基于二次最优阈值近似消息传递法的蒸发波导去噪重构
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摘要
针对蒸发波导时空态势感知过程中,压缩感知观测阶段混入噪声对高精度重构产生不利影响的问题,提出了基于二次最优阈值的近似消息传递法。所提方法综合了软、硬阈值函数的优势,设计了一种二次稳固阈值函数,改善AMP算法的重构性能,并在近似消息传递法的迭代过程中加入了基于共轭梯度法的最优阈值设置策略,加快收敛速度。理论分析和实验表明,所提算法比现有的几种主流重构算法的收敛速度更快,去噪重建误差更小。
To solve the problem that the mixed noise of compressed sensing observation stage had adverse effects on the high-precision reconstruction in the time-space situation awareness process of evaporative duct, an approximate message passing method based on quadratic optimal threshold was proposed. A quadratic stabilization threshold function which integrated advantages of soft and hard threshold functions was designed, and the optimal threshold setting policy was added to the iterative process based on conjugate gradient method to speed up convergence. Theoretical analysis and experiments show that, compared with several mainstream algorithms, the proposed algorithm has the faster convergence rate and lower denoising reconstruction error.
To solve the problem that the mixed noise of compressed sensing observation stage had adverse effects on the high-precision reconstruction in the time-space situation awareness process of evaporative duct, an approximate message passing method based on quadratic optimal threshold was proposed. A quadratic stabilization threshold function which integrated advantages of soft and hard threshold functions was designed, and the optimal threshold setting policy was added to the iterative process based on conjugate gradient method to speed up convergence. Theoretical analysis and experiments show that, compared with several mainstream algorithms, the proposed algorithm has the faster convergence rate and lower denoising reconstruction error.
引文
[1] YANG K, ZHANG Q, SHI Y, et al. On analyzing space time distribution of evaporation duct height over the global ocean[J]. Acta Oceanologica Sinica, 2016, 35(7):20-29.
[2]张金鹏,张玉石,吴振森,等.基于雷达海杂波的区域性非均匀蒸发波导反演方法[J].物理学报, 2015, 64(12):136-146.ZHANG J P, ZHANG Y S, WU Z S, et al. Inversion of regional range-dependent evaporation duct from radar sea clutter[J]. Acta Physica Sinica, 2015, 64(12):136-146.
[3]王明辉,陈冰怀,黄海,等.自动气象站常规传感器现场检测系统设计[J].气象科技,2019,47(03):402-407.WANG M H, CHEN B H, HUANG H Y, et al. Design of detection system for regular sensors of automatic weather stations[J]. Meteorological Science and Technology, 2019, 47(03):402-407.
[4]王超,韩笑冬,王睿,等.支持网络互连的可重构卫星平台关键技术研究[J].通信学报, 2017, 38(S1):83-87.WANG C, HAN X D, WANG R, et al. Study of key technology for reconfigurable satellite platform supporting network interconnection[J].Journal on Communications, 2017, 38(S1):83-87.
[5]王振会,杨璐,姚展予,等.卫星遥感资料在蒸发波导数值预报中的应用[J].电波科学学报, 2012, 27(04):819-824.WANG Z H, YANG L, YAO Z Y, et al. Application of satellite remote sensing data for numerical prediction of evaporation duct[J]. Chinese Journal of Radio Science, 2012, 27(04):819-824.
[6]田文飚,芮国胜,王绍班,等.三维观测模型下蒸发波导时空态势压缩感知[J].电波科学学报, 2014, 29(2):207-212.TIAN W B, RUI G S, WANG S B, et al. Situational compressed sensing of evaporation duct based on 3-dimensional measurement model[J].Chinese Journal of Radio Science, 2014, 29(2):207-212.
[7] DONOHO D L, MALEKI A, MONTANARI A. Message-passing algorithms for compressed sensing[J].Proceedings of the National Academy of Sciences, 2009, 106(45):18914-18919.
[8] RUSH C, VENKATARAMANAN R. Finite-sample analysis of approximate message passing.[J]. IEEE Transactions on Information Theory, 2017,(99):1-41.
[9] XIE Z H, MA L H. Structured approximate message passing algorithm with a Laplacian scale mixture prior[J]. Acta Electronica Sinica, 2018,46(3):520-528.
