Pub Date : 2021-10-27DOI: 10.1887/0750304359/B461C3
M. Bertero, P. Boccacci
{"title":"Examples of image blurring","authors":"M. Bertero, P. Boccacci","doi":"10.1887/0750304359/B461C3","DOIUrl":"https://doi.org/10.1887/0750304359/B461C3","url":null,"abstract":"","PeriodicalId":170802,"journal":{"name":"Introduction to Inverse Problems in Imaging","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124267021","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-27DOI: 10.1201/9781003032755-14
M. Bertero, P. Boccacci, Christine De MoI
{"title":"Conclusions","authors":"M. Bertero, P. Boccacci, Christine De MoI","doi":"10.1201/9781003032755-14","DOIUrl":"https://doi.org/10.1201/9781003032755-14","url":null,"abstract":"","PeriodicalId":170802,"journal":{"name":"Introduction to Inverse Problems in Imaging","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115021603","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-27DOI: 10.1201/9781439822067.CH10
M. Bertero, P. Boccacci
{"title":"Inversion methods revisited","authors":"M. Bertero, P. Boccacci","doi":"10.1201/9781439822067.CH10","DOIUrl":"https://doi.org/10.1201/9781439822067.CH10","url":null,"abstract":"","PeriodicalId":170802,"journal":{"name":"Introduction to Inverse Problems in Imaging","volume":"54 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133546349","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-27DOI: 10.1887/0750304359/B461C8
M. Bertero, P. Boccacci
{"title":"Examples of linear inverse problems","authors":"M. Bertero, P. Boccacci","doi":"10.1887/0750304359/B461C8","DOIUrl":"https://doi.org/10.1887/0750304359/B461C8","url":null,"abstract":"","PeriodicalId":170802,"journal":{"name":"Introduction to Inverse Problems in Imaging","volume":"184 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133971029","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-27DOI: 10.1201/9781003032755-13
M. Bertero, P. Boccacci, Christine De MoI
{"title":"Statistical methods in the case of Poisson data","authors":"M. Bertero, P. Boccacci, Christine De MoI","doi":"10.1201/9781003032755-13","DOIUrl":"https://doi.org/10.1201/9781003032755-13","url":null,"abstract":"","PeriodicalId":170802,"journal":{"name":"Introduction to Inverse Problems in Imaging","volume":"129 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132252946","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-27DOI: 10.1201/9781003032755-10
M. Bertero, P. Boccacci, Christine De MoI
{"title":"Sparsity-enforcing regularization","authors":"M. Bertero, P. Boccacci, Christine De MoI","doi":"10.1201/9781003032755-10","DOIUrl":"https://doi.org/10.1201/9781003032755-10","url":null,"abstract":"","PeriodicalId":170802,"journal":{"name":"Introduction to Inverse Problems in Imaging","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127020699","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-27DOI: 10.1887/0750304359/b461c6
M. Bertero, P. Boccacci
{"title":"Iterative regularization methods","authors":"M. Bertero, P. Boccacci","doi":"10.1887/0750304359/b461c6","DOIUrl":"https://doi.org/10.1887/0750304359/b461c6","url":null,"abstract":"","PeriodicalId":170802,"journal":{"name":"Introduction to Inverse Problems in Imaging","volume":"80 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126860635","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-27DOI: 10.1201/9781003032755-11
M. Bertero, P. Boccacci, Christine De MoI
{"title":"Statistical approaches to linear inverse problems","authors":"M. Bertero, P. Boccacci, Christine De MoI","doi":"10.1201/9781003032755-11","DOIUrl":"https://doi.org/10.1201/9781003032755-11","url":null,"abstract":"","PeriodicalId":170802,"journal":{"name":"Introduction to Inverse Problems in Imaging","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127505313","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-27DOI: 10.1201/9781003032755-12
M. Bertero, P. Boccacci, Christine De MoI
{"title":"Statistical methods in the case of additive Gaussian noise","authors":"M. Bertero, P. Boccacci, Christine De MoI","doi":"10.1201/9781003032755-12","DOIUrl":"https://doi.org/10.1201/9781003032755-12","url":null,"abstract":"","PeriodicalId":170802,"journal":{"name":"Introduction to Inverse Problems in Imaging","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130028485","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. In many inverse problems it is essential to use regularization methods that preserve edges in the reconstructions, and many reconstruction models have been developed for this task, such as the Total Variation (TV) approach. The associated algorithms are complex and require a good knowledge of large-scale optimization algorithms, and they involve certain tolerances that the user must choose. We present a simpler approach that relies only on standard computational building blocks in matrix computations, such as orthogonal transformations, preconditioned iterative solvers, Kronecker products, and the discrete cosine transform(cid:151)hence the term (cid:147)plug-and-play.(cid:148) We do not attempt to improve on TV reconstructions, but rather provide an easy-to-use approach to computing reconstructions with similar properties.
{"title":"Edge-preserving regularization","authors":"M. Bertero, P. Boccacci, Christine De MoI","doi":"10.1201/9781003032755-9","DOIUrl":"https://doi.org/10.1201/9781003032755-9","url":null,"abstract":". In many inverse problems it is essential to use regularization methods that preserve edges in the reconstructions, and many reconstruction models have been developed for this task, such as the Total Variation (TV) approach. The associated algorithms are complex and require a good knowledge of large-scale optimization algorithms, and they involve certain tolerances that the user must choose. We present a simpler approach that relies only on standard computational building blocks in matrix computations, such as orthogonal transformations, preconditioned iterative solvers, Kronecker products, and the discrete cosine transform(cid:151)hence the term (cid:147)plug-and-play.(cid:148) We do not attempt to improve on TV reconstructions, but rather provide an easy-to-use approach to computing reconstructions with similar properties.","PeriodicalId":170802,"journal":{"name":"Introduction to Inverse Problems in Imaging","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131149930","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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