Variational Multiscale Nonparametric Regression: Algorithms and Implementation
Many modern statistically efficient methods come with tremendous computational challenges, often leading to large-scale optimisation problems. In this work, we examine such computational issues for recently developed estimation methods in nonparametric regression with a specific view on image denois...
Uloženo v:
| Vydáno v: | Algorithms Ročník 13; číslo 11; s. 296 |
|---|---|
| Hlavní autoři: | , , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Basel
MDPI AG
01.11.2020
|
| Témata: | |
| ISSN: | 1999-4893, 1999-4893 |
| On-line přístup: | Získat plný text |
| Tagy: |
Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
|
| Abstract | Many modern statistically efficient methods come with tremendous computational challenges, often leading to large-scale optimisation problems. In this work, we examine such computational issues for recently developed estimation methods in nonparametric regression with a specific view on image denoising. We consider in particular certain variational multiscale estimators which are statistically optimal in minimax sense, yet computationally intensive. Such an estimator is computed as the minimiser of a smoothness functional (e.g., TV norm) over the class of all estimators such that none of its coefficients with respect to a given multiscale dictionary is statistically significant. The so obtained multiscale Nemirowski-Dantzig estimator (MIND) can incorporate any convex smoothness functional and combine it with a proper dictionary including wavelets, curvelets and shearlets. The computation of MIND in general requires to solve a high-dimensional constrained convex optimisation problem with a specific structure of the constraints induced by the statistical multiscale testing criterion. To solve this explicitly, we discuss three different algorithmic approaches: the Chambolle-Pock, ADMM and semismooth Newton algorithms. Algorithmic details and an explicit implementation is presented and the solutions are then compared numerically in a simulation study and on various test images. We thereby recommend the Chambolle-Pock algorithm in most cases for its fast convergence. We stress that our analysis can also be transferred to signal recovery and other denoising problems to recover more general objects whenever it is possible to borrow statistical strength from data patches of similar object structure. |
|---|---|
| AbstractList | Many modern statistically efficient methods come with tremendous computational challenges, often leading to large-scale optimisation problems. In this work, we examine such computational issues for recently developed estimation methods in nonparametric regression with a specific view on image denoising. We consider in particular certain variational multiscale estimators which are statistically optimal in minimax sense, yet computationally intensive. Such an estimator is computed as the minimiser of a smoothness functional (e.g., TV norm) over the class of all estimators such that none of its coefficients with respect to a given multiscale dictionary is statistically significant. The so obtained multiscale Nemirowski-Dantzig estimator (MIND) can incorporate any convex smoothness functional and combine it with a proper dictionary including wavelets, curvelets and shearlets. The computation of MIND in general requires to solve a high-dimensional constrained convex optimisation problem with a specific structure of the constraints induced by the statistical multiscale testing criterion. To solve this explicitly, we discuss three different algorithmic approaches: the Chambolle-Pock, ADMM and semismooth Newton algorithms. Algorithmic details and an explicit implementation is presented and the solutions are then compared numerically in a simulation study and on various test images. We thereby recommend the Chambolle-Pock algorithm in most cases for its fast convergence. We stress that our analysis can also be transferred to signal recovery and other denoising problems to recover more general objects whenever it is possible to borrow statistical strength from data patches of similar object structure. |
