First Order Algorithms in Variational Image Processing
Saved in:
| Title: | First Order Algorithms in Variational Image Processing |
|---|---|
| Authors: | Burger, Martin (Professor), Sawatzky, Alexander, Steidl, Gabriele (Professor) |
| Publication Year: | 2014 |
| Collection: | University of Kaiserslautern (TU): Kluedo - Kaiserslauterer uniweiter elektronischer Dokumentenserver |
| Subject Terms: | ddc:500 |
| Description: | Variational methods in imaging are nowadays developing towards a quite universal and exible tool, allowing for highly successful approaches on tasks like denoising, deblurring, inpainting, segmentation, super-resolution, disparity, and optical flow estimation. The overall structure of such approaches is of the form D(Ku) + alpha R(u) to min_u ; where the functional D is a data fidelity term also depending on some input data f and measuring the deviation of Ku from such and R is a regularization functional. Moreover K is a (often linear) forward operator modeling the dependence of data on an underlying image, and alpha is a positive regularization parameter. While D is often smooth and (strictly) convex, the current practice almost exclusively uses nonsmooth regularization functionals. The majority of successful techniques is using nonsmooth and convex functionals like the total variation and generalizations thereof, cf. [28, 31, 40], or l_1-norms of coeefficients arising from scalar products with some frame system, cf. [73] and references therein. The efficient solution of such variational problems in imaging demands for appropriate algorithms. Taking into account the specific structure as a sum of two very different terms to be minimized, splitting algorithms are a quite canonical choice. Consequently this field has revived the interest in techniques like operator splittings or augmented Lagrangians. In this chapter we shall provide an overview of methods currently developed and recent results as well as some computational studies providing a comparison of different methods and also illustrating their success in applications. We start with a very general viewpoint in the first sections, discussing basic notations, properties of proximal maps, firmly non-expansive and averaging operators, which form the basis of further convergence arguments. Then we proceed to a discussion of several state-of-the art algorithms and their (theoretical) convergence properties. After a section discussing issues related to the use ... |
| Document Type: | report |
| File Description: | application/pdf |
| Language: | English |
| Relation: | https://kluedo.ub.rptu.de/frontdoor/index/index/docId/3852; https://kluedo.ub.rptu.de/files/3852/algs_book_revision.pdf |
| Availability: | https://kluedo.ub.rptu.de/frontdoor/index/index/docId/3852 https://nbn-resolving.org/urn:nbn:de:hbz:386-kluedo-38524 https://kluedo.ub.rptu.de/files/3852/algs_book_revision.pdf |
| Rights: | Standard gemäß KLUEDO-Leitlinien vom 10.09.2012 ; https://kluedo.ub.rptu.de/download/lizenzen/kluedo_leitlinien_2012-09-10.pdf ; info:eu-repo/semantics/openAccess |
| Accession Number: | edsbas.97F4BA15 |
| Database: | BASE |
Nájsť tento článok vo Web of Science | FullText | Text: Availability: 0 CustomLinks: – Url: https://kluedo.ub.rptu.de/frontdoor/index/index/docId/3852# Name: EDS - BASE (s4221598) Category: fullText Text: View record from BASE – Url: https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=EBSCO&SrcAuth=EBSCO&DestApp=WOS&ServiceName=TransferToWoS&DestLinkType=GeneralSearchSummary&Func=Links&author=Burger%20M Name: ISI Category: fullText Text: Nájsť tento článok vo Web of Science Icon: https://imagesrvr.epnet.com/ls/20docs.gif MouseOverText: Nájsť tento článok vo Web of Science |
|---|---|
| Header | DbId: edsbas DbLabel: BASE An: edsbas.97F4BA15 RelevancyScore: 832 AccessLevel: 3 PubType: Report PubTypeId: report PreciseRelevancyScore: 831.644287109375 |
| IllustrationInfo | |
