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dc.contributor.author
Calvetti, Daniela
dc.contributor.author
Somersalo, Erkki
dc.contributor.author
Spies, Ruben Daniel
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dc.date.available
2017-02-22T18:31:36Z
dc.date.issued
2014-11
dc.identifier.citation
Calvetti, Daniela; Somersalo, Erkki; Spies, Ruben Daniel; Variable order smoothness priors for ill-posed inverse problems; Amer Mathematical Soc; Mathematics Of Computation; 84; 294; 11-2014; 1753-1773
dc.identifier.issn
0025-5718
dc.identifier.uri
http://hdl.handle.net/11336/13316
dc.description.abstract
In this article we discuss ill-posed inverse problems, with an emphasis on hierarchical variable order regularization. Traditionally, smoothness penalties in Tikhonov regularization assume a fixed degree of regularity of the unknown over the whole domain. Using a Bayesian framework with hierarchical priors, we derive a prior model, formally represented as a convex combination of autoregressive (AR) models, in which the parameter controlling the mixture of the AR models can dynamically change over the domain of the signal. Moreover, the mixture parameter itself is an unknown and is to be estimated using the data. Also, the variance of the innovation processes in the AR model is a free parameter, which leads to conditionally Gaussian priors that have been previously shown to be much more flexible than the traditional Gaussian priors, capable, e.g., to deal with sparsity type prior information. The suggested method, the Weighted Variable Order Autoregressive model (WVO-AR) is tested with a computed example.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Amer Mathematical Soc
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dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
Markov Autoregresive Models
dc.subject
Inverse Problems
dc.subject
Ill-Conditioned
dc.subject
Bayesian Models
dc.subject.classification
Matemática Pura
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dc.subject.classification
Matemáticas
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dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
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dc.title
Variable order smoothness priors for ill-posed inverse problems
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2016-11-23T20:13:14Z
dc.identifier.eissn
1088-6842
dc.journal.volume
84
dc.journal.number
294
dc.journal.pagination
1753-1773
dc.journal.pais
Estados Unidos
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dc.journal.ciudad
Providence
dc.description.fil
Fil: Calvetti, Daniela. Case Western Reserve University; Estados Unidos
dc.description.fil
Fil: Somersalo, Erkki. Case Western Reserve University; Estados Unidos
dc.description.fil
Fil: Spies, Ruben Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Matemática Aplicada "Litoral"; Argentina
dc.journal.title
Mathematics Of Computation
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dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/http://www.ams.org/journals/mcom/2015-84-294/S0025-5718-2014-02909-8/
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/https://doi.org/10.1090/S0025-5718-2014-02909-8
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