| Author | del Alamo, Miguel Werner, Frank Li, Housen Munk, Axel |
| Author_xml | – sequence: 1 givenname: Miguel surname: del Alamo fullname: del Alamo, Miguel – sequence: 2 givenname: Housen orcidid: 0000-0002-2434-9878 surname: Li fullname: Li, Housen – sequence: 3 givenname: Axel orcidid: 0000-0002-9181-9331 surname: Munk fullname: Munk, Axel – sequence: 4 givenname: Frank orcidid: 0000-0001-8446-3587 surname: Werner fullname: Werner, Frank |
| BookMark | eNptkE1LAzEQhoMo2FYP_oMFTx5qk012N_EmxY-CVhD1GqbJbE3Z3dQkPfjvXVspIp4yhGeemXmH5LDzHRJyxugl54pOgHHGaK7KAzJgSqmxkIof_qqPyTDGFaVloUo2IPM3CA6S8x002eOmSS4aaDCb-24NAVpMwZnsGZcBY-ypq-y6Wfrg0nsbM-hsNmvXDbbYpa3khBzV0EQ8_XlH5PX25mV6P354uptNrx_GhhcyjbGQJauMhKo2jAlTV1bZGpEaJkEIWS4sF2ALoIZzsALporCYo1AVWoUVH5HZzms9rPQ6uBbCp_bg9PbDh6WGkJxpUJcFyKosFgxtLRS3C0Vl3p_PTG0NzWXvOt-51sF_bDAmvfKb0OcRdS76NblSgvbUxY4ywccYsN5PZVR_R6_30ffs5A9r3C6fFMA1_3R8AeuriBk |
| CitedBy_id | crossref_primary_10_1146_annurev_statistics_040120_030531 |
| Cites_doi | 10.1109/TIP.2003.819861 10.1214/20-AOS2001 10.1088/0266-5611/28/6/065006 10.1007/978-1-4613-9940-7_3 10.1109/ICCV.2011.6126441 10.1007/978-1-4612-2222-4 10.3934/ipi.2014.8.685 10.1137/1.9781611971088 10.1111/j.2517-6161.1995.tb02032.x 10.1111/rssb.12047 10.1002/9781118625590 10.1109/CVPR.2017.294 10.1093/imaiai/iaaa001 10.1007/s10851-010-0248-9 10.1214/12-EJS671 10.1137/040611598 10.1214/009053607000000145 10.1007/b13794 10.1080/01621459.1995.10476626 10.1016/j.acha.2013.07.004 10.1137/1109020 10.1109/83.650852 10.1007/BF00927673 10.1093/biomet/81.3.425 10.1007/s10851-010-0251-1 10.1145/321105.321114 10.1093/oso/9780198523963.001.0001 10.1117/12.613494 10.1007/s10915-015-0048-x 10.1006/acha.1995.1008 10.1103/PhysRevA.83.023804 10.1007/s11263-010-0359-1 10.1109/ICPR.2010.579 10.1016/S0165-1684(02)00300-6 10.1214/aos/1176345969 10.1214/009053604000000995 10.1214/17-AIHP832 10.1007/978-3-319-91274-5 10.1111/j.1467-9868.2005.00486.x 10.1109/TIP.2013.2283400 10.1137/1.9781611970104 10.1016/j.jmaa.2017.02.068 10.1214/07-AOS538 10.1080/01621459.1983.10477029 10.1007/s10851-012-0368-5 10.1137/15M1020332 10.1137/03060062X 10.1109/TIP.2005.859378 10.1080/01630569408816580 10.1137/1.9781611970791 10.1051/m2an/2017061 10.1023/B:JMIV.0000011321.19549.88 10.1109/18.382009 10.1016/0167-2789(92)90242-F 10.1214/009053606000000074 10.1007/978-3-319-41589-5 10.1109/TIP.2017.2662206 10.1007/978-3-319-18461-6 10.1016/j.jmaa.2017.05.025 10.1137/1135065 10.1214/aos/1015952005 |
| ContentType | Journal Article |
| Copyright | 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
| Copyright_xml | – notice: 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
| DBID | AAYXX CITATION 3V. 7SC 7TB 7XB 8AL 8FD 8FE 8FG 8FK ABJCF ABUWG AFKRA ARAPS AZQEC BENPR BGLVJ CCPQU DWQXO FR3 GNUQQ HCIFZ JQ2 K7- KR7 L6V L7M L~C L~D M0N M7S P62 PHGZM PHGZT PIMPY PKEHL PQEST PQGLB PQQKQ PQUKI PRINS PTHSS Q9U DOA |
| DOI | 10.3390/a13110296 |
| DatabaseName | CrossRef ProQuest Central (Corporate) Computer and Information Systems Abstracts Mechanical & Transportation Engineering Abstracts ProQuest Central (purchase pre-March 2016) Computing Database (Alumni Edition) Technology Research Database ProQuest SciTech Collection ProQuest Technology Collection ProQuest Central (Alumni) (purchase pre-March 2016) Materials Science & Engineering Collection ProQuest Central (Alumni) ProQuest Central UK/Ireland Advanced Technologies & Computer Science Collection ProQuest Central Essentials - QC ProQuest Central ProQuest Technology Collection ProQuest One ProQuest Central Engineering