An adaptive low‐rank group sparse model based on edge‐preserving for eliminating mixed noise in SRTM

Abstract The Shuttle Radar Topography Mission (SRTM) is a digital representation of the terrain surface morphology that contains rich terrain information and is widely used in environmental analyses. However, SRTM is adversely affected by mixed noise, which typically include random and stripe noise. Mixed noise results in the significant loss of topographic information, which reduce the validity of related research. To eliminate mixed noise in SRTM data, we propose an adaptive low‐rank group sparse model based on edge preservation (ALGS_EP) to remove mixed noise from datasets. The method relies on a low‐rank group sparse model that considers the gradient features of the terrain. It calculates a terrain factor to adapt the noise elimination model to terrain changes. Additionally, it integrates with the edge structure of elevation data and applies a double‐gradient constraint to preserve the structural details of the elevation data. The proposed model, built upon the alternating direction multiplier method framework, enhances the traditional weighted kernel paradigm minimization algorithm by introducing variable weights that adjust according to the gradient of elevation data during iterations. Additionally, it incorporates the correlation between strip noise and residual data blocks when computing the iteration count, ensuring an iterative solution approach that converges to the optimal solution. We used ALGS_EP to process global SRTM 1 data and published a higher‐quality and higher‐precision elevation dataset. The elevation data noise before and after noise elimination were statistically analyzed. Simulated and empirical results show that the model is highly robust and more effective than existing methods in both visual and quantitative evaluations. The noise elimination rate was 97.6%, compared to the original data. Therefore, this research was valuable for applications that use digital elevation model as an important data layer.