基于稀疏贝叶斯学习的高分辨率Patch近场声全息
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摘要
针对基于空间二维Fourier变换的近场声全息技术的重建效果受到测量孔径与测点数影响的问题,提出一种基于稀疏贝叶斯学习的高分辨率Patch近场声全息方法。利用高斯核函数和稀疏贝叶斯学习算法对全息面声压进行插值和外推,利用插值和外推后的全息面声压进行近场声全息重建。仿真和实验结果表明,所提方法可有效抑制小全息孔径测量对重建精度的影响,同时可以在测点较少的情况下极大提升全息重建的空间分辨率。另外,仿真结果还证明了插值过程具有较好的稳定性,可以在一定程度上提高测量数据的信噪比。
An approach for super resolution patch near-field acoustic holography was proposed based on sparse Bayesian learning. The interpolation and extrapolation models were first established by use of the Gaussian kernel functions and the sparse Bayesian learning, and then the measured pressure was simultaneously interpolated and extrapolated to obtain a larger and denser virtual measurement. Finally,the interpolated and extrapolated pressures were used to perform near-field acoustic holography. Results of the simulation and experiment show that the aperture effect was greatly suppressed and the super resolution reconstruction can be achieved when using the Fourier-based near-field acoustic holography. It also shows that the measurement noise was suppressed in the process of interpolation.
An approach for super resolution patch near-field acoustic holography was proposed based on sparse Bayesian learning. The interpolation and extrapolation models were first established by use of the Gaussian kernel functions and the sparse Bayesian learning, and then the measured pressure was simultaneously interpolated and extrapolated to obtain a larger and denser virtual measurement. Finally,the interpolated and extrapolated pressures were used to perform near-field acoustic holography. Results of the simulation and experiment show that the aperture effect was greatly suppressed and the super resolution reconstruction can be achieved when using the Fourier-based near-field acoustic holography. It also shows that the measurement noise was suppressed in the process of interpolation.
引文
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[2]WILLIAMS E G,MAYNARD J.Holographic imaging without the wavelength resolution limit[J].Physical Review Letters,1980,45(7):554.
[3]HARRIS M C,BLOTTER J D,SOMMERFELDT S D.Obtaining the complex pressure field at the hologram surface for use in near-field acoustical holography when pressure and in-plane velocities are measured[J].The Journal of the Acoustical Society of America,2006,119(2):808-816.
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[10]WU S F.Methods for reconstructing acoustic quantities based on acoustic pressure measurements[J].The Journal of the Acoustical Society of America,2008,124(5):2680-2697.
[11]SAIJYOU K,YOSHIKAWA S.Reduction methods of the reconstruction error for large-scale implementation of nearfield acoustical holography[J].The Journal of the Acoustical Society of America,2001,110(4):2007-2023.
[12]WILLIAMS E G,HOUSTION B H,HERDIC P C.Fast Fourier transform and singular value decomposition formulations for patch nearfield acoustical holography[J].The Journal of the Acoustical Society of America,2003,114(3):1322-1333.
[13]徐亮,毕传兴,陈剑,等.基于波数域外推方法的近场声全息[J].机械工程学报,2007,43(9):84-90.XU Liang,BI Chuanxing,CHEN Jian,et al.Nearfield acoustic holography based on K-space data extrapolation method[J].Chinese Journal of Mechanical Engineering,2007,43(9):84-90.
[14]徐亮,毕传兴,王慧,等.全息声压场的加权范数外推方法[J].物理学报,2011,60(11):398-408.XU Liang,BI Chuanxing,WANG Hui,et al.Hologram pressure field weighted norm extrapolation method[J].Acta Physica Sinica,2011,60(11):398-408.
[15]SCHOLTE R,LOPEZ I,BERT ROOZEN N,et al.Truncated aperture extrapolation for Fourier-based near-field acoustic holography by means of border-padding[J].The Journal of the Acoustical Society of America,2009,125(6):3844-3854.
[16]ARTEAGA I L,SCHOLTE R,NIJMEIJER H.Improved source reconstruction in fourier-based near-field acoustic holography applied to small apertures[J].Mechanical Systems and Signal Processing,2012,32:359-373.
[17]徐亮,毕传兴,陈剑,等.基于波叠加法的patch近场声全息及其实验研究[J].物理学报,2007,56(5):2776-2783.XU Liang,BI Chuanxing,CHEN Jian,et al.Algorithm and experimental investigation of patch nearfield acoustic holography based on wave superposition approach[J].Acta Physica Sinica,2007,56(5):2776-2783.