Research Database ProQuest Central Student SciTech Collection (ProQuest) ProQuest Computer Science Collection Computer Science Database Civil Engineering Abstracts ProQuest Engineering Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional Computing Database Engineering Database ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Premium ProQuest One Academic (New) ProQuest Publicly Available Content Database ProQuest One Academic Middle East (New) ProQuest One Academic Eastern Edition (DO NOT USE) ProQuest One Applied & Life Sciences ProQuest One Academic (retired) ProQuest One Academic UKI Edition ProQuest Central China Engineering Collection ProQuest Central Basic DOAJ Directory of Open Access Journals |
| DatabaseTitle | CrossRef Publicly Available Content Database Computer Science Database ProQuest Central Student Technology Collection Technology Research Database Computer and Information Systems Abstracts – Academic ProQuest One Academic Middle East (New) Mechanical & Transportation Engineering Abstracts ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Essentials ProQuest Computer Science Collection Computer and Information Systems Abstracts ProQuest Central (Alumni Edition) SciTech Premium Collection ProQuest One Community College ProQuest Central China ProQuest Central ProQuest One Applied & Life Sciences ProQuest Engineering Collection ProQuest Central Korea ProQuest Central (New) Advanced Technologies Database with Aerospace Engineering Collection Advanced Technologies & Aerospace Collection Civil Engineering Abstracts ProQuest Computing Engineering Database ProQuest Central Basic ProQuest Computing (Alumni Edition) ProQuest One Academic Eastern Edition ProQuest Technology Collection ProQuest SciTech Collection Computer and Information Systems Abstracts Professional ProQuest One Academic UKI Edition Materials Science & Engineering Collection Engineering Research Database ProQuest One Academic ProQuest One Academic (New) ProQuest Central (Alumni) |
| DatabaseTitleList | Publicly Available Content Database CrossRef |
| Database_xml | – sequence: 1 dbid: DOA name: DOAJ Directory of Open Access Journals url: https://www.doaj.org/ sourceTypes: Open Website – sequence: 2 dbid: PIMPY name: Publicly Available Content Database url: http://search.proquest.com/publiccontent sourceTypes: Aggregation Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Computer Science |
| EISSN | 1999-4893 |
| ExternalDocumentID | oai_doaj_org_article_65a8765b1edf493db90820651cfdc028 10_3390_a13110296 |
| GroupedDBID | 23M 2WC 5VS 8FE 8FG AADQD AAFWJ AAYXX ABDBF ABJCF ABUWG ACUHS ADBBV AFFHD AFKRA AFPKN AFZYC ALMA_UNASSIGNED_HOLDINGS AMVHM ARAPS AZQEC BCNDV BENPR BGLVJ BPHCQ CCPQU CITATION DWQXO E3Z ESX GNUQQ GROUPED_DOAJ HCIFZ IAO J9A K6V K7- KQ8 L6V M7S MODMG M~E OK1 OVT P2P PHGZM PHGZT PIMPY PQGLB PQQKQ PROAC PTHSS TR2 TUS 3V. 7SC 7TB 7XB 8AL 8FD 8FK FR3 ICD JQ2 KR7 L7M L~C L~D M0N P62 PKEHL PQEST PQUKI PRINS Q9U |
| ID | FETCH-LOGICAL-c358t-e58617c8a7fc114cf7d9dfee0c18a4486bd34ad5a0c33ad4e0b5de2e497ed9e73 |
| IEDL.DBID | DOA |
| ISICitedReferencesCount | 2 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000593022100001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 1999-4893 |
| IngestDate | Fri Oct 03 12:53:23 EDT 2025 Fri Jul 25 12:16:52 EDT 2025 Sat Nov 29 07:17:04 EST 2025 Tue Nov 18 22:07:02 EST 2025 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 11 |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c358t-e58617c8a7fc114cf7d9dfee0c18a4486bd34ad5a0c33ad4e0b5de2e497ed9e73 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ORCID | 0000-0002-9181-9331 0000-0002-2434-9878 0000-0001-8446-3587 |
| OpenAccessLink | https://doaj.org/article/65a8765b1edf493db90820651cfdc028 |
| PQID | 2461739940 |
| PQPubID | 2032439 |
