高级搜索

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

时域流信号的多任务稀疏贝叶斯动态重构方法研究

董道广 芮国胜 田文飚

董道广, 芮国胜, 田文飚. 时域流信号的多任务稀疏贝叶斯动态重构方法研究[J]. 电子与信息学报, 2020, 42(7): 1758-1765. doi: 10.11999/JEIT190558
引用本文: 董道广, 芮国胜, 田文飚. 时域流信号的多任务稀疏贝叶斯动态重构方法研究[J]. 电子与信息学报, 2020, 42(7): 1758-1765. doi: 10.11999/JEIT190558
Daoguang DONG, Guosheng RUI, Wenbiao TIAN. Research on the Dynamic Sparse Bayesian Recovery of Multi-task Observed Streaming Signals in Time Domain[J]. Journal of Electronics and Information Technology, 2020, 42(7): 1758-1765. doi: 10.11999/JEIT190558
Citation: Daoguang DONG, Guosheng RUI, Wenbiao TIAN. Research on the Dynamic Sparse Bayesian Recovery of Multi-task Observed Streaming Signals in Time Domain[J]. Journal of Electronics and Information Technology, 2020, 42(7): 1758-1765. doi: 10.11999/JEIT190558

时域流信号的多任务稀疏贝叶斯动态重构方法研究

doi: 10.11999/JEIT190558
基金项目: 国家自然科学基金(41606117, 41476089, 61671016)
详细信息
    作者简介:

    董道广:男,1990年生,博士生,研究方向为贝叶斯统计学习、压缩感知和蒸发波导反演

    芮国胜:男,1968年生,教授,博士生导师,主要研究方向为混沌通信系统及现代滤波理论

    田文飚:男,1987年生,副教授,主要研究方向为压缩感知及蒸发波导反演

    通讯作者:

    董道广 sikongyu@yeah.net

  • 中图分类号: TN911.7; TP301.6

Research on the Dynamic Sparse Bayesian Recovery of Multi-task Observed Streaming Signals in Time Domain

Funds: The National Natural Science of China (41606117, 41476089, 61671016)
  • 摘要: 为了解决多任务观测条件下时域流信号动态重构面临的块效应问题,该文基于重叠正交变换(LOT)和稀疏贝叶斯学习的贪婪重构框架先后提出了一种流信号多任务稀疏贝叶斯学习算法及其鲁棒增强型的改进算法,前者将LOT时域滑窗推广到多任务条件下,通过贝叶斯概率建模将未知的噪声精度的估计任务从信号重构中解耦并省略,后者进一步引入了重构不确定性的度量,提高了算法的鲁棒性和抑制误差积累的能力。基于浮标实测数据的实验结果表明,相比多任务重构领域代表性较强的时间多稀疏贝叶斯学习(TMSBL)和多任务压缩感知(MT-CS)算法,本文算法在不同信噪比、观测数目和任务数目条件下具有显著更高的重构精度、成功率和效率。
  • 图  1  时域流信号的多任务在线滑窗观测

