Sparse radar imaging based on <italic>L</italic><sub>1/2</sub> regularization theory

Abstract

Sparse radar imaging seeks to provide high-performance radar imaging technique for observed scenes by using L 1/2 regularization method. This article surveys our systematic explorations and innovative practices for tackling such problem. The key contributions include a new sparse radar imaging theory based on L 1/2 regularization theory, a new sparse radar imaging model based on echo simulation operator, a new sparse radar imaging system evaluate approach based on 3D phase diagram. The synthetic aperture radar (SAR) imaging can be formulated as a L 1/2 regularization problem, which optimizes a quadratic error term of radar imaging. The method can implement SAR imaging effectively at lower sampling rates than Nyquist rate and produce higher quality images with reduced sidelobes. Echo simulation operator is constructed to generate SAR raw data by means of inverse of matched filter-based imaging procedure, instead of the exact observation matrix. The echo simulation operator based model forms a new radar imaging method, which reduces the computational complexity and memory occupation to the same order as matched filter imaging algorithm, and hence, makes L 1/2 regularization reconstruction of large-scale considered scene become possible. 3D phase diagram is employed to analyze and evaluate the performance of sparse radar imaging system. In 3D phase diagram, success rates of signal recovery can be derived from the statistics of relative errors between the ground truth and the recovered signals. The success rates for each combination of SNR, sparsity and sampling ratio are provided to form a three-dimensional phase diagram. The trend of success rates is presented accurately by taking advantage of 3D phase transition boundary. We design the sparse radar prototype and conduct a series of airborne experiments, which demonstrate the applicability and potentials of the sparse radar imaging. 3D phase diagram is used to evaluate the relationship between reconstruction performance and signal-to- noise ratio. The experimental results verity the effectiveness of the L 1/2 regularization method and the feasibility of 3D phase diagram. The sparse radar imaging based on L 1/2 regularization has promising application prospects. Firstly, it could be generalized to deal with 3D-SAR imaging, which achieves better flexibility for system design and super-resolution capability of height dimension for reconstruction property. Then, we review some of the most popular techniques to exploit sparsity, for recovering high-dimensional matrices and higher order tensors from compressive measurements, and further emphasize the broad application prospects of higher order compressive sensing in 3D-SAR imaging.