论文标题
通过凸优化的无分离光谱超分辨率
Separation-Free Spectral Super-Resolution via Convex Optimization
论文作者
论文摘要
最近，已经提出了原子规范方法用于光谱超分辨率，并在处理缺失的数据和其他噪声方面具有灵活性。然而，这些凸优化方法的臭名昭著的缺点是与传统方法（例如ESPRIT）相比，它们在高信噪比（SNR）方面的分辨率较低。在本文中，我们在现有的原子规范方法中设计了一个简单的加权方案，并表明在没有噪声的情况下，可以任意将所得凸优化方法的分辨率任意高，从而实现了所谓的无分离超级分辨率。双重证书的新颖，无内核的结构证明了这一点，其存在使用该方法确保了确切的超分辨率。提供了证实我们分析的数值结果。
Atomic norm methods have recently been proposed for spectral super-resolution with flexibility in dealing with missing data and miscellaneous noises. A notorious drawback of these convex optimization methods however is their lower resolution in the high signal-to-noise (SNR) regime as compared to conventional methods such as ESPRIT. In this paper, we devise a simple weighting scheme in existing atomic norm methods and show that the resolution of the resulting convex optimization method can be made arbitrarily high in the absence of noise, achieving the so-called separation-free super-resolution. This is proved by a novel, kernel-free construction of the dual certificate whose existence guarantees exact super-resolution using the proposed method. Numerical results corroborating our analysis are provided.