    图  2  不同算法的SER随观测数目变化的比较结果

    图  3  不同算法的SER随信噪比变化的比较结果

    图  4  不同算法的SR随观测数目变化的比较结果

    图  5  不同算法的SR随SNR变化的比较结果

    图  6  不同算法的运行时间随观测数目变化的比较结果

    图  7  不同算法的运行时间随SNR变化的比较结果

    表  1  目标函数、中间变量及超参数估计公式列表

    目标函数及其分解形式(其中${\tilde a_l} = 2{a_l} + M\left( {2d + 2} \right)$):
    $L\left( { { { {\bar{ \alpha } } }_t} } \right) = { { - \displaystyle\sum\limits_{l = 1}^L {\left\{ { { {\tilde a}_l}\ln \left( { {\bar{ y} }_{t,l}^{\rm{T} }{\bar{ C} }_l^{ - 1}{ { {\bar{ y} } }_{t,l} } + 2{b_l} } \right) + \ln \left| { { { {\bar{ C} } }_l} } \right|} \right\} } } / 2} \;\;\quad (29)$
    $L\left( { { { {\bar{ \alpha } } }_t} } \right) = { { - \displaystyle\sum\limits_{l = 1}^L {\left\{ { { {\tilde a}_l}\ln \left( {1 - \frac{ { { {q_{j,l}^2} / { {g_{j,l} } } } } }{ { {\alpha _j} + {s_{j,l} } } }} \right) + \ln \left( {1 - \alpha _j^{ - 1}{s_{j,l} } } \right)} \right\} } } / 2}\;\; (30)$
    中间变量:
    ${{\bar{ C}}_l} = {{I}} + {{{\varPsi }}_l}{\bar{ A}}_t^{ - 1}{{\varPsi }}_l^{\rm{T}},_{}^{}{{\bar{ C}}_{ - j,l}} = {{I}} + \displaystyle\sum\limits_{k \ne j} {\alpha _k^{ - 1}{{{\psi }}_{k,l}}{{\psi }}_{k,l}^{\rm{T}}} \left( {{\rm{SMT - SBL}}} \right)\;\; (31)$
    ${{\bar{ C}}_l} = {{\hat{ \varOmega }}_{t,l}} + {{{\varPsi }}_l}{\bar{ A}}_t^{ - 1}{{\varPsi }}_l^{\rm{T}},{{\bar{ C}}_{ - j,l}} = {{\hat{ \varOmega }}_{t,l}} + \displaystyle\sum\limits_{k \ne j} {\alpha _k^{ - 1}{{{\psi }}_{k,l}}{{\psi }}_{k,l}^{\rm{T}}} \left( {{\rm{SMT - RSBL}}} \right)\;\;\;(32)$
    ${s_{j,l}} = {{\psi }}_{j,l}^{\rm{T}}{\bar{ C}}_{ - j,l}^{ - 1}{{{\psi }}_{j,l}},_{}^{}{q_{j,l}} = {{\psi }}_{j,l}^{\rm{T}}{\bar{ C}}_{ - j,l}^{ - 1}{{\bar{ y}}_{t,l}},_{}^{}{g_{j,l}} = {\bar{ y}}_{t,l}^{\rm{T}}{\bar{ C}}_{ - j,l}^{ - 1}{{\bar{ y}}_{t,l}} + 2{b_l}\;\;\; (33)$
    ${S_{j,l}} = {{\psi }}_{j,l}^{\rm{T}}{\bar{ C}}_l^{ - 1}{{{\psi }}_{j,l}},_{}^{}{Q_{j,l}} = {{\psi }}_{j,l}^{\rm{T}}{\bar{ C}}_l^{ - 1}{{\bar{ y}}_{t,l}},_{}^{}{G_l} = {\bar{ y}}_{t,l}^{\rm{T}}{\bar{ C}}_l^{ - 1}{{\bar{ y}}_{t,l}} + 2{b_l}\;\;\; (34)$
    ${\alpha _j}$更新公式:
    ${\alpha _j} = \left\{ \begin{aligned} & {L / { {\theta _j} } },{\theta _j} > 0\\ & \infty ,\quad {\simfont\text{其他} } \end{aligned} \right.\;\;\;\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\quad (35)$
    ${\theta _j} = \displaystyle\sum\limits_{l = 1}^L {\frac{ { { {\tilde a}_l}({ {q_{j,l}^2} / { {g_{j,l} } } }) - {s_{j,l} } } }{ { {s_{j,l} }({s_{j,l} } - { {q_{j,l}^2} / { {g_{j,l} } } })} } } \;\;\;\;\qquad\qquad\qquad\qquad\qquad\qquad\quad (36)$
    下载: 导出CSV