[10] METZLER C A, MALEKI A, BARANIUK R G. From denoising to compressed sensing[J]. IEEE Transactions on Information Theory,2016, 62(9):5117-5144.
[11] MA Y, ZHU J, BARON D. Approximate message passing algorithm with universal denoising and gaussian mixture learning[J]. IEEE Transactions on Signal Processing, 2016, 64(21):5611-5622.
[12] FIGUEIREDO M A T, NOWAK R D, WRIGHT S J. Gradient projection for sparse reconstruction:application to compressed sensing and other inverse problems[J]. IEEE Journal of Selected Topics in Signal Processing, 2007, 1(4):586-597.
[13] CHEN S B, DONOHO D L, Saunders M A. Atomic decomposition by basis pursuit[J]. SIAM Journal on Scientific Computing, 1998,20(1):33-61.
[14] FORNASIER M, RAUHUT H. Iterative thresholding algorithm[J].Applied Computational harmonic analysis, 2008, 25:187-208.
[15] BABIN S M. A new model of the oceanic evaporation duct and its comparison with current models[D]. US:University of Maryland,1996.
[16]杨坤德,马远良,史阳.西太平洋蒸发波导的时空统计规律研究[J].物理学报, 2009,58(10):7339-7350.YANG K D, MA Y L, SHI Y. Spatio-temporal distributions of evaporation duct for the West Pacific Ocean[J]. Acta Physica Sinica,2009,58(10):7339-7350.
[17] MUSSONG L, GAUTHIER S, BRUTH E. A simple method to determine evaporation duct height in the surface boundary layer[J]. Radio Science, 1997, 27(9):193-204.
[18]刘成国,黄际英,江成荫,等.用伪折射率和相似理论计算海上蒸发波导剖面[J].电子学报, 2001, 29(7):970-972.LIU C G, HUANG J Y, JIANG C Y, et al. Modeling evaporation duct over sea with pseudo-refractivity and similarity theory[J]. Acta Electronica Sinica, 2001, 29(7):970-972.
[19]田文飚,芮国胜,董道广,等.基于盲自适应KLT的蒸发波导压缩感知方法[J].电子学报, 2018, 46(9):2068-2074.TIAN W B, RUI G S, DONG D G et al. Compressed sensing of evaporation duct based on blind adaptive KLT estimation[J].Acta Electronica Sinica, 2018, 46(9):2068-2074.
[20] DONOHO D L, JOHNSTONE I, MONTANARI A. Accurate prediction of phase transitions in compressed sensing via a connection to minimax denoising[J]. IEEE Transactions on Information Theory,2011, 59(6):3396-3433.
[21] MOUSAVI A, MALEKI A, BARANIUK R G. Parameterless optimal approximate message passing[J]. Statistics, arXiv:1311.0035v1, 2013.
[22] DAI W, MILENKOVIC O. Subspace pursuit for compressive sensing signal reconstruction[J]. IEEE Transactions on Information Theory,2008, 55(5):2230-2249.
[23] NEEDELL D, TROPP J A. CoSaMP:iterative signal recovery from incomplete and inaccurate samples[J]. Applied and Computational Harmonic Analysis, 2008, 26(3):301-321.
[2]张金鹏,张玉石,吴振森,等.基于雷达海杂波的区域性非均匀蒸发波导反演方法[J].物理学报, 2015, 64(12):136-146.ZHANG J P, ZHANG Y S, WU Z S, et al. Inversion of regional range-dependent evaporation duct from radar sea clutter[J]. Acta Physica Sinica, 2015, 64(12):136-146.
[3]王明辉,陈冰怀,黄海,等.自动气象站常规传感器现场检测系统设计[J].气象科技,2019,47(03):402-407.WANG M H, CHEN B H, HUANG H Y, et al. Design of detection system for regular sensors of automatic weather stations[J]. Meteorological Science and Technology, 2019, 47(03):402-407.
[4]王超,韩笑冬,王睿,等.支持网络互连的可重构卫星平台关键技术研究[J].通信学报, 2017, 38(S1):83-87.WANG C, HAN X D, WANG R, et al. Study of key technology for reconfigurable satellite platform supporting network interconnection[J].Journal on Communications, 2017, 38(S1):83-87.
