Estimation of off-the grid sparse spikes with over-parametrized projected gradient descent: theory and application

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.