Abstract
This leter develops a universal technique for analyzing discrete super-resolution algorithms with $\ell _1$ -norm based objective function. Though the super-resolution problem with sparsity constraints is of intense research interest in the past decade, only a modified Dantzig selector has been non-asymptotically analyzed without additional structural information whereas this theoretical guarantee does not match the numerical results in the Gaussian noise case. More importantly, the relation between the analyses of discrete super-resolution problem and other underdetermined inverse problems in compressed sensing is still not clear. Using the proposed universal technique, this letter aims to close this gap in understanding the characteristics of discrete super-resolution problem. The theoretical claims are demonstrated by extensive numerical experiments.
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