基于压缩感知的高分辨率近场声全息方法研究

项目名称： 基于压缩感知的高分辨率近场声全息方法研究

项目编号： No.51475134

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 机械、仪表工业

项目作者： 徐亮

作者单位： 合肥工业大学

项目金额： 80万元

中文摘要： 空间分辨率是近场声全息（NAH）性能的一个重要指标。普通NAH技术受Nyquist采样定理的限制，其所能达到的极限空间分辨率为全息面测量间隔。因此，实际中为了获得较高空间分辨率的重建结果，需要在全息面上进行大量的测量，这导致了系统硬件成本的增加和实施难度的增大，不利于NAH的应用推广。 为此，本课题拟建立一种基于压缩感知（CS）理论的高分辨率NAH方法。该方法仅需少量传感器在全息面上较少的测点处进行测量，便能获得空间分辨率超过普通NAH数倍的重建结果，有望解决上述不足。本课题将对CS理论中全息信号的稀疏表示问题，高效观测矩阵的构建方法，全息信号的高精度重构算法，重构过程的稳定性及正则化处理等关键问题展开系统研究，最终形成完善的高分辨率NAH技术流程，并开发出基于CS理论的高性能的NAH 测量分析系统，推动NAH走向工程应用。

中文关键词： 近场声全息；压缩感知；空间分辨率

英文摘要： The spatial resolution is an important performance index of the near field acoustic holography (NAH). Due to the limitation of the Nyquist sampling theorem, the upper limit of spatial resolution of the existing NAH is the measurement interval on hologram surface. Therefore, in order to obtain high spatial resolution, a large number of sensors is needed and a lot of measurement work should be done on the hologram surface. It led to an increase of hardware cost and implementation difficulty. To overcome this disadvantage of the existing NAH, a compressive sensing (CS) based NAH method without spatial resolution limit will be proposed and researched in this project. According to CS theory, a signal which can be sparse represented can be perfectly reconstructed with the sampling rate that far below the requirement of Nyquist sampling theorem. Therefore, it is possible for the proposed method to obtain a higher spatial resolution with fewer sensors and less measurement work. The spatial resolution limit of the existing NAH method is hopeful to be overcome. The key problems which will be studied detailly in the project contain the holographic signal analyzing the sparse representation of holographic signal, the efficient construction of the observation matrix method, the establishment of high spatial resolution reconstruction algorithm for holographic signal, the stability of the reconstruction process, the optimal selection of measurement parameters and the control of reconstructed errors and other key issues. Finally, the procedure of super-resolution NAH technology based on CS theory will be built and the measuring and analyzing system will be developed. The results of the project will promote engineering application of NAH.

英文关键词： near-field acoustic holoagraphy;compressive sensing;spatial resolution