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.

中文翻译：

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一种分析离散超分辨率算法的通用技术

这封信开发了一种通用技术，用于分析具有基于 $\ell_1$-norm 的目标函数的离散超分辨率算法。尽管具有稀疏约束的超分辨率问题在过去十年中引起了强烈的研究兴趣，但仅在没有额外结构信息的情况下对改进的 Dantzig 选择器进行了非渐近分析，而这种理论保证与高斯噪声情况下的数值结果不匹配。更重要的是，离散超分辨率问题的分析与压缩感知中的其他欠定逆问题之间的关系仍不清楚。使用所提出的通用技术，这封信旨在缩小在理解离散超分辨率问题特征方面的差距。