论文标题
快速离网稀疏恢复，过度参数投影梯度下降
Fast off-the-grid sparse recovery with over-parametrized projected gradient descent
论文作者
论文摘要
我们考虑从傅立叶测量中恢复离网尖峰的问题。成功的方法，例如滑行弗兰克 - 沃尔夫（Frank-Wolfe）和连续的正交匹配追踪（OPP），迭代地添加尖峰，然后在每次迭代中的所有参数上执行昂贵的（当尖峰数量很大）下降。在2D中，显示出，从网格过度参数的初始化中执行投影梯度下降（PGD）比连续的正交匹配追踪更快。在本文中，我们基于OMP提出了PGD的网格过度参数化初始化，该初始化允许完全避免网格，并在3D中提供更快的结果。
We consider the problem of recovering off-the-grid spikes from Fourier measurements. Successful methods such as sliding Frank-Wolfe and continuous orthogonal matching pursuit (OMP) iteratively add spikes to the solution then perform a costly (when the number of spikes is large) descent on all parameters at each iteration. In 2D, it was shown that performing a projected gradient descent (PGD) from a gridded over-parametrized initialization was faster than continuous orthogonal matching pursuit. In this paper, we propose an off-the-grid over-parametrized initialization of the PGD based on OMP that permits to fully avoid grids and gives faster results in 3D.
