{"title":"Model-based sparse source identification","authors":"Reza Khodayi-mehr, W. Aquino, M. Zavlanos","doi":"10.1109/ACC.2015.7170997","DOIUrl":null,"url":null,"abstract":"This paper presents a model-based approach for source identification using sparse recovery techniques. In particular, given an arbitrary domain that contains a set of unknown sources and a set of stationary sensors that can measure a quantity generated by the sources, we are interested in predicting the shape, location, and intensity of the sources based on a limited number of sensor measurements. We assume a PDE model describing the steady-state transport of the quantity inside the domain, which we discretize using the Finite Element method (FEM). Since the resulting source identification problem is underdetermined for a limited number of sensor measurements and the sought source vector is typically sparse, we employ a novel Reweighted l1 regularization technique combined with Least Squares Debiasing to obtain a unique, sparse, reconstructed source vector. The simulations confirm the applicability of the presented approach for an Advection-Diffusion problem.","PeriodicalId":223665,"journal":{"name":"2015 American Control Conference (ACC)","volume":"103 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2015-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"12","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2015 American Control Conference (ACC)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ACC.2015.7170997","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 12
Abstract
This paper presents a model-based approach for source identification using sparse recovery techniques. In particular, given an arbitrary domain that contains a set of unknown sources and a set of stationary sensors that can measure a quantity generated by the sources, we are interested in predicting the shape, location, and intensity of the sources based on a limited number of sensor measurements. We assume a PDE model describing the steady-state transport of the quantity inside the domain, which we discretize using the Finite Element method (FEM). Since the resulting source identification problem is underdetermined for a limited number of sensor measurements and the sought source vector is typically sparse, we employ a novel Reweighted l1 regularization technique combined with Least Squares Debiasing to obtain a unique, sparse, reconstructed source vector. The simulations confirm the applicability of the presented approach for an Advection-Diffusion problem.