论文标题
预计的梯度下降用于非凸稀疏尖峰估计
Projected gradient descent for non-convex sparse spike estimation
论文作者
论文摘要
我们提出了一种新的算法，用于从傅立叶测量值中进行稀疏尖峰估计。基于基于网格稀疏尖峰估计的非凸优化技术的理论结果，我们提出了一种预计的梯度下降算法以及光谱初始化过程。我们的算法允许通过随机傅立叶测量值估算2D中大量狄拉克的位置。 我们与算法一起介绍了理论定性见解，解释了我们的算法的成功。这为实用的离网尖峰估计带来了新的方向，并在成像应用中提供了理论保证。
We propose a new algorithm for sparse spike estimation from Fourier measurements. Based on theoretical results on non-convex optimization techniques for off-the-grid sparse spike estimation, we present a projected gradient descent algorithm coupled with a spectral initialization procedure. Our algorithm permits to estimate the positions of large numbers of Diracs in 2d from random Fourier measurements. We present, along with the algorithm, theoretical qualitative insights explaining the success of our algorithm. This opens a new direction for practical off-the-grid spike estimation with theoretical guarantees in imaging applications.