| ParticipantIDs | doaj_primary_oai_doaj_org_article_65a8765b1edf493db90820651cfdc028 proquest_journals_2461739940 crossref_primary_10_3390_a13110296 crossref_citationtrail_10_3390_a13110296 |
| PublicationCentury | 2000 |
| PublicationDate | 2020-11-01 |
| PublicationDateYYYYMMDD | 2020-11-01 |
| PublicationDate_xml | – month: 11 year: 2020 text: 2020-11-01 day: 01 |
| PublicationDecade | 2020 |
| PublicationPlace | Basel |
| PublicationPlace_xml | – name: Basel |
| PublicationTitle | Algorithms |
| PublicationYear | 2020 |
| Publisher | MDPI AG |
| Publisher_xml | – name: MDPI AG |
| References | Papafitsoros (ref_20) 2017; 454 Brown (ref_75) 2007; 35 ref_58 ref_13 ref_56 ref_11 ref_55 ref_54 Hestenes (ref_59) 1969; 4 Donoho (ref_74) 1995; 2 Donoho (ref_25) 1994; 81 Dong (ref_23) 2011; 40 Eggermont (ref_7) 2000; 28 Tao (ref_15) 2007; 35 ref_18 ref_17 Nemirovski (ref_14) 1985; 3 (ref_19) 2014; 8 Deutsch (ref_62) 1994; 15 Deng (ref_64) 2016; 66 ref_61 Morozov (ref_9) 1966; 6 Rudin (ref_10) 1992; 60 Cai (ref_49) 2002; 12 Nadaraya (ref_5) 1964; 9 Liu (ref_71) 2013; 22 Donoho (ref_12) 1995; 41 Wang (ref_67) 2004; 13 ref_69 ref_24 Frick (ref_31) 2012; 6 Munk (ref_76) 2020; 48 ref_66 ref_21 Dykstra (ref_60) 1983; 78 Phillips (ref_8) 1962; 9 Chambolle (ref_41) 2011; 40 Sheikh (ref_68) 2006; 15 Zhang (ref_50) 2005; 33 Guo (ref_28) 2002; 82 Birgin (ref_63) 2005; 26 ref_29 Munk (ref_35) 2005; 67 Kunisch (ref_65) 2006; 17 ref_26 Stone (ref_4) 1982; 10 Watson (ref_6) 1964; 26 Luke (ref_40) 2018; 457 ref_70 Frick (ref_32) 2013; 46 Donoho (ref_46) 1995; 90 ref_34 Labate (ref_27) 2005; Volume 5914 ref_33 Haltmeier (ref_53) 2014; 36 Grasmair (ref_16) 2018; Volume 54 Dong (ref_22) 2011; 92 Cai (ref_52) 2009; 37 ref_39 ref_37 Chambolle (ref_57) 2004; 20 Lepskii (ref_44) 1991; 35 Clason (ref_43) 2018; 52 Frick (ref_73) 2014; 76 Malgouyres (ref_30) 2002; 2 ref_42 Weyrich (ref_47) 1998; 7 Donoho (ref_45) 1995; 57 Abramovich (ref_51) 2006; 34 ref_1 ref_3 ref_2 Kramer (ref_38) 2016; 38 ref_48 Zhang (ref_72) 2017; 26 Frick (ref_36) 2012; 28 |
| References_xml | – volume: 26 start-page: 359 year: 1964 ident: ref_6 article-title: Smooth regression analysis publication-title: Sankhya Indian J. Stat. Ser. A – volume: 13 start-page: 600 year: 2004 ident: ref_67 article-title: Image quality assessment: From error visibility to structural similarity publication-title: IEEE Trans. Image Process. doi: 10.1109/TIP.2003.819861 – ident: ref_29 doi: 10.1214/20-AOS2001 – volume: 28 start-page: 065006 year: 2012 ident: ref_36 article-title: Shape-constrained regularization by statistical multiresolution for inverse problems: Asymptotic analysis publication-title: Inverse Probl. doi: 10.1088/0266-5611/28/6/065006 – ident: ref_61 doi: 10.1007/978-1-4613-9940-7_3 – ident: ref_69 doi: 10.1109/ICCV.2011.6126441 – ident: ref_26 – ident: ref_48 doi: 10.1007/978-1-4612-2222-4 – volume: 8 start-page: 685 year: 2014 ident: ref_19 article-title: An adaptive finite element method in L2-TV-based image denoising publication-title: Inverse Probl. Imaging doi: 10.3934/ipi.2014.8.685 – volume: 2 start-page: 1 year: 2002 ident: ref_30 article-title: Mathematical analysis of a model which combines total variation and wavelet for image restoration publication-title: J. Inf. Process. – volume: 12 start-page: 1241 year: 2002 ident: ref_49 article-title: On block thresholding in wavelet regression: Adaptivity, block size, and threshold level publication-title: Stat. Sin. – ident: ref_39 – ident: ref_55 doi: 10.1137/1.9781611971088 – volume: 57 start-page: 301 year: 1995 ident: ref_45 article-title: Wavelet shrinkage: Asymptopia? publication-title: J. R. Stat. Soc. Ser. B doi: 10.1111/j.2517-6161.1995.tb02032.x – ident: ref_42 – volume: 76 start-page: 495 year: 2014 ident: ref_73 article-title: Multiscale change point inference publication-title: J. R. Stat. Soc. Ser. B Stat. Methodol. doi: 10.1111/rssb.12047 – ident: ref_58 – ident: ref_1 doi: 