditional algorithms, and affects seriously the subsequent target detection and recognition. To solve the problem, based on robust principal component analysis theory, a joint low-rank and sparse model is established in echo and image domain respectively. The models are solved by Smoothing Fast Alternating Linearization (SFAL) method. Then, the target images are dealt with exponentially weighted multiply multi-domain image fusion to obtain the final image. The simulation results indicate that the algorithm has great speed and accuracy with effective improvement on imaging quality of targets.
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表 1 SFAL方法
输入：2维图像矩阵$ {\mathbf{I}} \in {{\mathbf{R}}^{P \times Q}} $，凸函数$f({\mathbf{x}}) = {\left\| {\mathbf{x}} \right\|_ * }$，凸函数$ g({\mathbf{x}}) = \gamma {\left\| {{\mathbf{I}} - {\mathbf{x}}} \right\|_1} $，正则化参数$ \gamma = 1/\sqrt {\max (P,Q)} $； 输出：杂波分量矩阵${ {\mathbf{I} }_{\text{w} } } = { {\mathbf{x} }^{k{{ - } }1} }$，目标分量矩阵${ {\mathbf{I} }_{ {\text{tg} } } } = {\mathbf{I} } - { {\mathbf{x} }^{k{{ - } }1} }$。 (1) 初始化参数：$\alpha = \beta = {10^{ - 6}}$,$ {{\mathbf{x}}^0} = {{\mathbf{y}}^0} = {{\mathbf{z}}^1} = 0 $, $ {\mu _f} = {\mu _g} = 1 $, ${\eta _1} = 1$；$k = 1$。 (2) 根据式(12)和式(14)进行光滑化处理。 (3) 迭代解未收敛时执行步骤(4)到(7) (4) 根据式(18)和式(19)进行交替迭代； (5) 根据式(20)更新$\eta $； (6) 根据式(21)更新${\mathbf{z}}$； (7) $k \leftarrow k + 1$ (8) 结束循环 
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表 2 各方法性能对比
算法类型 SFAL APG EALM IALM 目标杂波比(dB) 12.15 11.22 11.95 11.27 迭代次数(次) 8 163 13 39 迭代时间(s) 0.1327 1.4603 8.3925 0.5512
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表 3 各情况下的目标杂波比(dB)
原始回波
成像多域联合
成像背景对消
成像SVD算法
成像目标杂波比 3.89 25.21 16.27 13.17 较原始成像改善 0 21.32 12.38 9.28
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