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Research on reconstruction of atmospheric turbulence wavefront compressed sensing measurement
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摘要:
压缩感知技术用于大气湍流波前斜率测量能在很大程度上提高波前信号的测量速度，同时降低波前测量系统的硬件压力。与现有波前斜率测量方法不同，压缩感知波前测量方法增加了从波前斜率的稀疏测量值到波前斜率信号的重建过程，因此将压缩感知技术用于波前测量，需要快速、高精度的波前斜率重建算法。Smoothed L0 Norm (SL0)算法是一种近似L0范数估计的优化迭代重建算法，与其它算法相比，不需要事先知道信号的稀疏度，计算量低且估计精度高。本文以SL0算法为基础，对波前斜率信号分区域测量，再结合并行运算，通过理论分析和仿真实验实现了一种能够快速、高精度重建信号的分区域并行算法—Block-Smoothed L0 Norm (B-SL0)。实验结果表明，B-SL0在计算时间和精度都明显优于现有的其它重建算法，对压缩感知技术用于大气湍流波前测量的可行性进行了初步探索。
Abstract:Compressed sensing technology for atmospheric turbulence wavefront slope measurement can greatly improve the wavefront signal measurement speed, while reducing the pressure of wavefront measurement system hardware. Different from the existing wavefront slope measurement method, the compressed sensing wavefront measurement increase a process which from sparse measurement of wavefront slope value to the reconstruction of the wavefront slope signal. Therefore, a fast and accurate wavefront slope reconstruction algorithm is needed if the compressed sensing technology is used for wavefront measurement. Smoothed L0 Norm (SL0) algorithm is an optimized iterative reconstruction algorithm with approximate L0 norm estimation, and compared with other algorithms, it is not necessary to know the sparsity of the signal in advance, and the calculation is low and the estimation accuracy is high. Based on the SL0 algorithm, this paper implements a subregion parallel algorithm-Block-Smoothed L0 Norm (B-SL0) which can quickly and accurately reconstruct the signal by measuring the wavefront slope signal in subarea and parallel operations through theoretical analysis and experiments. The experimental results show that B-SL0 is significantly better than other existing reconstruction algorithms in the calculation time and accuracy, and explore the feasibility of compressed sensing technology for measurement of atmospheric turbulence wavefront preliminarily.
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Key words:
- compressed sensing /
- wavefront slope /
- SL0 algorithm /
- subregion /
- parallel operation
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Overview: Compressed sensing technology for atmospheric turbulence wavefront slope measurement can greatly improve the wavefront signal measurement speed, while reducing the pressure of wavefront measurement system hardware. Different from the existing wavefront slope measurement method, the compressed sensing wavefront measurement increase a process from sparse measurement of wavefront slope value to the reconstruction of the wavefront slope signal, which will increase the wavefront data processing time. So this means putting forward higher demands on the compressed sensing reconstruction algorithm. Therefore, it is necessary to reconstruct wavefront slope quickly and accurately with compressed sensing technology for wavefront measurement.
Smoothed L0 Norm (SL0) algorithm is an optimal iterative reconstruction algorithm with approximate L0 norm estimation. Compared with other algorithms, it does not need to know the sparsity of the signal in advance, and it has lower computational complexity and higher estimation accuracy. Because the SL0 algorithm is based on one-dimensional signal reconstruction, while the method of column by line serial reconstruction is used for two-dimensional signals such as wavefront slope. On the one hand, it belongs to serial operation and increases the reconstruction time, on the other hand, it destorys the relationship between the columns of the wavefront slope signal, which reduces the wavefront slope reconstruction precision.
Aiming at the shortcomings of its reconstruction accuracy and running speed, this paper implements a subregion parallel algorithm—Block-Smoothed L0 Norm (B-SL0), which can quickly and accurately reconstruct the signal by measuring the wavefront slope signal in subarea and parallel operations through theoretical analysis and simulation experiments based on the SL0 algorithm the wavefront derivative compressed sensing (DCS). The B-SL0 algorithm uses subregional parallel operation, which not only reduces the running time of the reconstruction algorithm, but also reduces the damage to the internal information of the wavefront slope signal and further improves the reconstruction accuracy of the wavefront phase.
The simulation results show that the B-SL0 algorithm is superior to the SL0 algorithm in terms of the running time of the wavefront slope reconstruction, and the wavefront phase accuracy restored by the reconstructed wavefront slope is better than that of the SL0 algorithm. In addition, compared with some classical algorithms, such as OMP, SP and BP, the B-SL0 algorithm in the same conditions not only greatly improves the running time of the wavefront slope reconstruction, and the reconstructed wavefront slope signal can restore the atmospheric turbulence wavefront phase better, which reflects the performance of the B-SL0 algorithm is good in reconstructing phase screen.
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图 1 波前斜率压缩感知测量过程
Figure 1. The measurement process of wavefront slope compressed sensing
图 4 r=0.3时，B-SL0和SL0重建和重建误差对比图。(a)原图；(b) B-SL0重建图；(c) B-SL0重建误差图；(d) SL0重建图；(e) SL0重建误差图
Figure 4. The reconstruction comparison of B-SL0 and SL0 when r=0.3. (a) Original image; (b) Reconstruction of B-SL0; (c) Reconstruction error of B-SL0; (d) Reconstruction of SL0; (e) Reconstruction error of SL0
图 5 合成相位ϕ峰值信噪比与均方误差分析曲线
Figure 5. The analysis curve about curve peak signal to noise ratio and mean square error of synthetic phase ϕ
图 7 任意一幅相位屏重建对比图。(a)原图；(b) B-SL0重建图；(c) B-SL0重建误差图；(d) SL0重建图；(e) SL0重建误差图
Figure 7. The reconstruction comparison of any one phase screen. (a) Original image; (b) Reconstruction of B-SL0; (c) Reconstruction error of B-SL0; (d) Reconstruction of SL0; (e) Reconstruction error of SL0
图 8 不同信噪比下的PSNR与MSE对比图
Figure 8. Comparison of PSNR and MSE under different signal to noise ratio
表 1 不同相位屏的SL0与B-SL0重建质量对比
Table 1. The reconstruction quality comparison of SL0 and B-SL0 algorithm under different phase screens
Algorithms PSNR/dB MSE Running time/s ϕx ϕy B-SL0 48.48 0.43 0.27 0.24 SL0 35.25 9.70 1.55 1.52 
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表 2 各算法重建质量对比
Table 2. The reconstruction quality comparison of different algorithms
Algorithms PSNR/dB MSE Running time/s ϕx ϕy B-SL0 56.67 0.40 0.26 0.24 SL0 45.09 5.80 1.56 1.54 OMP 44.09 7.30 4.24 4.81 SP 32.73 99.88 1.59 1.59 BP 34.13 72.27 24.26 30.96
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