Sparse microwave imaging is the combination of microwave imaging and sparse signal processing, which aims to extract physical and geometry information of sparse or transformed sparse scene from least number of radar measurements. As a primary investigation on its performance, this paper focuses on the performance guarantee for a one-dimensional radar, which detects delays of several point targets located at a sparse scene via randomly sub-sampling of radar returns. Based on the Lasso framework, the quantity relationship among three important factors is discussed, including the sub-sampling ratio ρM, sparse ratio ρK and signal-to-noise ratio (SNR), where ρM is the ratio of number of random sub-sampling to that of Nyquist's sampling, and ρK is the ratio of sparsity to the number of unknowns. In particular, to ensure correct delay detection and accurate back scattering coefficient reconstruction for each target, one needs ρM to be greater than C(ρK)ρKlogN and the input SNR be of order logN, where N is the number of range cells in scene.
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