基于平滑l_0范数的压缩感知近场声全息方法
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摘要
传统平面近场声全息(CPNAH)是一类典型的不适定问题,采用波数域滤波或Tikhonov正则化等方法都无法彻底解决,因此,提出一种基于平滑l_0范数的压缩感知平面近场声全息法(SL0-CS-PNAH)。根据全息面上测量声压的特点,采用symlets8小波函数构建正交小波变换矩阵,将其作为重建面质点法向振速的稀疏基。将CPNAH中使用的瑞利(Rayleigh)第一积分公式离散化,确定SL0-CS-PNAH中满足约束等距原则的测量矩阵,设置合适的压缩比,利用测量矩阵对稀疏信号进行压缩采样。在由感知矩阵、全息面测量声压和稀疏向量共同构成的约束条件下,建立稀疏向量的最小l_0范数优化模型,采用平滑l_0范数重建算法求解此模型下的最优化问题,得到质点法向振速的最优稀疏解,再将最优稀疏解和稀疏基相乘恢复重建面质点法向振速。在数值仿真实验中,将测量点由64×64减少到32×64的情况下将传统CPNAH、基于正交匹配追踪算法的压缩感知近场声全息(OMPCS-PNAH)、基于子空间追踪算法的压缩感知近场声全息(SP-CS-PNAH)和SL0-CS-PNAH进行比较。实验结果表明,在相同采样率和压缩比条件下,采用SL0-CS-PNAH的声场重建质量较好且重建效率较高。
As the traditional planar near-filed acoustic holography(CPNAH)is an ill-posed problem,which cannot be solved completely with the wave number domain filtering or Tikhonov regularization method.A planar nearfield acoustic holography based on compressive sensing by using the smoothed l_0 norm(SL0-CS-PNAH)was proposed in this work.According to the characteristics of the sound measurement on the holography plane,the orthogonal wavelet transform matrix is built by using the symlets8 wavelet function,which is used as a sparse basis for the particle normal velocity of the reconstructed plane.The Rayleigh first integral formula used in CPNAH is discretized for obtaining the measurement matrix conforming to the restricted isometry property(RIP)used in SL0-CS-PNAH,and the measurement matrix is used to sample the data in a proper compression ratio.The sparse vector least l_0 norm optimization model is established in the constraint condition consisting of sensing matrix,measurement sound pressure of holographic plane,and sparse vector,which is solved by SL0-CS-PNAH,then the optimal sparse solutions is obtained,then the particle normal velocity is reconstructed by multiplying the optimal sparse solutions and sparse matrix.In simulation experiments,SL0-CS-PNAH is compared with CPNAH,orthogonal matching pursuit algorithm planar near-field acoustic holography based on Compressive sensing(OMP-CS-PNAH),subspace pursuit algorithm planar near-field acoustic holography based on Compressive sensing(SP-CS-PNAH)with measurement elements reducing from 64×64 to 32×64.The experimental results indicate that SL0-CS-PNAH has a better reconstruction precision and higher reconstruction efficiency under the condition of the same sampling rate and compression ratio.
As the traditional planar near-filed acoustic holography(CPNAH)is an ill-posed problem,which cannot be solved completely with the wave number domain filtering or Tikhonov regularization method.A planar nearfield acoustic holography based on compressive sensing by using the smoothed l_0 norm(SL0-CS-PNAH)was proposed in this work.According to the characteristics of the sound measurement on the holography plane,the orthogonal wavelet transform matrix is built by using the symlets8 wavelet function,which is used as a sparse basis for the particle normal velocity of the reconstructed plane.The Rayleigh first integral formula used in CPNAH is discretized for obtaining the measurement matrix conforming to the restricted isometry property(RIP)used in SL0-CS-PNAH,and the measurement matrix is used to sample the data in a proper compression ratio.The sparse vector least l_0 norm optimization model is established in the constraint condition consisting of sensing matrix,measurement sound pressure of holographic plane,and sparse vector,which is solved by SL0-CS-PNAH,then the optimal sparse solutions is obtained,then the particle normal velocity is reconstructed by multiplying the optimal sparse solutions and sparse matrix.In simulation experiments,SL0-CS-PNAH is compared with CPNAH,orthogonal matching pursuit algorithm planar near-field acoustic holography based on Compressive sensing(OMP-CS-PNAH),subspace pursuit algorithm planar near-field acoustic holography based on Compressive sensing(SP-CS-PNAH)with measurement elements reducing from 64×64 to 32×64.The experimental results indicate that SL0-CS-PNAH has a better reconstruction precision and higher reconstruction efficiency under the condition of the same sampling rate and compression ratio.
