Sparse decomposition of atmospheric turbulence wavefront gradient
Li Juanjuan1, Cai Dongmei1, Jia Peng1, Li Can2     
1. Institute of Physics and Optoelectronics, Taiyuan University of Technology, Taiyuan, Shanxi 030024, China;
2. Institute of Information Engineering, Taiyuan University of Technology, Taiyuan, Shanxi 030024, China

Overview: In astronomical imaging observation, the image quality of observation object decreases because of the influence of atmospheric turbulence and noise. Adaptive optics technique is an effective method to correct atmospheric turbulence disturbance. Wavefront sensor, as the eye of the adaptive system, can detect the distorted wavefront which is affected by atmospheric turbulence in real time. As the aperture of the telescope expands, the resolution is improved and the compressive sensing technique is used to measure the atmospheric turbulent wavefront gradient. Compressive sensing can greatly reduce the amount of measured data, and effectively reduce the pressure of data transmission and storage, which is good for real-time measurement of the turbulent wavefront. But this requires the measurement signal is sparse or can be sparsely represented in one transform domain. In this paper, the sparsity of atmospheric turbulence wavefront gradient signal is studied. Based on the statistical characteristics of atmospheric turbulence, the turbulent power spectrum is sampled by golden section (GS) in the frequency domain, to establish a sparse basis that conforms to the physical characteristics of the atmospheric turbulence, and this basis verifies the sparsity of turbulent wavefront gradient. The sparse decomposition of the wavefront gradient is simulated by using the GS sparse base, and the sparse decomposition effect on the wavefront gradient is compared under different bases such as discrete Fourier transform(DFT), over complete discrete Fourier transform (ODFT), and Zernike. Changing the sparse coefficient value K, the sparse representation performances of different sparse basis were discussed. Simulation results show that the sparse decomposition performance of sparse basis GS established in this paper is better than that other sparse bases, the PSNR of sparse basis is improved 2 dB~5 dB, and the MAER of sparse basis is 0~0.04 decreased. Then the gradients of 60 phase screens are selected for sparse decomposition, which fully verifies that GS basis effect is better than other sparse bases. On the GS basis, the training base (KSVD-GS) is obtained through K-singular value decomposition (KSVD) method, the sparse representation performance of the training basis of the wavefront gradient signal is analyzed, the PSNR is increased 2 dB, and the MAER is decreased 0.01. Finally, by increasing the noise and comparing the robustness of each sparse base, the robustness of the GS base is better than that of other sparse bases. In this paper, we mainly study the sparse decomposition of the wavefront gradient and provide the precondition for the application of compressive sensing.

Supported by Young Scientist Funds of National Natural Science Foundation of China (11503018) and Joint Research Fund in Astronomy (U1631133)