TADCG: A Novel Gridless Tomographic SAR Imaging Approach Based on the Alternate Descent Conditional Gradient Algorithm With Robustness and Efficiency

Sparse signal processing techniques, such as compressed sensing (CS), are commonly used in tomographic synthetic aperture radar (TomoSAR) imaging due to the sparsity present in the elevation direction. However, classical CS methods, such as
$\ell _{1}$
-norm regularization and orthogonal matching pursuit (OMP), suffer from the off-grid effect. Specifically, they discretize the elevation axis into multiple grids and assume that scatterers are located precisely on the grids, leading to reconstruction results that deviate from the true heights of the scatterers. Although gridless CS methods, such as atomic norm minimization (ANM), have achieved gridless reconstruction in specific scenarios, they face challenges such as the requirement of uniformly distributed baselines and large computational cost. In this article, we propose a gridless CS method based on the alternate descent conditional gradient (ADCG) kernel for TomoSAR inversion and compare it with ANM, iterative soft thresholding (IST), and OMP. We show through numerical simulations and experimental results that our proposed method is applicable not only to scenarios with uniformly distributed baselines but also to scenarios with nonuniformly distributed baselines, and it resolves the off-grid effect in both cases. Finally, we demonstrate the effectiveness of our proposed method by implementing gridless reconstruction using an actual dataset of urban buildings in Yuncheng.