## 4 CReSL0 Algorithm
### Selection of Optimization Method
Firstly, after the CIPF approximation function is introduced, the combined approximation model of the Gauss function and CIPF function is proposed, which reduces the run-time of the algorithm to a certain extent compared with the single CIPF approximation model. Then, the optimization objective equation is established. Furthermore, after combining the advantages of the steepest descent method, which does not require the accurate initial value, and the second-order convergence of the Newton method, a combined optimization method is added, which greatly improves the reconstruction performance of the algorithm. Then, the CReSL0 algorithm is proposed. The whole paper introduces the basic theory of compressed sensing and the basic content of the ReSL0 algorithm, and then introduces the CReSL0 algorithm proposed in this paper and makes a detailed analysis and explanation of it. Compared with several popular algorithms, the CReSL0 algorithm proposed in this paper has achieved excellent results with regard to the PSNR and running time, in both one-dimensional Gauss signal reconstruction and two-dimensional image reconstruction. Conceptualization, B.W. ; Data curation, B.W. ; Formal analysis, L.W. ; Funding acquisition, B.W. ; Investigation, B.W. ; Methodology, H.Y. ; Project administration, B.W. ; Resources, B.W. ; Software, L.W. ; Supervision, B.W. ; Validation, B.W. ; Visualization, L.W. ; Writing--original draft, B.W. and L.W. ; Writing--review & editing, F.X. This research was funded by the Natural Science Foundation of Hebei Province (No. F2018501051). The authors declare no conflict of interest. ## References

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\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**CR**} & \multicolumn{3}{c}{**PSNR (dB)**} & \multicolumn{3}{c}{**Time (s)**} & \multicolumn{3}{c}{**PSNR/Time**} \\ \cline{2-10}  & **CReSL0** & **ReSL0** & **WReSL0** & **CReSL0** & **ReSL0** & **WReSL0** & **CReSL0** & **ReSL0** & **WReSL0** \\ \hline
0.4 & 27.55 & 26.85 & 27.23 & 3.23 & 2.71 & 4.45 & 8.53 & 9.91 & 6.12 \\ \hline
0.6 & 32.04 & 30.82 & 31.42 & 4.75 & 4.11 & 5.85 & 6.75 & 7.50 & 5.37 \\ \hline
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