    表  2  相关的快速更新公式列表

    添加原子${{{\psi }}_{j,l}}$删除原子${{{\psi }}_{j,l}}$维持原子${{{\psi }}_{j,l}}$说明
    $ {\rm{SMT - SBL}}:$$ {\rm{SMT - SBL}}:$$ {\rm{SMT - SBL}}:$添加情形中:
    $ \begin{array}{l} {{\tilde{\hat{ \varSigma }}}}_{t,l}^{{\bar{ w}}} = [{\hat{ \varSigma }}_{t,l}^{{\bar{ w}}} + {{\hat \varSigma }_{jj,l}}{\hat{ \varSigma }}_{t,l}^{{\bar{ w}}}{{\varPsi }}_l^{\rm{T}}{{{\psi }}_{j,l}}{{\psi }}_{j,l}^{\rm{T}}{{{\varPsi }}_l}{\hat{ \varSigma }}_{t,l}^{{\bar{ w}}},\\ - {{\hat \varSigma }_{jj,l}}{\hat{ \varSigma }}_{t,l}^{{\bar{ w}}}{{\varPsi }}_l^{\rm{T}}{{{\psi }}_{j,l}}; - {{\hat \varSigma }_{jj,l}}{{\psi }}_{j,l}^{\rm{T}}{{\varPsi }}_l^{}{\hat{ \varSigma }}_{t,l}^{{\bar{ w}}},{{\hat \varSigma }_{jj,l}}]\\ {\tilde{ \mu }}_{t,l}^{{\bar{ w}}} = [{{\mu }}_{t,l}^{{\bar{ w}}} + {\mu _{j,l}}{\hat{ \varSigma }}_{t,l}^{{\bar{ w}}}{{\varPsi }}_l^{\rm{T}}{{{\psi }}_{j,l}};{\mu _{j,l}}]\\ {{{e}}_{j,l}} = {{{\psi }}_{j,l}} - {{{\varPsi }}_l}{\hat{ \varSigma }}_{t,l}^{{\bar{ w}}}{{\varPsi }}_l^{\rm{T}}{{{\psi }}_{j,l}} \end{array}$$ \begin{array}{l} {{\tilde S}_{k,l}} = {S_{k,l}} + {{{{({\hat{ \varSigma }}_{j,l}^{\rm{T}}{{\varPsi }}_l^{\rm{T}}{{{\psi }}_{k,l}})}^2}} / {{{\hat \varSigma }_{jj,l}}}}\\ {{\tilde Q}_{k,l}} = {Q_{k,l}} + {{{\mu _{j,l}}{\hat{ \varSigma }}_{j,l}^{\rm{T}}{{\varPsi }}_l^{\rm{T}}{{{\psi }}_{k,l}}} / {{{\hat \varSigma }_{jj,l}}}}\\ {{\tilde G}_l} = {G_l} + {{{{({\hat{ \varSigma }}_{j,l}^{\rm{T}}{{\varPsi }}_l^{\rm{T}}{{{\bar{ y}}}_{t,l}})}^2}} / {{{\hat \varSigma }_{jj,l}}}} \end{array}$$ \begin{array}{l} {{\tilde S}_{k,l}} = {S_{k,l}} + {\gamma _{j,l}}{({\hat{ \varSigma }}_{j,l}^{\rm{T}}{{\varPsi }}_l^{\rm{T}}{{{\psi }}_{k,l}})^2}\\ {{\tilde Q}_{k,l}} = {Q_{k,l}} + {\gamma _{j,l}}{\mu _{j,l}}{\hat{ \varSigma }}_{j,l}^{\rm{T}}{{\varPsi }}_l^{\rm{T}}{{{\psi }}_{k,l}}\\ {{\tilde G}_l} = {G_l} + {\gamma _{j,l}}{({\hat{ \varSigma }}_{j,l}^{\rm{T}}{{\varPsi }}_l^{\rm{T}}{{{\bar{ y}}}_{t,l}})^2} \end{array}$$ \begin{array}{l} {{\hat \varSigma }_{jj,l}} = {\left( {{{\tilde \alpha }_j} + {S_{j,l}}} \right)^{ - 1}},\\ {\mu _{j,l}} = {{\hat \varSigma }_{jj,l}}{Q_{j,l}} \end{array}$
