*Article* **A Sparse-Model-Driven Network for Efficient and High-Accuracy InSAR Phase Filtering**

**Nan Wang, Xiaoling Zhang \*, Tianwen Zhang, Liming Pu, Xu Zhan, Xiaowo Xu, Yunqiao Hu, Jun Shi and Shunjun Wei**

> School of Information and Communication Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China; wangnan@std.uestc.edu.cn (N.W.); twzhang@std.uestc.edu.cn (T.Z.); puliming@std.uestc.edu.cn (L.P.); zhanxu@std.uestc.edu.cn (X.Z.); xuxiaowo@std.uestc.edu.cn (X.X.); hyq@std.uestc.edu.cn (Y.H.); shijun@uestc.edu.cn (J.S.); weishunjun@uestc.edu.cn (S.W.) **\*** Correspondence: xlzhang@uestc.edu.cn

**Abstract:** Phase filtering is a vital step for interferometric synthetic aperture radar (InSAR) terrain elevation measurements. Existing phase filtering methods can be divided into two categories: traditional model-based and deep learning (DL)-based. Previous studies have shown that DL-based methods are frequently superior to traditional ones. However, most of the existing DL-based methods are purely data-driven and neglect the filtering model, so that they often need to use a large-scale complex architecture to fit the huge training sets. The issue brings a challenge to improve the accuracy of interferometric phase filtering without sacrificing speed. Therefore, we propose a sparse-modeldriven network (SMD-Net) for efficient and high-accuracy InSAR phase filtering by unrolling the sparse regularization (SR) algorithm to solve the filtering model into a network. Unlike the existing DL-based filtering methods, the SMD-Net models the physical process of filtering in the network and contains fewer layers and parameters. It is thus expected to ensure the accuracy of the filtering without sacrificing speed. In addition, unlike the traditional SR algorithm setting the spare transform by handcrafting, a convolutional neural network (CNN) module was established to adaptively learn such a transform, which significantly improved the filtering performance. Extensive experimental results on the simulated and measured data demonstrated that the proposed method outperformed several advanced InSAR phase filtering methods in both accuracy and speed. In addition, to verify the filtering performance of the proposed method under small training samples, the training samples were reduced to 10%. The results show that the performance of the proposed method was comparable on the simulated data and superior on the real data compared with another DL-based method, which demonstrates that our method is not constrained by the requirement of a huge number of training samples.

**Keywords:** interferometric phase filtering; sparse regularization (SR); deep learning (DL); neural convolutional network (CNN)
