We consider the problem of recovering off-the-grid spikes from linear measurements. The state of the art Over-Parametrized Continuous Orthogonal Matching Pursuit (OP-COMP) with Projected Gradient Descent (PGD) successfully recovers those signals. In most cases, the main computational cost lies in a unique global descent on all parameters (positions and amplitudes). In this paper, we propose to improve this algorithm by accelerating this descent step. We introduce a new algorithm, based on Block Coordinate Descent, that takes advantages of the sparse structure of the problem. Based on qualitative theoretical results, this algorithm shows improvement in calculation times in realistic synthetic microscopy experiments.

翻译：我们研究了从线性测量中恢复离网格尖峰的问题。当前最先进的超参数化连续正交匹配追踪（OP-COMP）结合投影梯度下降（PGD）方法能够成功恢复这些信号。在大多数情况下，主要计算成本在于对所有参数（位置和振幅）进行单次全局下降。本文提出通过加速该下降步骤来改进该算法。我们引入了一种基于块坐标下降的新算法，利用问题的稀疏结构。基于定性理论结果，该算法在真实合成显微镜实验中显示出计算时间的显著改善。