[18]毕传兴,袁艳,贺春东,等.基于分布源边界点法的局部近场声全息技术[J].物理学报,2010,59(12):8646-8654.BI Chuanxing,YUAN Yan,HE Chundong,et al.Patch nearfield acoustic holography based on the distributed source boundary point method[J].Acta Physica Sinica,2010,59(12):8646-8654.
[19]PASCAL J C,PAILLASSEUR S,THOMAS J H,et al.Patch near-field acoustic holography:regularized extension and statistically optimized methods[J].Journal of the Acoustical Society of America,2009,126(3):1264-1268.
[20]VALDIVIA N P,WILLIAMS E G,HERDIC P C.Approximations of inverse boundary element methods with partial measurements of the pressure field[J].The Journal of the Acoustical Society of America,2008,123(1):109-120.
[21]MAYNARD J D,WILLIAMS E G,LEE Y.Nearfield acoustic holography:I.Theory of generalized holography and the development of NAH[J].The Journal of the Acoustical Society of America,1985,78(4):1395-1413.
[22]SCHABACK R.Limit problems for interpolation by analytic radial basis functions[J].Journal of Computational&Applied Mathematics,2008,212(2):127-149.
[23]FASSHAUER G E,MCCOURT M J.Stable evaluation of gaussian radial basis function interpolants[J].Siam Journal on Scientific Computing,2012,34(2):737-762.
[24]石光明,刘丹华,高大化,等.压缩感知理论及其研究进展[J].电子学报,2009,37(5):1070-1081.SHI Guangming,LIU Danhua,GAO Dahua,et al.Advances in theory and application of compressed sensing[J].Acta Electronica Sinica,2009,37(5):1070-1081.
[25]TIPPING M E.Sparse bayesian learning and the relevance vector machine[J].Journal of Machine Learning Research,2001(1):211-244.
[26]蔡泽民,赖剑煌.一种基于超完备字典学习的图像去噪方法[J].电子学报,2009,37(2):347-350.CAI Zemin,LAI Jianhuang.An over-complete learned dictionary-based image de-noising method[J].Acta Electronica Sinica,2009,37(2):347-350.
[2]WILLIAMS E G,MAYNARD J.Holographic imaging without the wavelength resolution limit[J].Physical Review Letters,1980,45(7):554.
[3]HARRIS M C,BLOTTER J D,SOMMERFELDT S D.Obtaining the complex pressure field at the hologram surface for use in near-field acoustical holography when pressure and in-plane velocities are measured[J].The Journal of the Acoustical Society of America,2006,119(2):808-816.
[4]XU L,BI C,CHEN X,et al.Resolution enhancement of nearfield acoustic holography by interpolation using bandlimited signal restoration method[J].Chinese Science Bulletin,2008,53(20):3142-3150.
[5]徐亮,陈心昭,毕传兴,等.近场声全息分辨率增强的正交球面波插值方法[J].浙江大学学报(工学版),2009,43(10):1808-1811.XU Liang,CHEN Xinzhao,BI Chuanxing,et al.Nearfield acoustic holography resolution enhancing method based on interpolation using orthogonal spherical wave source[J].Journal of Zhejiang University(Engineering Science),2009,43(10):1808-1811.
[6]张小正,毕传兴,徐亮,等.基于波叠加法的近场声全息空间分辨率增强方法[J].物理学报,2010,59(8):5564-5571.ZHANG Xiaozheng,BI Chuanxing,XU Liang,et al.Resolution enhancement of nearfield acoustic holography by the wave superposition approach[J].Acta Physica Sinica,2010,59(8):5564-5571.
[7]毛荣富,朱海潮,柳志忠,等.利用支持向量回归插值减少全息面测量点数方法的试验研究[J].振动与冲击,2010,29(3):128-131.MAO Rongfu,ZHU Haichao,LIU Zhizhong,et al.Experimental study on reduction of measuring points number on hologram using support vector regression[J].Journal of Vibration and Shock,2010,29(3):128-131.
[8]孙超,何元安,商德江,等.全息数据外推与插值技术的极限学习机方法[J].哈尔滨工程大学学报,2014,35(5):544-551.SUN Chao,HE Yuanan,SHANG Dejiang,et al.Hologram data extrapolation and interpolation method based on the extreme learning machine[J].Journal of Harbin Engineering University,2014,35(5):544-551.
