Gridless Sparse ISAR Imaging via 2-D Fast Reweighted Atomic Norm Minimization

Aiming at acquiring high-resolution ISAR image effectively and quickly, a new fast gridless imaging method with a sound two-dimensional (2-D) reweighting strategy is proposed in this letter. First, the received echo is characterized as a weighted linear combination of 2-D frequencies chosen from a matrix-form atom set, forming a new nonconvex optimization model for 2-D gridless ISAR imaging based on the 2-D atomic norm minimization (2-D ANM) framework. Next, a reweighting optimization strategy is adopted, which iteratively carries out the 2-D ANM to determine the preference of 2-D frequencies selection based on the latest estimation, to enhance sparsity and resolution. Furthermore, a feasible algorithm based on alternating direction method of multipliers (ADMM) is used in each iteration to further decrease the computational complexity. Once the optimization problem is solved, the 2-D frequencies encoded in two one-level Toeplitz matrices can be obtained using the Vandermonde decomposition (VD). Numerical experiments demonstrate that the proposed method is able to achieve high-resolution ISAR image, while it has a remarkable computational efficiency.