10.1002/9781118625590 – ident: ref_34 doi: 10.1109/CVPR.2017.294 – ident: ref_33 doi: 10.1093/imaiai/iaaa001 – volume: 40 start-page: 82 year: 2011 ident: ref_23 article-title: Automated regularization parameter selection in multi-scale total variation models for image restoration publication-title: J. Math. Imaging Vis. doi: 10.1007/s10851-010-0248-9 – volume: 6 start-page: 231 year: 2012 ident: ref_31 article-title: Statistical multiresolution Dantzig estimation in imaging: Fundamental concepts and algorithmic framework publication-title: Electron. J. Stat. doi: 10.1214/12-EJS671 – volume: 17 start-page: 159 year: 2006 ident: ref_65 article-title: Path-following methods for a class of constrained minimization problems in function space publication-title: SIAM J. Optim. doi: 10.1137/040611598 – volume: 35 start-page: 2219 year: 2007 ident: ref_75 article-title: Variance estimation in nonparametric regression via the difference sequence method publication-title: Ann. Stat. doi: 10.1214/009053607000000145 – ident: ref_13 doi: 10.1007/b13794 – volume: 90 start-page: 1200 year: 1995 ident: ref_46 article-title: Adapting to unknown smoothness via wavelet shrinkage publication-title: J. Am. Stat. Assoc. doi: 10.1080/01621459.1995.10476626 – volume: 36 start-page: 434 year: 2014 ident: ref_53 article-title: Extreme value analysis of empirical frame coefficients and implications for denoising by soft-thresholding publication-title: Appl. Comput. Harmon. Anal. doi: 10.1016/j.acha.2013.07.004 – volume: 9 start-page: 141 year: 1964 ident: ref_5 article-title: On estimating regression publication-title: Theory Probab. Appl. doi: 10.1137/1109020 – volume: 7 start-page: 82 year: 1998 ident: ref_47 article-title: Wavelet shrinkage and generalized cross validation for image denoising publication-title: IEEE Trans. Image Process. doi: 10.1109/83.650852 – volume: 4 start-page: 303 year: 1969 ident: ref_59 article-title: Multiplier and gradient methods publication-title: J. Optim. Theory Appl. doi: 10.1007/BF00927673 – volume: 81 start-page: 425 year: 1994 ident: ref_25 article-title: Ideal spatial adaptation by wavelet shrinkage publication-title: Biometrika doi: 10.1093/biomet/81.3.425 – volume: 40 start-page: 120 year: 2011 ident: ref_41 article-title: A first-order primal-dual algorithm for convex problems with applications to imaging publication-title: J. Math. Imaging Vis. doi: 10.1007/s10851-010-0251-1 – volume: 9 start-page: 84 year: 1962 ident: ref_8 article-title: A technique for the numerical solution of certain integral equations of the first kind publication-title: J. ACM doi: 10.1145/321105.321114 – ident: ref_17 – ident: ref_2 doi: 10.1093/oso/9780198523963.001.0001 – volume: Volume 5914 start-page: 59140U year: 2005 ident: ref_27 article-title: Sparse multidimensional representation using shearlets publication-title: Wavelets XI doi: 10.1117/12.613494 – volume: 66 start-page: 889 year: 2016 ident: ref_64 article-title: On the global and linear convergence of the generalized alternating direction method of multipliers publication-title: J. Sci. Comput. doi: 10.1007/s10915-015-0048-x – volume: 2 start-page: 101 year: 1995 ident: ref_74 article-title: Nonlinear solution of linear inverse problems by wavelet–vaguelette decomposition publication-title: Appl. Comput. Harmon. Anal. doi: 10.1006/acha.1995.1008 – ident: ref_70 doi: 10.1103/PhysRevA.83.023804 – volume: 92 start-page: 296 year: 2011 ident: ref_22 article-title: A multi-scale vectorial Lτ-TV framework for color image restoration publication-title: Int. J. Comput. Vis. doi: 10.1007/s11263-010-0359-1 – ident: ref_66 doi: 10.1109/ICPR.2010.579 – ident: ref_3 – volume: 82 start-page: 1519 year: 2002 ident: ref_28 article-title: New multiscale transforms, minimum total variation synthesis: Applications to edge-preserving image reconstruction publication-title: Signal