Structured Sparse mmWave 3-D SAR Imaging via Truncated-DCT and Toeplitz Matrix Methods

High-resolution millimeter-wave (mmWave) 3-D Synthetic Aperture Radar (SAR) imaging typically requires dense spatial sampling over large arrays or structured scanning trajectories. This substantially increases hardware cost and scanning times. Sparse reconstruction approaches based on compressed sensing (CS) and matrix completion (MC) have been explored to alleviate this burden. However, existing methods mainly rely on random sparse sampling or calibrated scanning patterns that limit practical deployment. To address this, we implement a mmWave 3-D SAR imaging system and propose a structured sparse scanning trajectory, termed Expandable Uniform Row (EUR), which effectively reduces scanning positions and accelerates data acquisition. An efficient MC-based algorithm is then developed to reconstruct the structured sparse SAR data acquired with EUR. The algorithm first incorporates a truncated discrete cosine transform (truncated-DCT) to compress the preliminary data and enhance the reconstruction efficiency. It further employs a class of Toeplitz matrix methods for data recovery, where two Toeplitz transformations are applied to the entire matrix to handle structured sparsity. The lifted Toeplitz matrices are subsequently solved within a factorized Alternating Direction Method of Multipliers (ADMM) framework, avoiding singular value decomposition (SVD) and large-scale matrix inversion. Extensive experiments demonstrate that the proposed algorithm achieves high-fidelity reconstruction and imaging within 5 seconds for a 100×201 echo matrix across various objects and sampling rates, enabling up to a 75% reduction in data acquisition time with the EUR trajectory.