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

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 multi-ℓ₁ norm, a multitotal variation norm, a joint-sparsity ℓ₂₁ norm, and a tree-sparsity overlapping ℓ₂₁ norm. Simulation and experimental results demonstrate the superior performance of the proposed approach in terms of both efficiency and convergence speed.

I. Introduction

Radar imaging is an inverse scattering problem whereby electromagnetic signal pulses are transmitted on to a scene and a spatial map of reflectivity is reconstructed from measurements of scattered electric fields. A synthetic aperture radar (SAR) imaging system usually operates with a moving antenna probe, which samples the target scene at a high bandwidth and high spatial resolution, demanding high sampling rates in both frequency and space domains if the images are reconstructed according to the Shannon–Nyquist theorem [1]. However, recent advances in compressed sensing (CS) [2]–[6] pose the SAR image reconstruction as finding sparse solutions to a set of underdetermined linear equations, which is capable of producing high-resolution images with measurements that are lower than the Nyquest sampling rate. The CS-SAR approach has been successfully applied to various far-field applications, which usually produce high spatial resolution images of the stationary surface targets and terrain from a moving platform, such as an airplane or a satellite [7]–[9]. For example, [10] proposes an alternative to matched filtering for the retrieval of the illuminated scene by using a regularized orthogonal matching pursuit algorithm to realize the azimuth compression. Zhu et. al. [11] use norm optimization to reduce the sampling rate in the azimuth direction. Xu et. al. [12] achieve both range and azimuth compressed sampling based on Bayesian CS, which requires minor change to the traditional SAR system. Besides, CS has also been applied to other far-field applications, such as inverse SAR and tomographic SAR [13]–[15].