论文标题
在任意细网格上积极来源的超分辨率
Super-Resolution of Positive Sources on an Arbitrarily Fine Grid
论文作者
论文摘要
在超分辨率中，有必要从高精度点源来定位，从F_C限制的低频噪声观察到信号的频谱。在点源为正且位于网格上的情况下，最近已经确定，可以通过稳定的方式通过线性编程来解决超分辨率问题，并且从最小值意义上讲，该方法几乎是最佳的。重建的质量严重取决于信号支持的瑞利规律性；也就是说，在侧面长度内可能发生的最大源数量上，大约1/f_c。这项工作扩展了较早的结果，并表明当点源的位置是任意的，即网格是任意罚款时的结论。证明依赖于傅立叶分析中的新插值结构。
In super-resolution it is necessary to locate with high precision point sources from noisy observations of the spectrum of the signal at low frequencies capped by f_c. In the case when the point sources are positive and are located on a grid, it has been recently established that the super-resolution problem can be solved via linear programming in a stable manner and that the method is nearly optimal in the minimax sense. The quality of the reconstruction critically depends on the Rayleigh regularity of the support of the signal; that is, on the maximum number of sources that can occur within an interval of side length about 1/f_c. This work extends the earlier result and shows that the conclusion continues to hold when the locations of the point sources are arbitrary, i.e., the grid is arbitrarily fine. The proof relies on new interpolation constructions in Fourier analysis.
