基于总变分低秩组稀疏的全球雷达数据修复算法

Global-scale radar data restoration algorithm based on total variation and low-rank group sparsity

针对航天飞机雷达地形测绘任务(SRTM)中存在由大量尖峰、斑点和多向条纹误差形成的混合噪声对后续应用产生严重干扰的问题,提出了一种基于总变分约束的低秩组稀疏(LRGS_TV)算法。首先,利用数据在局部范围低秩方向上的唯一性来正则化全局多方向条带误差结构,同时使用变分思想进行单向约束;其次,使用加权核范数的非局部自相似性来消除随机噪声,并结合总变分(TV)正则对数据梯度进行约束,以减小局部范围变化差值;最后,使用交替方向乘子优化对低秩组稀疏模型进行求解,从而保证了模型的收敛性。把所提算法与TV、单方向总变分(UTV)、低秩单图像分解(LRSID)和低秩组稀疏(LRGS)模型这4种算法进行定量评估的结果表明,LRGS_TV的峰值信噪比(PSNR)可以达到38.53 dB,结构相似性(SSIM)可以达到0.97,均为5种算法中的最优。同时,坡度与坡向结果表明,经LRGS_TV处理后,数据的后续应用有显著改善。实验结果表明,LRGS_TV能够在保证地形轮廓特征基本不变的情况下更好地修复原始数据,可对SRTM可靠性的提高与后续应用提供重要的支持。

The mixed noise formed by a large number of spikes,speckles and multi-directional stripe errors in Shuttle Radar Terrain Mission(SRTM)will cause serious interference to the subsequent applications.In order to solve the problem,a Low-Rank Group Sparsity_Total Variation(LRGS_TV)algorithm was proposed.Firstly,the uniqueness of the data in the local range low-rank direction was used to regularize the global multi-directional stripe error structure,and the variational idea was used to perform unidirectional constraints.Secondly,the non-local self-similarity of the weighted kernel norm was used to eliminate the random noise,and the Total Variation(TV)regularity was combined to constrain the data gradient,so as to reduce the difference of local range changes.Finally,the low-rank group sparse model was solved by the alternating direction multiplier optimization to ensure the convergence of model.Quantitative evaluation shows that,compared with four algorithms such as TV,Unidirectional Total Variation(UTV),Low-Rank-based Single-Image Decomposition(LRSID)and Low-Rank Group Sparsity(LRGS)model,the proposed LRGS_TV has the Peak Signal-to-Noise Ratio(PSNR)of 38.53 dB and the Structural SIMilarity(SSIM)of 0.97,which are both better than the comparison algorithms.At the same time,the slope and aspect results show that after LRGS_TV processing,the subsequent applications of the data can be significantly improved.The experimental results show that,the proposed LRGS_TV can repair the original data better while ensuring that the terrain contour features are basically unchanged,and can provide important support to the reliability improvement and subsequent applications of SRTM.