In this article, we study the problem of recovering sparse spikes with over-parametrized projected descent. We first provide a theoretical study of approximate recovery with our chosen initialization method: Continuous Orthogonal Matching Pursuit without Sliding. Then we study the effect of over-parametrization on the gradient descent which highlights the benefits of the projection step. Finally, we show the improved calculation times of our algorithm compared to state-of-the-art model-based methods on realistic simulated microscopy data.

中文翻译：

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利用超参数化投影梯度下降估计离网稀疏尖峰：理论与应用

在本文中，我们研究了通过超参数化投影下降来恢复稀疏尖峰的问题。我们首先提供了使用我们选择的初始化方法进行近似恢复的理论研究：无滑动的连续正交匹配追踪。然后我们研究过度参数化对梯度下降的影响，这凸显了投影步骤的好处。最后，我们展示了与基于真实模拟显微镜数据的最先进的基于模型的方法相比，我们的算法缩短了计算时间。