**7. Conclusions**

In this article, we propose a sparse-model-driven network (SMD-Net) for efficient and high-accuracy InSAR phase filtering. The SMD-Net was designed by casting the mathematical derivation steps of the traditional ISTA algorithm into the network structure. Unlike the ISTA algorithm, in each block of the SMD-Net, a CNN module was established to adaptively learn the sparse transform instead of the hand-crafted setting. The SMD-Net not only significantly reduced the network complexity, but was also combined with the merit of automatically learning the parameters and sparse transform of CNN. It can thus improve the filtering performance and speed at the same time. Finally, plenty of experiments were performed to validate the proposed method.

We assessed the proposed method qualitatively and quantitatively on the simulated and measured InSAR data. The experimental results on the simulated and measured data demonstrated that the proposed method could better balance the abilities of the noise suppression and phase fringe texture preservation than the several reference filtering methods. In addition, the speed of the proposed method was very fast. Compared with the PFNet, the SMD-Net was 85.5% and 51.9% faster on the simulated and measured data, respectively. Aiming to validate the performance of the proposed method was not limited by the requirement of the number of training samples, so the experiments were carried out again when the number of training samples was decreased to 10%. Compared with the PFNet trained with 2250 samples, the performance of the proposed method was comparable on the simulated data. In the experiments on the real data, the Qs of the results obtained by processing high-coherence and low-coherence areas with the proposed method were 5.6% and 17.1% higher, respectively. This proves that the comprehensive performance of our method outperformed that of the six competitive approaches, even with small samples.

**Author Contributions:** Conceptualization, N.W. and T.Z.; Methodology, N.W., X.Z. (Xiaoling Zhang) and X.Z. (Xu Zhan); Software, N.W., T.Z. and J.S.; Validation, N.W., L.P. and S.W.; Formal analysis, N.W., X.Z. (Xu Zhan) and Y.H.; Investigation, N.W., L.P. and J.S.; Resources, X.Z. (Xiaoling Zhang) and J.S.; Data curation, N.W. and L.P.; Writing—original draft preparation, N.W., X.Z. (Xu Zhan) and S.W.; Writing—review and editing, N.W., T.Z., X.X. and X.Z. (Xu Zhan); Visualization, N.W., X.Z. (Xiaoling Zhang) and L.P.; Supervision, T.Z., X.Z. (Xu Zhan), Y.H. and X.X.; Project administration, X.Z. (Xiaoling Zhang); Funding acquisition, X.Z. (Xiaoling Zhang). All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was supported in part by the National Natural Science Foundation of China under gran<sup>t</sup> 61571099.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** We would like to thank all of the editors and reviewers for their valuable comments in improving this manuscript.

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