Ariel Hafftka, H. Celik, A. Cloninger, W. Czaja, R. Spencer
{"title":"2D sparse sampling algorithm for ND Fredholm equations with applications to NMR relaxometry","authors":"Ariel Hafftka, H. Celik, A. Cloninger, W. Czaja, R. Spencer","doi":"10.1109/SAMPTA.2015.7148914","DOIUrl":null,"url":null,"abstract":"In [1], Cloninger, Czaja, Bai, and Basser developed an algorithm for compressive sampling based data acquisition for the solution of 2D Fredholm equations. We extend the algorithm to N dimensional data, by randomly sampling in 2 dimensions and fully sampling in the remaining N-2 dimensions. This new algorithm has direct applications to 3-dimensional nuclear magnetic resonance relaxometry and related experiments, such as T1-D-T2 or T1-T1,ρ-T2. In these experiments, the first two parameters are time-consuming to acquire, so sparse sampling in the first two parameters can provide significant experimental time savings, while compressive sampling is unnecessary in the third parameter.","PeriodicalId":311830,"journal":{"name":"2015 International Conference on Sampling Theory and Applications (SampTA)","volume":"80 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2015-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2015 International Conference on Sampling Theory and Applications (SampTA)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SAMPTA.2015.7148914","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 6
Abstract
In [1], Cloninger, Czaja, Bai, and Basser developed an algorithm for compressive sampling based data acquisition for the solution of 2D Fredholm equations. We extend the algorithm to N dimensional data, by randomly sampling in 2 dimensions and fully sampling in the remaining N-2 dimensions. This new algorithm has direct applications to 3-dimensional nuclear magnetic resonance relaxometry and related experiments, such as T1-D-T2 or T1-T1,ρ-T2. In these experiments, the first two parameters are time-consuming to acquire, so sparse sampling in the first two parameters can provide significant experimental time savings, while compressive sampling is unnecessary in the third parameter.