**5. Conclusions**

In this paper, a matching pursuit algorithm for backtracking regularization based on energy sorting (ESBRMP) was proposed. The algorithm uses energy sorting to carry out two atomic screening and uses backtracking to delete individual unreliable atoms. Experimental results showed that the ESBRMP algorithm could reconstruct sparse signals with a high probability and had a high reconstruction accuracy without a noisy environment.

**Author Contributions:** H.Z. proposed the framework of this work and carried out all of the experiments, and S.X. drafted the manuscript. P.Z. offered useful suggestions and helped to modify the manuscript. All authors have read and agreed to the published version of the manuscript.

**Funding:** This study was funded by the Huaian Natural Science Research Project (Grant No. HABZ201919), the project of application research and science and technology of Huaian (industrial and agricultural) (Grant Nos. HAGZ2014009), Young excellent talent support program of Huaiyin Normal University (Grant No. 13HSQNZ01), Science and Technology Guiding Project of Fujian Province, China (2019Y0046), Natural Science Foundation of Fujian Province of China (No. 2019J01846, No. 2018J01555, No. 2017J01773), Special subject of Ningde normal university serving local enterprises (Grant Nos. 2019ZX403 and 2018ZX409).

**Conflicts of Interest:** This study is for academic research and submission purposes only. The authors in this study declare that they have no competing interests.