[9]WILLIAMS E G.傅里叶声学:声辐射与近场声全息[M].卢奂采译.北京:清华大学出版社,2016.
[10]WU S F.Methods for reconstructing acoustic quantities based on acoustic pressure measurements[J].The Journal of the Acoustical Society of America,2008,124(5):2680-2697.
[11]SAIJYOU K,YOSHIKAWA S.Reduction methods of the reconstruction error for large-scale implementation of nearfield acoustical holography[J].The Journal of the Acoustical Society of America,2001,110(4):2007-2023.
[12]WILLIAMS E G,HOUSTION B H,HERDIC P C.Fast Fourier transform and singular value decomposition formulations for patch nearfield acoustical holography[J].The Journal of the Acoustical Society of America,2003,114(3):1322-1333.
[13]徐亮,毕传兴,陈剑,等.基于波数域外推方法的近场声全息[J].机械工程学报,2007,43(9):84-90.XU Liang,BI Chuanxing,CHEN Jian,et al.Nearfield acoustic holography based on K-space data extrapolation method[J].Chinese Journal of Mechanical Engineering,2007,43(9):84-90.
[14]徐亮,毕传兴,王慧,等.全息声压场的加权范数外推方法[J].物理学报,2011,60(11):398-408.XU Liang,BI Chuanxing,WANG Hui,et al.Hologram pressure field weighted norm extrapolation method[J].Acta Physica Sinica,2011,60(11):398-408.
[15]SCHOLTE R,LOPEZ I,BERT ROOZEN N,et al.Truncated aperture extrapolation for Fourier-based near-field acoustic holography by means of border-padding[J].The Journal of the Acoustical Society of America,2009,125(6):3844-3854.
[16]ARTEAGA I L,SCHOLTE R,NIJMEIJER H.Improved source reconstruction in fourier-based near-field acoustic holography applied to small apertures[J].Mechanical Systems and Signal Processing,2012,32:359-373.
[17]徐亮,毕传兴,陈剑,等.基于波叠加法的patch近场声全息及其实验研究[J].物理学报,2007,56(5):2776-2783.XU Liang,BI Chuanxing,CHEN Jian,et al.Algorithm and experimental investigation of patch nearfield acoustic holography based on wave superposition approach[J].Acta Physica Sinica,2007,56(5):2776-2783.
[18]毕传兴,袁艳,贺春东,等.基于分布源边界点法的局部近场声全息技术[J].物理学报,2010,59(12):8646-8654.BI Chuanxing,YUAN Yan,HE Chundong,et al.Patch nearfield acoustic holography based on the distributed source boundary point method[J].Acta Physica Sinica,2010,59(12):8646-8654.
[19]PASCAL J C,PAILLASSEUR S,THOMAS J H,et al.Patch near-field acoustic holography:regularized extension and statistically optimized methods[J].Journal of the Acoustical Society of America,2009,126(3):1264-1268.
[20]VALDIVIA N P,WILLIAMS E G,HERDIC P C.Approximations of inverse boundary element methods with partial measurements of the pressure field[J].The Journal of the Acoustical Society of America,2008,123(1):109-120.
[21]MAYNARD J D,WILLIAMS E G,LEE Y.Nearfield acoustic holography:I.Theory of generalized holography and the development of NAH[J].The Journal of the Acoustical Society of America,1985,78(4):1395-1413.
[22]SCHABACK R.Limit problems for interpolation by analytic radial basis functions[J].Journal of Computational&Applied Mathematics,2008,212(2):127-149.
[23]FASSHAUER G E,MCCOURT M J.Stable evaluation of gaussian radial basis function interpolants[J].Siam Journal on Scientific Computing,2012,34(2):737-762.
[24]石光明,刘丹华,高大化,等.压缩感知理论及其研究进展[J].电子学报,2009,37(5):1070-1081.SHI Guangming,LIU Danhua,GAO Dahua,et al.Advances in theory and application of compressed sensing[J].Acta Electronica Sinica,2009,37(5):1070-1081.
[25]TIPPING M E.Sparse bayesian learning and the relevance vector machine[J].Journal of Machine Learning Research,2001(1):211-244.
[26]蔡泽民,赖剑煌.一种基于超完备字典学习的图像去噪方法[J].电子学报,2009,37(2):347-350.CAI Zemin,LAI Jianhuang.An over-complete learned dictionary-based image de-noising method[J].Acta Electronica Sinica,2009,37(2):347-350.