基于SL_0的高分辨率Radon变换及数据重建

High resolution Radon transform based on SL_0 and its application in data reconstruction

L_0范数是度量数据稀疏度的最优方法,但它具有的非凸性造成求解困难。本文将光滑L_0范数(Smoothed L_0 Norm,SL_0)稀疏约束引入Radon变换中,降低了其求解难度,并进一步提高了Radon变换的分辨率。即通过构建平滑的连续函数逼近L_0范数,以此作为抛物线Radon变换的目标函数,采用最速下降法和梯度投影原理获得最优解。理论模型和实际地震数据重建试验结果表明,该方法进一步提高了Radon变换分辨率,较好地恢复了缺失地震数据的连续性和AVO特性。

The L_0 norm is the optimal way to measure the sparsity of data,however it is difficult to solve the L_0 due to its non convexity.This paper introduce smoothed L_0 norm(SL_0)into the Radon transform to overcome the difficulty of solving and further to improve the resolution of Radon transform.We first use smoothed continuous functions as objective functions of the parabolic Radon transform to approximate the L_0 norm,and then we use the steepest descent method and gradient projection principle to approach the optimal solution.Experiments on both theoretical model and field data show that the proposed method not only improves the resolution of Radon transform,but also restores the continuity of seismic data and AVO characteristics.