[5]王振会,杨璐,姚展予,等.卫星遥感资料在蒸发波导数值预报中的应用[J].电波科学学报, 2012, 27(04):819-824.WANG Z H, YANG L, YAO Z Y, et al. Application of satellite remote sensing data for numerical prediction of evaporation duct[J]. Chinese Journal of Radio Science, 2012, 27(04):819-824.
[6]田文飚,芮国胜,王绍班,等.三维观测模型下蒸发波导时空态势压缩感知[J].电波科学学报, 2014, 29(2):207-212.TIAN W B, RUI G S, WANG S B, et al. Situational compressed sensing of evaporation duct based on 3-dimensional measurement model[J].Chinese Journal of Radio Science, 2014, 29(2):207-212.
[7] DONOHO D L, MALEKI A, MONTANARI A. Message-passing algorithms for compressed sensing[J].Proceedings of the National Academy of Sciences, 2009, 106(45):18914-18919.
[8] RUSH C, VENKATARAMANAN R. Finite-sample analysis of approximate message passing.[J]. IEEE Transactions on Information Theory, 2017,(99):1-41.
[9] XIE Z H, MA L H. Structured approximate message passing algorithm with a Laplacian scale mixture prior[J]. Acta Electronica Sinica, 2018,46(3):520-528.
[10] METZLER C A, MALEKI A, BARANIUK R G. From denoising to compressed sensing[J]. IEEE Transactions on Information Theory,2016, 62(9):5117-5144.
[11] MA Y, ZHU J, BARON D. Approximate message passing algorithm with universal denoising and gaussian mixture learning[J]. IEEE Transactions on Signal Processing, 2016, 64(21):5611-5622.
[12] FIGUEIREDO M A T, NOWAK R D, WRIGHT S J. Gradient projection for sparse reconstruction:application to compressed sensing and other inverse problems[J]. IEEE Journal of Selected Topics in Signal Processing, 2007, 1(4):586-597.
[13] CHEN S B, DONOHO D L, Saunders M A. Atomic decomposition by basis pursuit[J]. SIAM Journal on Scientific Computing, 1998,20(1):33-61.
[14] FORNASIER M, RAUHUT H. Iterative thresholding algorithm[J].Applied Computational harmonic analysis, 2008, 25:187-208.
[15] BABIN S M. A new model of the oceanic evaporation duct and its comparison with current models[D]. US:University of Maryland,1996.
[16]杨坤德,马远良,史阳.西太平洋蒸发波导的时空统计规律研究[J].物理学报, 2009,58(10):7339-7350.YANG K D, MA Y L, SHI Y. Spatio-temporal distributions of evaporation duct for the West Pacific Ocean[J]. Acta Physica Sinica,2009,58(10):7339-7350.
[17] MUSSONG L, GAUTHIER S, BRUTH E. A simple method to determine evaporation duct height in the surface boundary layer[J]. Radio Science, 1997, 27(9):193-204.
[18]刘成国,黄际英,江成荫,等.用伪折射率和相似理论计算海上蒸发波导剖面[J].电子学报, 2001, 29(7):970-972.LIU C G, HUANG J Y, JIANG C Y, et al. Modeling evaporation duct over sea with pseudo-refractivity and similarity theory[J]. Acta Electronica Sinica, 2001, 29(7):970-972.
[19]田文飚,芮国胜,董道广,等.基于盲自适应KLT的蒸发波导压缩感知方法[J].电子学报, 2018, 46(9):2068-2074.TIAN W B, RUI G S, DONG D G et al. Compressed sensing of evaporation duct based on blind adaptive KLT estimation[J].Acta Electronica Sinica, 2018, 46(9):2068-2074.
[20] DONOHO D L, JOHNSTONE I, MONTANARI A. Accurate prediction of phase transitions in compressed sensing via a connection to minimax denoising[J]. IEEE Transactions on Information Theory,2011, 59(6):3396-3433.
[21] MOUSAVI A, MALEKI A, BARANIUK R G. Parameterless optimal approximate message passing[J]. Statistics, arXiv:1311.0035v1, 2013.
[22] DAI W, MILENKOVIC O. Subspace pursuit for compressive sensing signal reconstruction[J]. IEEE Transactions on Information Theory,2008, 55(5):2230-2249.
[23] NEEDELL D, TROPP J A. CoSaMP:iterative signal recovery from incomplete and inaccurate samples[J]. Applied and Computational Harmonic Analysis, 2008, 26(3):301-321.
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