Some statistical models based on least squares estimation will produce large bias when there are outliers in the data. The least absolute deviation has strong resistance to outliers. Considering the influence of the outliers in the data, the square loss was replaced with the absolute loss. Aiming at the linear model of a structure that has both variable sparsity and sparsity of adjacent coefficient differences, the least absolute deviation fused broken adaptive ridge estimation model （LAD-Fused-BAR）was proposed. The square of the reciprocal of the regression coefficient estimated in the previous step was taken as the penalty weight for the next step, different penalties were adaptively given to different variables, and the final solution was obtained through continuous iteration. The alternating direction multiplier method （ADMM）was adopted to solve the LAD-Fused-BAR model and prove the convergence of the ADMM algorithm. Additionally, numerical simulation and empirical analysis confirm the efficacy and robustness of the proposed methodology.