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

Abstract

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