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

IF 2 2区数学 Q1 MATHEMATICS, APPLIED

Inverse Problems Pub Date : 2024-03-14 DOI:10.1088/1361-6420/ad33e4

Pierre-Jean Bénard, Yann Traonmilin, Jean-François Aujol, Emmanuel Soubies

引用次数: 2

Abstract

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.

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用过参数化投射梯度下降法估计离网稀疏尖峰：理论与应用

在本文中，我们研究了用过参数化投影下降法恢复稀疏尖峰的问题。我们首先从理论上研究了我们所选择的初始化方法的近似恢复：无滑动连续正交匹配追寻。然后，我们研究了过度参数化对梯度下降的影响，突出了投影步骤的优势。最后，我们展示了与基于模型的先进方法相比，我们的算法在现实模拟显微镜数据上的计算时间得到了改善。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Inverse Problems 数学-物理：数学物理

CiteScore

4.40

自引率

14.30%

发文量

115

审稿时长

2.3 months

期刊介绍： An interdisciplinary journal combining mathematical and experimental papers on inverse problems with theoretical, numerical and practical approaches to their solution. As well as applied mathematicians, physical scientists and engineers, the readership includes those working in geophysics, radar, optics, biology, acoustics, communication theory, signal processing and imaging, among others. The emphasis is on publishing original contributions to methods of solving mathematical, physical and applied problems. To be publishable in this journal, papers must meet the highest standards of scientific quality, contain significant and original new science and should present substantial advancement in the field. Due to the broad scope of the journal, we require that authors provide sufficient introductory material to appeal to the wide readership and that articles which are not explicitly applied include a discussion of possible applications.