    $ {\rm{SMT - RSBL}}:$$ {\rm{SMT - RSBL}}:$$ {\rm{SMT - RSBL}}:$删除情形中:
    $ \begin{array}{l} {{\tilde{\hat{ \varSigma }}}}_{t,l}^{{\bar{ w}}} = [{\hat{ \varSigma }}_{t,l}^{{\bar{ w}}} + {{\hat \varSigma }_{jj,l}}{\hat{ \varSigma }}_{t,l}^{{\bar{ w}}}{{\varPsi }}_l^{\rm{T}}{\hat{ \varOmega }}_{t,l}^{ - 1}{{{\psi }}_{j,l}}{{\psi }}_{j,l}^{\rm{T}}{\hat{ \varOmega }}_{t,l}^{ - 1}{{{\varPsi }}_l}{\hat{ \varSigma }}_{t,l}^{{\bar{ w}}},\\ - {{\hat \varSigma }_{jj,l}}{\hat{ \varSigma }}_{t,l}^{{\bar{ w}}}{{\varPsi }}_l^{\rm{T}}{\hat{ \varOmega }}_{t,l}^{ - 1}{{{\psi }}_{j,l}}; - {{\hat \varSigma }_{jj,l}}{{\psi }}_{j,l}^{\rm{T}}{\hat{ \varOmega }}_{t,l}^{ - 1}{{\varPsi }}_l^{}{\hat{ \varSigma }}_{t,l}^{{\bar{ w}}},{{\hat \varSigma }_{jj,l}}]\\ {\tilde{ \mu }}_{t,l}^{{\bar{ w}}} = [{{\mu }}_{t,l}^{{\bar{ w}}} + {\mu _{j,l}}{\hat{ \varSigma }}_{t,l}^{{\bar{ w}}}{{\varPsi }}_l^{\rm{T}}{\hat{ \varOmega }}_{t,l}^{ - 1}{{{\psi }}_{j,l}};{\mu _{j,l}}]\\ {{{e}}_{j,l}} = ({\hat{ \varOmega }}_{t,l}^{ - 1} - {\hat{ \varOmega }}_{t,l}^{ - 1}{{{\varPsi }}_l}{\hat{ \varSigma }}_{t,l}^{{\bar{ w}}}{{\varPsi }}_l^{\rm{T}}{\hat{ \varOmega }}_{t,l}^{ - 1}){{{\psi }}_{j,l}} \end{array}$$ \begin{array}{l} {{\tilde S}_{k,l}} = {S_{k,l}} + {{{{({\hat{ \varSigma }}_{j,l}^{\rm{T}}{{\varPsi }}_l^{\rm{T}}{\hat{ \varOmega }}_{t,l}^{ - 1}{{{\psi }}_{k,l}})}^2}} / {{{\hat \varSigma }_{jj,l}}}}\\ {{\tilde Q}_{k,l}} = {Q_{k,l}} + {{{\mu _{j,l}}{\hat{ \varSigma }}_{j,l}^{\rm{T}}{{\varPsi }}_l^{\rm{T}}{\hat{ \varOmega }}_{t,l}^{ - 1}{{{\psi }}_{k,l}}} / {{{\hat \varSigma }_{jj,l}}}}\\ {{\tilde G}_l} = {G_l} + {{{{({\hat{ \varSigma }}_{j,l}^{\rm{T}}{{\varPsi }}_l^{\rm{T}}{\hat{ \varOmega }}_{t,l}^{ - 1}{{{\bar{ y}}}_{t,l}})}^2}} / {{{\hat \varSigma }_{jj,l}}}} \end{array}$$ \begin{array}{l} {{\tilde S}_{k,l}} = {S_{k,l}} + {\gamma _{j,l}}{({\hat{ \varSigma }}_{j,l}^{\rm{T}}{{\varPsi }}_l^{\rm{T}}{\hat{ \varOmega }}_{t,l}^{ - 1}{{{\psi }}_{k,l}})^2}\\ {{\tilde Q}_{k,l}} = {Q_{k,l}} + {\gamma _{j,l}}{\mu _{j,l}}{\hat{ \varSigma }}_{j,l}^{\rm{T}}{{\varPsi }}_l^{\rm{T}}{\hat{ \varOmega }}_{t,l}^{ - 1}{{{\psi }}_{k,l}}\\ {{\tilde G}_l} = {G_l} + {\gamma _{j,l}}{({\hat{ \varSigma }}_{j,l}^{\rm{T}}{{\varPsi }}_l^{\rm{T}}{\hat{ \varOmega }}_{t,l}^{ - 1}{{{\bar{ y}}}_{t,l}})^2} \end{array}$${\hat \varSigma _{jj,l}}$是${\hat{ \varSigma }}_{t,l}^{{\bar{ w}}}$的第$j$个对角元素,${{\hat{ \varSigma }}_{j,l}}$是${\hat{ \varSigma }}_{t,l}^{{\bar{ w}}}$的第$j$列,${\mu _{j,l}}$是${{\mu }}_{t,l}^{{\bar{ w}}}$的第$j$个元素。
    通用公式:通用公式:通用公式:维持情形中:
    $ \begin{array}{l} {{\tilde S}_{k,l}} = {S_{k,l}} - {{\hat \varSigma }_{jj,l}}{({{\psi }}_{k,l}^{\rm{T}}{{{e}}_{j,l}})^2}\\ {{\tilde Q}_{k,l}} = {Q_{k,l}} - {\mu _{j,l}}{{\psi }}_{k,l}^{\rm{T}}{{{e}}_{j,l}}\\ {{\tilde G}_l} = {G_l} - {{\hat \varSigma }_{jj,l}}{({\bar{ y}}_{t,l}^{\rm{T}}{{{e}}_{j,l}})^2}\\ 2\Delta L = \sum\nolimits_{l = 1}^L {\ln \left[ {{{{{\tilde \alpha }_j}} / {\left( {{{\tilde \alpha }_j} + {s_{j,l}}} \right)}}} \right]} \\ \mathop {}\nolimits - \sum\nolimits_{l = 1}^L {{{\tilde a}_l}\ln \left[ {1 - {{\left( {{{q_{j,l}^2} / {{g_{j,l}}}}} \right)} / {\left( {{{\tilde \alpha }_j} + {s_{j,l}}} \right)}}} \right]} \end{array}$$ \begin{array}{l} 2\Delta L = - \sum\nolimits_{l = 1}^L {\ln \left( {1 - {{{S_{j,l}}} / {{\alpha _j}}}} \right)} \\ \mathop {}\nolimits \mathop {}\nolimits - \sum\nolimits_{l = 1}^L {{{\tilde a}_l}} \ln \left[ {1 + \frac{{{{Q_{j,l}^2} / {{G_l}}}}}{{{\alpha _j} - {S_{j,l}}}}} \right]\\ {{\tilde{\hat{ \varSigma }}}}_{t,l}^{{\bar{ w}}} = {\hat{ \varSigma }}_{t,l}^{{\bar{ w}}} - {{{{{\hat{ \varSigma }}}_{j,l}}{\hat{ \varSigma }}_{j,l}^{\rm{T}}} / {{{\hat \varSigma }_{jj,l}}}}\\ {\tilde{ \mu }}_{t,l}^{{\bar{ w}}} = {{\mu }}_{t,l}^{{\bar{ w}}} - {\mu _{j,l}}{{{{{\hat{ \varSigma }}}_{j,l}}} / {{{\hat \varSigma }_{jj,l}}}} \end{array}$$ \begin{array}{l} 2\Delta L = \sum\nolimits_{l = 1}^L {\left( {{{\tilde a}_l} - 1} \right)\ln \left( {1 + \frac{{{\alpha _j} - {{\tilde \alpha }_j}}}{{{\alpha _j}{{\tilde \alpha }_j}}}} \right)} \\ + \sum\nolimits_{l = 1}^L {{{\tilde a}_l}} \ln \frac{{\left[ {\left( {{\alpha _j} + {s_{j,l}}} \right){g_{j,l}} - q_{j,l}^2} \right]{{\tilde \alpha }_j}}}{{\left[ {\left( {{{\tilde \alpha }_j} + {s_{j,l}}} \right){g_{j,l}} - q_{j,l}^2} \right]{\alpha _j}}}\\ {{\tilde{\hat{ \varSigma }}}}_{t,l}^{{\bar{ w}}} = {\hat{ \varSigma }}_{t,l}^{{\bar{ w}}} - {\gamma _{j,l}}{{{\hat{ \varSigma }}}_{j,l}}{\hat{ \varSigma }}_{j,l}^{\rm{T}}\\ {\tilde{ \mu }}_{t,l}^{{\bar{ w}}} = {{\mu }}_{t,l}^{{\bar{ w}}} - {\gamma _{j,l}}{\mu _{j,l}}{{{\hat{ \varSigma }}}_{j,l}} \end{array}$${\hat \varSigma _{jj,l}},{{\hat{ \varSigma }}_{j,l}},{\mu _{j,l}}$与前述相同,${\gamma _{j,l}} = {\left[ {{{\hat \varSigma }_{jj,l}} + {{\left( {{{\tilde \alpha }_j} - {\alpha _j}} \right)}^{ - 1}}} \right]^{ - 1}}$。
    下载: 导出CSV
  • [1] LEINONEN M, CODREANU M, and JUNTTI M. Sequential compressed sensing with progressive signal reconstruction in wireless sensor networks[J]. IEEE Transactions on Wireless Communications, 2015, 14(3): 1622–1635. doi:  10.1109/TWC.2014.2371017
    [2] ASIF M S and ROMBERG J. Sparse recovery of streaming signals using 1-homotopy[J]. IEEE Transactions on Signal Processing, 2014, 62(16): 4209–4223. doi:  10.1109/TSP.2014.2328981
    [3] 周超杰, 张杰, 杨俊钢, 等. 基于ROMS模式的南海SST与SSH四维变分同化研究[J]. 海洋学报, 2019, 41(1): 32–40. doi:  10.3969/j.issn.0253-4193.2019.01.005

