**6. Conclusions**

Multiple attenuation is an important problem in seismic data processing. The suppression results directly affect the quality of stacked seismic data. Radon transform is an efficient and low-cost method. In order to solve the problem of low resolution of Radon transform, a sparse parabolic Radon transform in the frequency domain with the nonconvex *Lq*<sup>1</sup> − *Lq*<sup>2</sup> (0 < *q*1, *q*<sup>2</sup> < 1) mixed regularization is proposed. This method has higher sparsity, and it can restrict primaries and multiples, respectively. The mappings of multiple seismic events are muted directly in the Radon domain. The theoretical data and field data results show that the resolution of the parabolic Radon transform and reconstruction capability are improved when using SPRT*Lq*<sup>1</sup> − *Lq*<sup>2</sup> (*q*<sup>1</sup> = *q*<sup>2</sup> = 1/2), especially at near offset. The effectiveness of the sparse constraint method is demonstrated in the aspect of seismic event continuity. This method greatly improves the effect of multiple attenuation and reduces the unnecessary energy loss of useful signals, which provides high-quality data for the subsequent primary imaging.

The proposed method can also be used in other processing methods, such as data reconstruction, interpolation and dispersion curve extraction.

**Author Contributions:** Conceptualization, Q.W. and B.H.; methodology, Q.W. and B.H.; software, B.H.; validation, Q.W., B.H. and J.Z.; formal analysis, Q.W. and B.H.; investigation, Q.W.; resources, C.L.; data curation, Q.W. and B.H.; writing—original draft preparation, Q.W.; writing—review and editing, Q.W., B.H. and J.Z.; visualization, Q.W.; project administration, C.L.; funding acquisition, C.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Natural Science Foundation of China, grant number 41874125.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** The authors give thanks for the open-source program of Matlab.

**Conflicts of Interest:** The authors declare no conflict of interest.
