基于平滑l_0范数的压缩感知近场声全息方法

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。

Near field Acoustic Holography Based on Compressive Sensing by Using the Smoothed l0 Norm Method

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 near field acoustic holography based on compressive sensing by using the smoothed l0 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 l0 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.