A Sparse Reconstruction Algorithm Based on Constrained Inhomogeneous Grid Optimization

The dictionary grid mismatch problem in sparse processing is an important factor affecting parameter reconstruction. The existing grid correction algorithms are limited by the initial grid division and the accurate estimation of the support set vector. Furthermore, these methods fail if multiple scattering points fall into the same grid interval. In this paper, a constrained inhomogeneous grid optimization sparse processing algorithm is proposed. The proposed method includes two sub-processes, namely initial grid optimization and the support set vector correction. The optimization of the initial grid is to use the idea of the coordinate descent method to iteratively generate an updated grid vector, which is used for the inhomogeneous fission of the grid around the target from coarse to dense. Moreover, under the constraint of dictionary atom maximum correlation, multiple scattering points are separated in different grids, which improves the search accuracy of support set atoms. The correction process of the support set vector is to use the first-order Taylor expansion of the dictionary grid to linearly approximate the real parameters of the target, to achieve adaptive correction of dictionary mismatched atoms. According to the simulation experiment of the frequency agile radar scenario, the proposed algorithm can achieve higher range-Doppler parameter joint estimation accuracy in the multi-scattering point scenario in comparison with the conventional sparse recovery algorithm and grid point correction algorithm.