<p>This paper presents an extended shifted coprime array(ESCA) with lower mutual coupling characteristics, while further expanding the virtual continuous degrees of freedom(DOF) of the array. In order to improve the accuracy of direction-of-arrival (DOA) estimation for ESCA, enhance the utilization of received information, and avoid grid mismatch issues, this paper proposes a second-order alternating direction method of multipliers (ADMM) algorithm based on the atomic norm theory. First, an atomic norm minimization(ANM) model under the ESCA is constructed, and the corresponding optimization problem is addressed by formulating the Lagrangian function. Subsequently, the optimization problem is decomposed based on block variables. When solving the local optimal problem under the constraints, the Hessian matrix of the objective function is introduced to improve the step size adaptation mechanism and direction adjustment strategy, thereby enhancing the convergence rate and algorithm performance. The simulation results demonstrate that the proposed algorithm maintains high angle estimation accuracy while improving computational efficiency.</p>