Point Source Super-resolution Via Non-convex $$L_1$$ L 1 Based Methods
Point Source Super-resolution Via Non-convex $$L_1$$ L 1 Based Methods
复制标题
通过基于非凸 $$L_1$$ L 1 的方法实现点源超分辨率
DOI：
10.1007/s10915-016-0169-x
复制
发表时间：
2016
影响因子：
2.5
通讯作者：
Xin, Jack
中科院分区：
文献类型：
--
作者：
Lou, Yifei;Yin, Penghang;Xin, Jack
我们研究的超分辨率（SR）的问题，恢复点源组成的一组孤立的和适当分离的尖峰，只有低频测量。如果峰值分离高于瑞利长度（物理分辨率极限）的（1，2）中的因子，则保证最小化以恢复这样的稀疏信号。然而，在这样的临界长度尺度下，特别是在瑞利长度下，证书就不复存在了。我们展示了两个非凸罚函数的极限点的几个局部性质（局部极小值、方向平稳性和稀疏性），这两个罚函数分别是andnorms（）和capped（C）的差，它们受测量约束.在一维和二维的数值随机共振算例中，无论是在恢复真实值的精度上，还是在找到更精确地满足约束条件的稀疏解方面，凸函数差分算法的局部最优解都优于瑞利尺度附近或以下的全局解.
We study the super-resolution (SR) problem of recovering point sources consisting of a collection of isolated and suitably separated spikes from only the low frequency measurements. If the peak separation is above a factor in (1, 2) of the Rayleigh length (physical resolution limit),minimization is guaranteed to recover such sparse signals. However, below such critical length scale, especially the Rayleigh length, thecertificate no longer exists. We show several local properties (local minimum, directional stationarity, and sparsity) of the limit points of minimizing twobased nonconvex penalties, the difference ofandnorms () and capped(C), subject to the measurement constraints. In one and two dimensional numerical SR examples, the local optimal solutions from difference of convex function algorithms outperform the globalsolutions near or below Rayleigh length scales either in the accuracy of ground truth recovery or in finding a sparse solution satisfying the constraints more accurately.