Efficient Near-Field Radar Microwave Imaging Based on Joint Constraints of Low-Rank and Structured Sparsity at Low SNR

With the continuous development of near-field radar microwave imaging technology, low-rank or compressed sensing (CS) methods have shown great potential in solving high-resolution microwave imaging under sparse aperture. However, traditional low-rank or CS methods are restricted to handling random sampling data. When specific random sampling conditions are not satisfied, the radar images may lose target details and have severe side lobes. Moreover, radar images often suffer from defocusing under low signal-to-noise ratio (SNR) conditions. To address these challenges, this article first establishes a near-field radar imaging model and analyzes the impact of low-rank and sparse priors on microwave imaging. Subsequently, we investigate three sparse sampling patterns and propose a triple prior-constrained optimization model with low-rank joint structured sparsity and noise. This model utilizes low-rank and structured sparsity priors to recover the potential target structural information while using the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\boldsymbol {l_{2}}$ </tex-math></inline-formula> norm to eliminate noise. On this basis, we derive a numerical algorithm within an augmented Lagrange multipliers (ALM) framework using the alternating direction method of multipliers (ADMM) to achieve high-precision image reconstruction. Furthermore, a linearization technique based on Taylor series expansion avoids the inverse problem of high-dimensional matrices, effectively reducing computational complexity. Experimental results using simulated data and multifrequency measured data validate the effectiveness of the proposed method and its strong robustness to noise.