Far-field imaging beyond the Rayleigh limit is one of the most important challenges in optics, microwave, and ultrasonics. We propose a novel sparsity-promoted super-oscillation imaging scheme for reconstructing more universal objects in subwavelength scales, which solves a weighted optimization problem constrained by lp-norm-based sparsity regularization (). We demonstrate numerically that the proposed imaging technique improves the resolution related to existing approaches remarkably for the case of very high signal-to-noise ratio (SNR), including the traditional super-oscillation imaging and sparsity-based super-resolution imaging. The standard superoscillation based super-resolution imaging approach can be regarded as the first-iteration solution of the proposed scheme. Numerical results for one- and two-dimensional super-resolution imaging are presented for validation.
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