大气湍流畸变波前斜率的稀疏分解

利用压缩感知技术对大气湍流波前探测数据进行压缩，可使测量数据量大幅度减少，能有效降低数据的传输与存储压力，有利于湍流波前的实时测量；但压缩条件要求波前信号是稀疏的或在某个变换域内能够稀疏表示。本文对大气湍流波前斜率信号的稀疏性进行了初步研究，基于大气湍流的统计特性，在频域内对湍流功率谱作黄金分割采样(GS)，建立符合大气湍流斜率物理特征的稀疏基，明确了湍流波前斜率的稀疏性。利用该GS 稀疏基对波前斜率进行稀疏分解，并通过仿真实验对比了不同稀疏基对波前斜率的稀疏分解效果。在此基础上，以GS 基作为训练基的初始化字典，进行K 奇异值分解字典训练(KSVD)，得到训练基(KSVD-GS)，分析了该训练基对波前斜率信号的稀疏表示性能。本文验证了波前斜率能够稀疏分解，建立了一个较好的稀疏基，为压缩感知的应用提供了前提基础。

Abstract

Using compressive sensing technology in atmospheric turbulent wavefront detected data compression can greatly reduce the amount of measured data, can effectively reduce the pressure of data transmission and storage, which is good for real-time measurement of turbulent wavefront. However, the wavefront signal is required to be sparse or can be sparsely represented in one transform domain. In this paper, a preliminary study of the sparsity of the atmospheric turbulent wavefront gradient signal is carried out. Based on the statistical characteristics of atmospheric turbulence, the golden section (GS) is used to make the turbulent power spectrum in the frequency domain, and the sparse basis is established to meet the physical characteristics of the turbulent gradient, then the sparsity of the gradient of the turbulent wavefront is clarified. The sparse decomposition of the wavefront gradient is simulated by using the GS sparse base, and the sparse decomposition effect of different sparsity bases on the wavefront gradient is compared. On this basis, using the GS basis as the initialization training dictionary, K singular value decomposition (KSVD) dictionary training is carried out to get the training base (KSVD-GS), and then the sparse representation performance of this training base to the wavefront gradient signal is analyzed. This paper verifies that the wavefront gradient can be sparsely decomposed and build a better sparse basis, and provides the precondition for the application of compressive sensing.

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李娟娟, 蔡冬梅, 贾鹏, 李灿. 大气湍流畸变波前斜率的稀疏分解[J]. 光电工程, 2018, 45(2): 170616. Li Juanjuan, Cai Dongmei, Jia Peng, Li Can. Sparse decomposition of atmospheric turbulence wavefront gradient[J]. Opto-Electronic Engineering, 2018, 45(2): 170616.

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