中文摘要：

本文提出了一种基于梯度向量域上字典学习的InSAR相位的降噪算法．首先利用字典学习，建立了干涉相位滤波的优化模型．鉴于该模型难以求解，本文采用分裂技术和增广拉格朗日框架，获得非线性约束松弛优化模型，最后引入交替方向乘子法对松弛问题求解，获得最终的相位滤波结果．具体地，通过先从InSAR复相位图的水平和垂直梯度域依顺序训练字典，然后从这两个梯度向量的稀疏表达式出发重建所需的干涉相位图．对仿真和实测数据的处理结果显示这种新的InSAR相位降噪方法在残点数、均方误差和边缘完整性保持等方面优于几种经典的滤波方法．

英文摘要：

A novel phase noise filtering algorithm for InSAR using dictionary learning in the gradient vector domain is proposed. With this technique, the original optimization problem for the InSAR noise reduction is first established. However, due to the non-convexity of the optimization problem, it is difficult to solve. Then, by using the splitting technique and employing the augmented Lagrangian framework, we obtain a relaxed nonlinear constraint optimization problem with l1-norm regularization which can be solved efficiently by the alternating direction method of multipliers. Specifically, we first train dictionaries from the horizontal and vertical gradients of the InSAR complex phase image sequentially, and then reconstruct the desired image from the sparse representations of both gradients. Numerical experiments on simulated and measured data show that the new InSAR phase noise reduction method has a better performance than several standard phase filtering methods in terms of residual counts, mean square error and maintenance of the fringe completeness.