| Items | – Name: Title Label: Title Group: Ti Data: First Order Algorithms in Variational Image Processing – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Burger%2C+Martin+%28Professor%29%22">Burger, Martin (Professor)</searchLink><br /><searchLink fieldCode="AR" term="%22Sawatzky%2C+Alexander%22">Sawatzky, Alexander</searchLink><br /><searchLink fieldCode="AR" term="%22Steidl%2C+Gabriele+%28Professor%29%22">Steidl, Gabriele (Professor)</searchLink> – Name: DatePubCY Label: Publication Year Group: Date Data: 2014 – Name: Subset Label: Collection Group: HoldingsInfo Data: University of Kaiserslautern (TU): Kluedo - Kaiserslauterer uniweiter elektronischer Dokumentenserver – Name: Subject Label: Subject Terms Group: Su Data: <searchLink fieldCode="DE" term="%22ddc%3A500%22">ddc:500</searchLink> – Name: Abstract Label: Description Group: Ab Data: Variational methods in imaging are nowadays developing towards a quite universal and exible tool, allowing for highly successful approaches on tasks like denoising, deblurring, inpainting, segmentation, super-resolution, disparity, and optical flow estimation. The overall structure of such approaches is of the form D(Ku) + alpha R(u) to min_u ; where the functional D is a data fidelity term also depending on some input data f and measuring the deviation of Ku from such and R is a regularization functional. Moreover K is a (often linear) forward operator modeling the dependence of data on an underlying image, and alpha is a positive regularization parameter. While D is often smooth and (strictly) convex, the current practice almost exclusively uses nonsmooth regularization functionals. The majority of successful techniques is using nonsmooth and convex functionals like the total variation and generalizations thereof, cf. [28, 31, 40], or l_1-norms of coeefficients arising from scalar products with some frame system, cf. [73] and references therein. The efficient solution of such variational problems in imaging demands for appropriate algorithms. Taking into account the specific structure as a sum of two very different terms to be minimized, splitting algorithms are a quite canonical choice. Consequently this field has revived the interest in techniques like operator splittings or augmented Lagrangians. In this chapter we shall provide an overview of methods currently developed and recent results as well as some computational studies providing a comparison of different methods and also illustrating their success in applications. We start with a very general viewpoint in the first sections, discussing basic notations, properties of proximal maps, firmly non-expansive and averaging operators, which form the basis of further convergence arguments. Then we proceed to a discussion of several state-of-the art algorithms and their (theoretical) convergence properties. After a section discussing issues related to the use ... – Name: TypeDocument Label: Document Type Group: TypDoc Data: report – Name: Format Label: File Description Group: SrcInfo Data: application/pdf – Name: Language Label: Language Group: Lang Data: English – Name: NoteTitleSource Label: Relation Group: SrcInfo Data: https://kluedo.ub.rptu.de/frontdoor/index/index/docId/3852; https://kluedo.ub.rptu.de/files/3852/algs_book_revision.pdf – Name: URL Label: Availability Group: URL Data: https://kluedo.ub.rptu.de/frontdoor/index/index/docId/3852<br />https://nbn-resolving.org/urn:nbn:de:hbz:386-kluedo-38524<br />https://kluedo.ub.rptu.de/files/3852/algs_book_revision.pdf – Name: Copyright Label: Rights Group: Cpyrght Data: Standard gemäß KLUEDO-Leitlinien vom 10.09.2012 ; https://kluedo.ub.rptu.de/download/lizenzen/kluedo_leitlinien_2012-09-10.pdf ; info:eu-repo/semantics/openAccess – Name: AN Label: Accession Number Group: ID Data: edsbas.97F4BA15 |
| PLink | https://erproxy.cvtisr.sk/sfx/access?url=https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsbas&AN=edsbas.97F4BA15 |
| RecordInfo | BibRecord: BibEntity: Languages: – Text: English Subjects: – SubjectFull: ddc:500 Type: general Titles: – TitleFull: First Order Algorithms in Variational Image Processing Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Burger, Martin (Professor) – PersonEntity: Name: NameFull: Sawatzky, Alexander – PersonEntity: Name: NameFull: Steidl, Gabriele (Professor) IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Type: published Y: 2014 Identifiers: – Type: issn-locals Value: edsbas – Type: issn-locals Value: edsbas.oa |
| ResultId | 1 |