Gridless Sparse ISAR Imaging Method Based on Modified Reweighted Atomic Norm Minimization

For high-resolution inverse synthetic aperture radar (ISAR) imaging situations, the continuous sparse recovery (SR) approach is very appropriate as it can accomplish high-precision reconstruction of missing signals. Existing high-resolution sparse ISAR imaging method based on the reweighted atomic norm (RAM) can avoid the grid mismatch problem, but it come with a lengthy calculation time, due to the high dimensionality of the ISAR echo matrix. To address this problem, a sparse ISAR imaging method based on the modified reweighted atomic norm (MRAM) was proposed in this paper. Firstly, the atomic representation model of ISAR signal was built, and utilizing the semi-definite property of atomic norm to transform the problem of minimizing atomic norm into a semi-definite programming (SDP) problem. Subsequently, a new non-convex surrogate function was introduced to reduce the number of iterations of the RAM method. Secondly, to swiftly handle SDP problem, the alternating direction multiplier method (ADMM) was used. Finally, Vandermonde decomposition was used to obtain amplitude and frequency information of scattering points, and imaging was completed through fast Fourier transform. The effectiveness of the proposed method was verified through experiments with real data.