    ZHOU Chaojie, ZHANG Jie, YANG Jungang, et al. 4DVAR assimilation of SST and SSH data in South China Sea based on ROMS[J]. Acta Oceanologica Sinica, 2019, 41(1): 32–40. doi:  10.3969/j.issn.0253-4193.2019.01.005
    [4] ZHANG Yonggang, ZHANG Jianxue, JIAO Lin, et al. Algorithms of wave reflective critical angle on interface[C]. SPIE 10250, International Conference on Optical and Photonics Engineering, Chengdu, China, 2017: 8–13. doi: 10.1117/12.2266713.
    [5] AO Dongyang, WANG Rui, HU Cheng, et al. A sparse SAR imaging method based on multiple measurement vectors model[J]. Remote Sensing, 2017, 9(3): 297. doi:  10.3390/rs9030297
    [6] TIPPING M E and FAUL A. Fast marginal likelihood maximisation for sparse Bayesian models[C]. The 9th International Workshop on Artificial Intelligence and Statistics, Key West, USA, 2003: 3–6.
    [7] WIPF D P and RAO B D. An empirical bayesian strategy for solving the simultaneous sparse approximation problem[J]. IEEE Transactions on Signal Processing, 2007, 55(7): 3704–3716. doi:  10.1109/tsp.2007.894265
    [8] ZHANG Zhilin and RAO B D. Sparse signal recovery in the presence of correlated multiple measurement vectors[C]. 2010 IEEE International Conference on Acoustics, Speech and Signal Processing, Dallas, USA, 2010: 3986–3989. doi: 10.1109/ICASSP.2010.5495780.
    [9] ZHANG Zhilin and RAO B D. Iterative reweighted algorithms for sparse signal recovery with temporally correlated source vectors[C]. 2011 IEEE International Conference on Acoustics, Speech and Signal Processing, Prague, Czech Republic, 2011: 3932–3935. doi: 10.1109/ICASSP.2011.5947212.
    [10] ZHANG Zhilin and RAO B D. Sparse signal recovery with temporally correlated source vectors using sparse Bayesian learning[J]. IEEE Journal of Selected Topics in Signal Processing, 2011, 5(5): 912–926. doi:  10.1109/JSTSP.2011.2159773
    [11] JI Shihao, DUNSON D, and CARIN L. Multitask compressive sensing[J]. IEEE Transactions on Signal Processing, 2009, 57(1): 92–106. doi:  10.1109/tsp.2008.2005866
    [12] ZHANG Zhilin and RAO B D. Extension of SBL algorithms for the recovery of block sparse signals with intra-block correlation[J]. IEEE Transactions on Signal Processing, 2013, 61(8): 2009–2015. doi:  10.1109/TSP.2013.2241055
    [13] BERNAL E A and LI Qun. Tensorial compressive sensing of jointly sparse matrices with applications to color imaging[C]. 2017 IEEE International Conference on Image Processing, Beijing, China, 2018: 2781–2785. doi: 10.1109/ICIP.2017.8296789.
    [14] HAN Ningning and SONG Zhanjie. Bayesian multiple measurement vector problem with spatial structured sparsity patterns[J]. Digital Signal Processing, 2018, 75: 184–201. doi:  10.1016/j.dsp.2018.01.015
    [15] QIN Yanhua, LIU Yumin, and YU Zhongyuan. Underdetermined DOA estimation using coprime array via multiple measurement sparse Bayesian learning[J]. Signal, Image and Video Processing, 2019, 13(7): 1311–1318. doi:  10.1007/s11760-019-01480-x
    [16] DU Yang, DONG Binhong, ZHU Wuyong, et al. Joint channel estimation and multiuser detection for uplink Grant-Free NOMA[J]. IEEE Wireless Communications Letters, 2018, 7(4): 682–685. doi:  10.1109/LWC.2018.2810278
