Accelerating cross-validation with total variation and its application to super-resolution imaging.

Accelerating cross-validation with total variation and its application to super-resolution imaging.

We develop an approximation formula for the cross-validation error (CVE) of a sparse linear regression penalized by ℓ1-norm and total variation terms, which is based on a perturbative expansion utilizing the largeness of both the data dimensionality and the model. The developed formula allows us to...

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Main Authors: Tomoyuki Obuchi, Shiro Ikeda, Kazunori Akiyama, Yoshiyuki Kabashima
Format: Article
Language:English
Published: Public Library of Science (PLoS) 2017-01-01
Series:PLoS ONE
Online Access:http://europepmc.org/articles/PMC5720762?pdf=render
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spelling doaj-4e707dde93d046ebbd7b82a20695a7432020-11-25T01:51:08ZengPublic Library of Science (PLoS)PLoS ONE1932-62032017-01-011212e018801210.1371/journal.pone.0188012Accelerating cross-validation with total variation and its application to super-resolution imaging.Tomoyuki ObuchiShiro IkedaKazunori AkiyamaYoshiyuki KabashimaWe develop an approximation formula for the cross-validation error (CVE) of a sparse linear regression penalized by ℓ1-norm and total variation terms, which is based on a perturbative expansion utilizing the largeness of both the data dimensionality and the model. The developed formula allows us to reduce the necessary computational cost of the CVE evaluation significantly. The practicality of the formula is tested through application to simulated black-hole image reconstruction on the event-horizon scale with super resolution. The results demonstrate that our approximation reproduces the CVE values obtained via literally conducted cross-validation with reasonably good precision.http://europepmc.org/articles/PMC5720762?pdf=render
collection DOAJ
language English
format Article
sources DOAJ
author Tomoyuki Obuchi
Shiro Ikeda
Kazunori Akiyama
Yoshiyuki Kabashima
spellingShingle Tomoyuki Obuchi
Shiro Ikeda
Kazunori Akiyama
Yoshiyuki Kabashima
Accelerating cross-validation with total variation and its application to super-resolution imaging.
PLoS ONE
author_facet Tomoyuki Obuchi
Shiro Ikeda
Kazunori Akiyama
Yoshiyuki Kabashima
author_sort Tomoyuki Obuchi
title Accelerating cross-validation with total variation and its application to super-resolution imaging.
title_short Accelerating cross-validation with total variation and its application to super-resolution imaging.
title_full Accelerating cross-validation with total variation and its application to super-resolution imaging.
title_fullStr Accelerating cross-validation with total variation and its application to super-resolution imaging.
title_full_unstemmed Accelerating cross-validation with total variation and its application to super-resolution imaging.
title_sort accelerating cross-validation with total variation and its application to super-resolution imaging.
publisher Public Library of Science (PLoS)
series PLoS ONE
issn 1932-6203
publishDate 2017-01-01
description We develop an approximation formula for the cross-validation error (CVE) of a sparse linear regression penalized by ℓ1-norm and total variation terms, which is based on a perturbative expansion utilizing the largeness of both the data dimensionality and the model. The developed formula allows us to reduce the necessary computational cost of the CVE evaluation significantly. The practicality of the formula is tested through application to simulated black-hole image reconstruction on the event-horizon scale with super resolution. The results demonstrate that our approximation reproduces the CVE values obtained via literally conducted cross-validation with reasonably good precision.
url http://europepmc.org/articles/PMC5720762?pdf=render
work_keys_str_mv AT tomoyukiobuchi acceleratingcrossvalidationwithtotalvariationanditsapplicationtosuperresolutionimaging
AT shiroikeda acceleratingcrossvalidationwithtotalvariationanditsapplicationtosuperresolutionimaging
AT kazunoriakiyama acceleratingcrossvalidationwithtotalvariationanditsapplicationtosuperresolutionimaging
AT yoshiyukikabashima acceleratingcrossvalidationwithtotalvariationanditsapplicationtosuperresolutionimaging
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