Multifrequency Compressed Sensing for 2-D Near-Field Synthetic Aperture Radar Image Reconstruction

Abstract

This paper investigates a new multifrequency compressed sensing (CS) model for 2-D near-field microwave and millimeter-wave synthetic aperture radar (SAR) imaging system, which usually collects multifrequency sparse data. Spatial data of each frequency are represented as a hierarchical tree structure under a wavelet basis and spatial data of different frequencies are modeled as a joint structure, because they are highly correlated. Based on the developed multifrequency CS model, a new CS approach is proposed by exploiting both the intrafrequency and interfrequency correlations, and enriches the existing CS approaches for 2-D near-field microwave and millimeter-wave SAR image reconstruction from undersampled measurements. Combining a splitting Bregman update with a variation of the parallel Fast Iterative Shrinkage-Thresholding Algorithm-like proximal algorithm, the proposed CS approach minimizes a linear combination of five terms: a least squares data fitting, a $\textrm {multi-}\ell _{1}$ norm, a multitotal variation norm, a joint-sparsity $\ell _{21}$ norm, and a tree-sparsity overlapping $\ell _{21}$ norm. Simulation and experimental results demonstrate the superior performance of the proposed approach in terms of both efficiency and convergence speed.