# A Two-Stage Method to Test the Robustness of the Generalized Approximate Message Passing Algorithm
## 4 Bernoulli-Gaussian Pursuit GAMP Algorithm
We create the sensing matrix by DCT transform: \(\mathbf{A}(i;)=(1/N)(\mathrm{DCT}(\Phi(i;)))^{T}\), where every element of \(\Phi\) is drawn from \(\mathcal{N}(0,1)\), and then multiplied a scale factor \(1/\sqrt{M}\) to it. Figure 3a shows the modulus

Figure 1: Reconstruction performance comparison of the Non-zero mean sensing matrix. (**a**) Type-1 sensing matrix; (**b**) Type-2 sensing matrix. Figure 2: Reconstruction performance comparison of the highly column correlations sensing matrix. (**a**) Type-1 sensing matrix; (**b**) Type-2 sensing matrix. of DCT coefficients of the original signal, and Figure 3b shows the modulus of DCT coefficients of the recovered signal. We can see that the major energy has been recovered from the compressed measurements. ## 6 Conclusions

In this paper we propose a new compressed sensing algorithm, the two-stage method. This algorithm pursues the support of a sparse vector sequentially, an meanwhile estimates the amplitudes of the sparse vector by the FS-GAMP process. Numerical experiments with simulation and real world data confirm that our new algorithm performs very well in correctness and robustness. In future work we plan to analyze the variation rate of the marginal posterior probability \(\pi\) to obtain better results. **Acknowledgments:** The author would like to thank the anonymous reviews for their comments that helped to improve the quality of the paper. This research was supported by the National Natural Science Foundation of China (NSFC) under Grant U1533125, and the Scientific Research Program of the Education Department of Sichuan under Grant 16 ZB0032. **Author Contributions:** [PERSON], [PERSON] and [PERSON] conceived and designed the experiments; [PERSON] performed the experiments; [PERSON] wrote the paper. **Conflicts of Interest:** The authors declare no conflict of interest. ## References

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