基于图信号处理的大口径阵面测量数据恢复
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摘要
针对热载荷和器件老化等因素造成空间大口径阵列上的测量传感器失效问题,提出大口径阵面测量数据恢复方法。根据图信号模型得到测量数据的图拉普拉斯矩阵,并基于矩阵填充理论建立了数据恢复模型,采用交替迭代方法求解对应的正则化优化问题。利用阵列的图结构特性,能够在存在单元失效和非均匀误差情况下高精度恢复测量数据。仿真验证了所提方法的有效性以及在失效率较大情况下的稳健性。
The thermal load and the element aging can lead to the failure of the measurement sensors in the large aperture array.This paper proposes a method for recovering measurement data.We first obtain the graph signal model and the graph Laplacian matrix.Then the data recovery model is established based on the matrix completion method.Finally,the regularization optimization problem is solved by alternating iteration.The proposed method can make use of the characteristics of the array graph structure and reach a high precision for the restored results in case of element failure and non-uniform errors.The simulation verifies the effectiveness and the robustness in the condition of a large failure rate.
The thermal load and the element aging can lead to the failure of the measurement sensors in the large aperture array.This paper proposes a method for recovering measurement data.We first obtain the graph signal model and the graph Laplacian matrix.Then the data recovery model is established based on the matrix completion method.Finally,the regularization optimization problem is solved by alternating iteration.The proposed method can make use of the characteristics of the array graph structure and reach a high precision for the restored results in case of element failure and non-uniform errors.The simulation verifies the effectiveness and the robustness in the condition of a large failure rate.
引文
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[3]WANG H S C.Performance of phased-array antennas with mechanical errors[J].IEEE Trans.on Aerospace and Electronic Systems,1992,28(2):535-545.
[4]ZAITSEV E,HOFFMAN J.Phased array flatness effects on antenna system performance[C]∥Proc.of the International Symposium on Phased Array Systems and Technology,2010:121-125.
[5]MCWATTERS D,FREEDMAN A,MICHEI T,et al.Antenna auto-calibration and metrology for the AFRL/JPL space based radar[C]∥Proc.of the Radar Conference,2004:21-26.
[6]PETERMAN D,JAMES K,GLAVAC V.Distortion measurement and compensation in a synthetic aperture radar phasedarray antenna[C]∥Proc.of the International Symposium on Antenna Technology and Applied Electromagnetics and the American Electromagnetics Conference,2010:1-5.
[7]TAKAHASHI T,NAKAMOTO N,OHTSUKA M,et al.On-board calibration methods for mechanical distortions of satellite phased array antennas[J].IEEE Trans.on Antennas and Propagation,2012,60(3):1362-1372.
[8]PITZ W,MILLER D.The TerraSAR-X satellite[J].IEEETrans.on Geoscience and Remote Sensing,2010,48(2):615-622.
[9]施法中.计算机辅助几何设计与非均匀有理B样条[M].北京:高等教育出版社,2001.SHI F Z.Computer-aided geometric design and the non-uniform rational B-spline curves and surfaces[M].Beijing:Higher Education Press,2001.
[10]SHAHID N,PERRAUDIN N,KALOFOLIAS V,et al.Fast robust PCA on graphs[J].IEEE Journal of Selected Topics in Signal Processing,2016,10(4):740-756.
[11]MICHAEL B,JOAN B,YANN L,et al.Geometric deep learning going beyond Euclidean data[J].IEEE Signal Processing Magazine,2017,34(4):18-42.
[12]CAI J F,CANDES E J,SHEN Z W.A singular value thresholding algorithm for matrix completion[J].SIAM Journal on Optimization,2008,20(4):1956-1982.
[13]GOLDFARB D,MA S.Convergence of fixed-point continuation algorithms for matrix rank minization[M].New York:Springer Verlag,2011.
[14]LIN Z,CHEN M,MA Y.The augmented Lagrange multiplier method for exact recovery of corrupted low rank matrices[J].Eprint Arxiv,2010,9.
[15]CANDES E J,PLAN Y.Matrix completion with noise[J].Proceedings of the IEEE,2010,98(6):925-936.
[16]MA H,ZHOU D,LIU C,et al.Recommender system with social regularization[C]∥Proc.of the Web Search and Data Mining,2011:287-296.
[17]KALOFOLLAS V,BRESSON X,BRONSTEIN M,et al.Matrix completion on graphs[EB/OL].[2018-04-25].http:∥arxiv.org/abs/1408.1717v3.
[18]NARANG,SUNIL K,ORTEGA,et al.The emerging field of signal processing on graphs[J].IEEE Signal Processing Magazine,2013,30(3):83-98.
[19]CANDES E J,LI X,MA Y,et al.Robust principal component analysis[J].Journal of the ACM,2011,58(3):1-37.
[20]BELKIN M,NIYOGI P.Laplacian eigenmaps and spectral techniques for embedding and clustering[J].Advances in Neural Information Processing Systems,2001,14(6):585-591.
[21]DONG X,THANOU D,FROSSARD P.et al.Learning Laplacian matrix in smooth graph signal representations[J].IEEE Trans.on Signal Processing,2016,64(23):6160-6173.
[22]BOYD S,PARIKH N,CHU E,et al.Distributed optimization and statistical learning via the alternating direction method of multipliers[J].Foundation and Trends in Machine Learning,2011,3(1):1-122.
[23]CANDES E J,RECHT B.Exact low-rank matrix completion via convex optimization[C]∥Proc.of the Communication Control and Computing Conference,2008:806-812.