基于交叠组稀疏非凸Lp伪范数高阶全变分的地震随机噪声压制

针对高阶全变分模型在地震资料去噪中存在严重阶梯效应的问题，引入交叠组稀疏去噪技术；为提升对局部细节的保护能力，加入非凸L_p伪范数正则化，形成一种改进的去噪模型。该模型是从传统孤立的数据点向四周延伸，充分挖掘信号的邻域相似性。由于改进模型存在耦合问题，进一步采用交替方向乘子迭代法将其转化为四个子问题，并在求解过程中采用最大最小值算法和加权方向迭代L₁算法以提高计算精度和效率。模拟数据和实际资料的应用结果表明，所提方法不仅能有效减弱阶梯效应，压制地震数据中的随机噪声，而且具有保护弱小信号局部细节的能力。

Random noises suppression based on overlapping group sparsity,non-convex Lp-pseudo-norm regula-rization and higher-order total variation

Suffering serious staircase effects, the higher-order total variation model provides unsatisfactory denoising results. In this paper, we introduce a technique of overlapping group sparsity, and utilize the non-convex L_p-pseudo-norm for preserving weak signals. Our new model can fully exploit local similarity of signals instead of unrelated individual data. To solve the multi-constrained problem, we adopt the alternating direction method of multipliers to divide the whole problem into four sub-problems. The iteratively re-weighted alternating direction L₁-norm and majorization minimization algorithm are added into the algorithm to improve the efficiency and accuracy. Applied to synthetic and field data, the improved method not only reduced staircase effects and attenuated random noises, but also effectively preserved weak signals.