{"title":"Estimation of off-the grid sparse spikes with over-parametrized projected gradient descent: theory and application","authors":"Pierre-Jean Bénard, Yann Traonmilin, Jean-François Aujol, Emmanuel Soubies","doi":"10.1088/1361-6420/ad33e4","DOIUrl":null,"url":null,"abstract":"\n 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.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":null,"pages":null},"PeriodicalIF":2.0000,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Inverse Problems","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1088/1361-6420/ad33e4","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
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.
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.
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