引文
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[11]杜宝,罗健,胡飞,等.基于压缩感知的平面近场声全息方法及其应用[J].机械强度,2016,38(3):485-489.
[12]TROPP J,GILBERT A C.Signal recovery from random measurements via orthogonal matching pursui[J].IEEE Transactions on Information Theory,2008,53(12):4655-4666.
[13]DAI W,MILENKOVIC O.Subspace pursuit for compressive sensing signal reconstruction[J].IEEE Transactions on Information Theory,2009,55(5):2230-2249.
[14]MOHIMANI H,BABAIE-ZADEH M,JUTTEN C.A fast approach for overcomplete sparse decomposition based on smoothed l0 norm[J].IEEE Transactions on Signal Processing,2008,57(1):289-301.
[15]李颖,王泽,王军华,等.基于l0范数近似最小化的稀疏信号重构方法[J].计算机工程与应用,2015,51(10):200-204.
[16]ABUSAG N M,CHAPPELL D J.On sparse reconstructions in near-field acoustic holography using the method of superposition[J].Journal of Computational Acoustics,2016,30(3):472-482.
[17]谢晓春.压缩感知理论在雷达成像中的应用研究[D].北京:中国科学院空间科学与应用研究中心,2010:78-80.
[2]VERONESI W A,MAYNARD J D.Nearfield acoustic holography(NAH):II.Holographic reconstruction algorithms and computer implementation[J].Journal of the Acoustical Society of America,1987,81(5):1307-1322.
[3]王迪,苏小平.基于近场声全息技术的发动机噪声测量与分析[J].机械科学与技术,2014,33(9):1382-1386.
[4]姬庆,程锦房,肖大为.基于不同格林函数的噪声源定位方法研究[J].压电与声光,2017,39(3):378-382.JI Qing,CHEN Jingfang,XIAO Dawei.Research on method of the noise source localization based on different green function[J].Piezoelectrics&Acoustooptics,2017,39(3):378-382.
[5]鲁文波,蒋伟康.基于近场声全息的故障诊断方法及系统实现[J].振动与冲击,2013,32(5):48-51.
[6]陈心昭.近场声全息技术及其应用[M].北京:科学出版社,2013:18-38.
[7]WILLIAMS E G.Regularization methods for near-field acoustical holography[J].Journal of the Acoustical Society of America,2001,110(4):1976-1988..
[8]DONOHO D L.Compressed sensing[J].IEEE Transactions on Information Theory,2006,52(4):1289-1306.
[9]TSAIG Y,DONOHO D.Extensions of compressed sensing[J].Signal Processing,2006,86(3):549-571.
[10]CHARDON G,DAUDET L,PEILLOT A,et al.Nearfield acoustic holography using sparse regularization and compressive sampling principles[J].Journal of the Acoustical Society of America,2012,132(3):2715-2724.
[11]杜宝,罗健,胡飞,等.基于压缩感知的平面近场声全息方法及其应用[J].机械强度,2016,38(3):485-489.
[12]TROPP J,GILBERT A C.Signal recovery from random measurements via orthogonal matching pursui[J].IEEE Transactions on Information Theory,2008,53(12):4655-4666.
[13]DAI W,MILENKOVIC O.Subspace pursuit for compressive sensing signal reconstruction[J].IEEE Transactions on Information Theory,2009,55(5):2230-2249.
[14]MOHIMANI H,BABAIE-ZADEH M,JUTTEN C.A fast approach for overcomplete sparse decomposition based on smoothed l0 norm[J].IEEE Transactions on Signal Processing,2008,57(1):289-301.
[15]李颖,王泽,王军华,等.基于l0范数近似最小化的稀疏信号重构方法[J].计算机工程与应用,2015,51(10):200-204.
[16]ABUSAG N M,CHAPPELL D J.On sparse reconstructions in near-field acoustic holography using the method of superposition[J].Journal of Computational Acoustics,2016,30(3):472-482.
[17]谢晓春.压缩感知理论在雷达成像中的应用研究[D].北京:中国科学院空间科学与应用研究中心,2010:78-80.