# 基于压缩感知理论的卫星云图重构技术研究The Research on Satellite Image Reconstruction Based on Compressed Sensing Theory

Abstract: The theory of compressive sensing breaks the limit of traditional SyQuest sampling theory in-cluded traditional compression coding technology. It is based on the sparsity of the signal, the randomness of the measurement matrix and the nonlinear optimization algorithm to complete the sampling compression and reconstruction of the signal. This new theory can effectively overcome the shortcomings of traditional compression coding technology, and solve the difficulties of high sampling rate, large data volume and real-time transmission in high resolution satellite cloud compression. In this paper, the basic theory of compressed sensing is summarized, and the research of satellite image compression based on compressed sensing theory is discussed in detail; The compressed sensing theory is widely used in the orthogonal matching pursuit algorithm, which makes it more suitable for the processing of satellite imagery; The optimized algorithm of satellite cloud image simulation about the reconstruction effect is carried out, clear the problems in the research, and elaborate the research direction of the next step.

1. 引言

2. 压缩感知理论

$Y=\Phi X=\Phi \Psi \alpha =\theta \alpha$ (1)

$Y=\Phi X=\Phi \Psi \alpha =\theta \alpha$ (2)

Figure 1. Compressed sensing linear measurement process

3. 基于压缩感知的卫星云图处理

3.1. 对卫星云图的稀疏处理

(3)

3.2. 对测量矩阵的选取

(4)

3.3. 对卫星云图的重建处理

(a) 原始图像 (b) 采样率M/N = 0.5(c) 采样率M/N = 0.4 (d) 采样率M/N = 0.3

Figure 2. CS theory combines wavelet transform and classical OMP algorithm to reconstruct satellite image reconstruction

Figure 3. The CS theory combines the wavelet transform and the PSNR of different sampling rates under the classic OMP algorithm

Figure 4. CS theory combines wavelet transform and MSE of different sampling rate under the classical OMP algorithm

3.4. 对卫星云图的重建处理的算法改进

4. 仿真实验结果与对比

Table 1. The comparison of PSNR values of reconstructed images with different sampling rates of different sampling rates is presented

Table 2. 28/5000 The MSE value of the reconstructed image is compared with the different mean square error

(a) 原始图像 (b) 采样率M/N = 0.5(c) 采样率M/N = 0.4 (d) 采样率M/N = 0.3

Figure 5. The reconstruction effect of 8 x 8 block in different sampling rate

(a) 原始图像 (b) 采样率M/N = 0.5(c) 采样率M/N = 0.4 (d) 采样率M/N = 0.3

Figure 6. The reconstruction effect of 16 x 16 block in different sampling rate

5. 结束语

[1] Donoho, D.L. (2006) Compressed Sensing. IEEE Transactions on Information Theory, 52, 1289-1306. https://doi.org/10.1109/TIT.2006.871582

[2] Candès, E. (2006) Compressive Sampling. Marta Sanz Solé, 1433-1452.

[3] Mallat, S. (1989) Multifrequency Channel Decomposition of Images and Wavelet Models. IEEE Transactions on Acoustics Speech and Signal Processing, 37, 2091-2110. https://doi.org/10.1109/29.45554

[4] Taubman, D. and Zakhor, A. (1994) Mulirate 3-D Subband Coding of Video. IEEE Transactions on Acoustics Speech and Signal Processing, 3, 572-588.

[5] Xiong, Z., Ranchandran, K., Orchard, M.T., et al. (1999) A Comparative Study of DCT-and Wavelet-Based Images Coding. IEEE Transactions on Circuits and Systems for Video Technology, 9, 692-695. https://doi.org/10.1109/76.780358

[6] Candès, E. and Rom, B. (2007) Sparsity and Incoherence in Compressive Sampling. Inverse Problems, 23, 969-985. https://doi.org/10.1088/0266-5611/23/3/008

[7] Tropp, J.A. and Gilbert, A.C. (2007) Signal Recovery from Rand m Measurements Via Orthogonal Matching Pursuit. IEEE Transactions on Information Theory, 53, 4655- 4666. https://doi.org/10.1109/TIT.2007.909108

[1] Donoho, D.L. (2006) Compressed Sensing. IEEE Transactions on Information Theory, 52, 1289-1306.
https://doi.org/10.1109/TIT.2006.871582

[2] Candès, E. (2006) Compressive Sampling. Marta Sanz Solé, 1433-1452.

[3] Mallat, S. (1989) Multifrequency Channel Decomposition of Images and Wavelet Models. IEEE Transactions on Acoustics Speech and Signal Processing, 37, 2091-2110.
https://doi.org/10.1109/29.45554

[4] Taubman, D. and Zakhor, A. (1994) Mulirate 3-D Subband Coding of Video. IEEE Transactions on Acoustics Speech and Signal Processing, 3, 572-588.

[5] Xiong, Z., Ranchandran, K., Orchard, M.T., et al. (1999) A Comparative Study of DCT-and Wavelet-Based Images Coding. IEEE Transactions on Circuits and Systems for Video Technology, 9, 692-695.
https://doi.org/10.1109/76.780358

[6] Candès, E. and Rom, B. (2007) Sparsity and Incoherence in Compressive Sampling. Inverse Problems, 23, 969-985.
https://doi.org/10.1088/0266-5611/23/3/008

[7] Tropp, J.A. and Gilbert, A.C. (2007) Signal Recovery from Rand m Measurements Via Orthogonal Matching Pursuit. IEEE Transactions on Information Theory, 53, 4655- 4666.
https://doi.org/10.1109/TIT.2007.909108

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