Millimeter-Wave SAR Sparse Imaging With 2-D Spatially Pseudorandom Spiral-Sampling Pattern

For real-time millimeter-wave (MMW) imaging applications, spatially 2-D sparse sampling is one of the most promising techniques to reduce the heavy cost of signal acquisition. Therefore, in this article, we develop a new MMW synthetic aperture radar (SAR) sparse imaging method by establishing a 2-D pseudorandom spiral-sampling pattern. The method consists of two phases: sparse sampling-pattern design and sparse-imaging processing. The sparse sampling-pattern design is modeled as an optimization programming problem, in which the initial sampling pattern is a classical Archimedes spiral, and then, the number of samples per cycle is adjusted by coming up with a modified sigmoid function. This function is employed to increase the angular aperiodicity and randomness over the whole planar aperture. For sparse-imaging processing, a singular value thresholding (SVT) algorithm is applied to reconstruct the complete echo from partial samples observed by sparse sampling, and then, the inversion can be performed via the traditional imaging algorithms. In particular, a performance-guarantee condition of SVT is introduced to control the minimum number of samples, which bridges the relationship between pattern optimization and reconstruction performance. Our motivation is to answer what the undersampling pattern is and to estimate the extent to which the number of samples can be reduced by the current sparse imaging method. Finally, simulations and experiments validate the feasibility and effectiveness of the proposed sampling pattern, and the imaging results further demonstrate that our method with partially observed samples can offer the performance comparable to dense sampling.