Abstract: The combined wall clutter suppression and image reconstruction iterative solution method is one of the advanced through-the-wall radar imaging(TWRI) algorithms. However, there are problems such as slow convergence speed, excessive manual intervention, and sensitivity to the selection of initial values, which makes it difficult to quickly and accurately perform target imaging. This paper proposes a TWRI method that combines low-rank and sparse decomposition-driven learnable deep iterative networks. Considering the low-rank characteristics of the wall clutter and the sparse characteristics of the target image in the through-wall-radar scene, the through wall radar imaging problem is modeled as a regularization optimization problem driven by low-rank and jointly sparse decomposition. A variational framework and a rotation strategy are used to transform the optimization problem into two quasi-linear optimization sub-problems and derive their update formulas. Finally, the above iterative update formulas are mapped into a network structure, and expanded into a deep iterative network model, and adopt an end-to-end learning strategy to form a learnable deep iterative network framework that integrates physical models. The simulation results show that this method can effectively suppress wall clutter and significantly improves the target imaging accuracy and speed compared to other methods.