    [17] SHAHIN S, SHAYEGH F, MORTAHEB S, et al. Improvement of flexible design matrix in sparse Bayesian learning for multi task fMRI data analysis[C]. The 23rd Iranian Conference on Biomedical Engineering and 20161st International Iranian Conference on Biomedical Engineering, Tehran, Iran, 2017: 3823–3826. doi: 10.1109/ICBME.2016.7890927.
    [18] FENG Weike, GUO Yiduo, ZHANG Yongshun, et al. Airborne radar space time adaptive processing based on atomic norm minimization[J]. Signal Processing, 2018, 148: 31–40. doi:  10.1016/j.sigpro.2018.02.008
    [19] WU Jingjing, LI Siwei, ZHANG Saiwen, et al. Fast analysis method for stochastic optical reconstruction microscopy using multiple measurement vector model sparse Bayesian learning[J]. Optics Letters, 2018, 43(16): 3977–3980. doi:  10.1364/OL.43.003977
    [20] WIJEWARDHANA U L and CODREANU M. A Bayesian approach for online recovery of streaming signals from compressive measurements[J]. IEEE Transactions on Signal Processing, 2017, 65(1): 184–199. doi:  10.1109/TSP.2016.2614489
    [21] MALVAR H S and STAELIN D H. The LOT: Transform coding without blocking effects[J]. IEEE Transactions on Acoustics, Speech, and Signal Processing, 1989, 37(4): 553–559. doi:  10.1109/29.17536
    [22] BABIN S M, YOUNG G S, and CARTON J A. A new model of the oceanic evaporation duct[J]. Journal of Applied Meteorology, 1997, 36(3): 193–204. doi:  10.1175/1520-0450(1997)036<0193:ANMOTO>2.0.CO;2
  • [1] 邱天爽.  相关熵与循环相关熵信号处理研究进展, 电子与信息学报. doi: 10.11999/JEIT190646
    [2] 孙文军, 芮国胜, 张洋, 陈强.  基于系统一阶摄动解主频功率比的弱信号检测方法, 电子与信息学报. doi: 10.11999/JEIT150510
    [3] 杨翔, 顾洪宇.  基于到达时间差直方图的信号分选算法研究, 电子与信息学报. doi: 10.11999/JEIT150209
    [4] 张东伟, 郭英, 齐子森, 侯文林, 张波, 李教.  多跳频信号波达方向与极化状态联合估计算法, 电子与信息学报. doi: 10.11999/JEIT141315
    [5] 朱航, 张淑宁, 赵惠昌.  单通道多分量伪码调制脉冲串信号分离及参数提取, 电子与信息学报. doi: 10.11999/JEIT141317
    [6] 沈志博, 董春曦, 黄龙, 赵国庆.  一种基于稀疏分解的窄带信号频率估计算法, 电子与信息学报. doi: 10.11999/JEIT140878
    [7] 王峰, 向新, 易克初, 熊磊.  基于隐变量贝叶斯模型的稀疏信号恢复, 电子与信息学报. doi: 10.11999/JEIT140169
    [8] 郭瑞, 蔡志明, 姚直象.  线性调频信号主瓣不展宽旁瓣抑制方法, 电子与信息学报. doi: 10.3724/SP.J.1146.2013.00421
    [9] 刘哲, 陈路, 杨静.  一种基于块局部最优维纳滤波的图像重构算法, 电子与信息学报. doi: 10.3724/SP.J.1146.2013.01884
    [10] 杨学敏, 李广军, 郑植.  基于稀疏表示的相干分布式非圆信号的参数估计, 电子与信息学报. doi: 10.3724/SP.J.1146.2013.00444
    [11] 李实锋, 王玉林, 华宇, 袁江斌.  罗兰-C信号快速捕获方法及其性能分析, 电子与信息学报. doi: 10.3724/SP.J.1146.2012.01660
    [12] 田鹏武, 康荣宗, 于宏毅.  非均匀块稀疏信号的压缩采样与盲重构算法, 电子与信息学报. doi: 10.3724/SP.J.1146.2012.00598
    [13] 郭黎利, 周彬, 孙志国, 刘湘蒲.  对称升余弦键控信号相关性分析, 电子与信息学报. doi: 10.3724/SP.J.1146.2011.01361
    [14] 王超, 刘伟, 袁培苑.  基于细粒度任务分配的空时自适应并行处理算法研究, 电子与信息学报. doi: 10.3724/SP.J.1146.2011.00683
    [15] 杨鹏, 柳征, 姜文利.  基于最小描述长度准则的稀疏多带信号频谱感知算法, 电子与信息学报. doi: 10.3724/SP.J.1146.2011.01324
    [16] 张昀, 张志涌.  复数离散Hopfield网络盲检测64QAM信号, 电子与信息学报. doi: 10.3724/SP.J.1146.2010.00921
    [17] 王堃, 吴嗣亮, 侯建刚.  实际COSPAS-SARSAT信号TOA估计算法研究, 电子与信息学报. doi: 10.3724/SP.J.1146.2011.00338
    [18] 张路平, 王建新.  MQAM信号调制方式盲识别, 电子与信息学报. doi: 10.3724/SP.J.1146.2010.00472
    [19] 阮秀凯, 张志涌.  基于连续Hopfield型神经网络的QAM信号盲检测, 电子与信息学报. doi: 10.3724/SP.J.1146.2010.01271
    [20] 胡文, 刘中, 李春彪.  距离-速度-加速度联合模糊函数计算:信号动力学表示方法, 电子与信息学报. doi: 10.3724/SP.J.1146.2007.00770
  • 加载中
  • 图(7) / 表ll (2)
    计量
    • 文章访问数:  763
    • HTML全文浏览量:  335
    • PDF下载量:  18
    • 被引次数: 0
    出版历程
    • 收稿日期:  2019-07-25
    • 修回日期:  2020-03-26
    • 网络出版日期:  2020-04-24
    • 刊出日期:  2020-07-23

    目录

      /

      返回文章
      返回

      官方微信,欢迎关注