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.