Process. doi: 10.1016/S0165-1684(02)00300-6 – volume: 10 start-page: 1040 year: 1982 ident: ref_4 article-title: Optimal global rates of convergence for nonparametric regression publication-title: Ann. Stat. doi: 10.1214/aos/1176345969 – volume: 33 start-page: 54 year: 2005 ident: ref_50 article-title: General empirical Bayes wavelet methods and exactly adaptive minimax estimation publication-title: Ann. Stat. doi: 10.1214/009053604000000995 – volume: Volume 54 start-page: 1058 year: 2018 ident: ref_16 article-title: Variational multiscale nonparametric regression: Smooth functions publication-title: Annales de l’Institut Henri Poincaré, Probabilités et Statistiques doi: 10.1214/17-AIHP832 – ident: ref_21 doi: 10.1007/978-3-319-91274-5 – volume: 67 start-page: 19 year: 2005 ident: ref_35 article-title: On difference-based variance estimation in nonparametric regression when the covariate is high dimensional publication-title: J. R. Stat. Soc. Ser. B Stat. Methodol. doi: 10.1111/j.1467-9868.2005.00486.x – ident: ref_37 – volume: 22 start-page: 5226 year: 2013 ident: ref_71 article-title: Single-image noise level estimation for blind denoising publication-title: IEEE Trans. Image Process. doi: 10.1109/TIP.2013.2283400 – ident: ref_11 doi: 10.1137/1.9781611970104 – volume: 457 start-page: 1568 year: 2018 ident: ref_40 article-title: A globally linearly convergent method for pointwise quadratically supportable convex-concave saddle point problems publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2017.02.068 – volume: 37 start-page: 569 year: 2009 ident: ref_52 article-title: A data-driven block thresholding approach to wavelet estimation publication-title: Ann. Stat. doi: 10.1214/07-AOS538 – volume: 78 start-page: 837 year: 1983 ident: ref_60 article-title: An algorithm for restricted least squares regression publication-title: J. Am. Stat. Assoc. doi: 10.1080/01621459.1983.10477029 – volume: 46 start-page: 370 year: 2013 ident: ref_32 article-title: Statistical multiresolution estimation for variational imaging: With an application in Poisson-biophotonics publication-title: J. Math. Imaging Vis. doi: 10.1007/s10851-012-0368-5 – volume: 38 start-page: C533 year: 2016 ident: ref_38 article-title: Parallel statistical multiresolution estimation for image reconstruction publication-title: SIAM J. Sci. Comput. doi: 10.1137/15M1020332 – volume: 26 start-page: 1405 year: 2005 ident: ref_63 article-title: Robust stopping criteria for Dykstra’s algorithm publication-title: SIAM J. Sci. Comput. doi: 10.1137/03060062X – volume: 6 start-page: 170 year: 1966 ident: ref_9 article-title: Regularization of incorrectly posed problems and the choice of regularization parameter publication-title: Zhurnal Vychislitel’noi Mat. I Mat. Fiz. – volume: 15 start-page: 430 year: 2006 ident: ref_68 article-title: Image information and visual quality publication-title: IEEE Trans. Image Process. doi: 10.1109/TIP.2005.859378 – volume: 15 start-page: 537 year: 1994 ident: ref_62 article-title: The rate of convergence of Dykstra’s cyclic projections algorithm: The polyhedral case publication-title: Numer. Funct. Anal. Optim. doi: 10.1080/01630569408816580 – ident: ref_56 doi: 10.1137/1.9781611970791 – volume: 48 start-page: 655 year: 2020 ident: ref_76 article-title: Multidimensional multiscale scanning in exponential families: Limit theory and statistical consequences publication-title: Ann. Stat. – volume: 3 start-page: 50 year: 1985 ident: ref_14 article-title: Nonparametric estimation of smooth regression functions publication-title: Izv. Akad. Nauk. SSR Teckhn. Kibernet – ident: ref_54 – volume: 52 start-page: 275 year: 2018 ident: ref_43 article-title: Total variation regularization of multi-material topology optimization publication-title: ESAIM Math. Model. Numer. Anal. doi: 10.1051/m2an/2017061 – volume: 20 start-page: 89 year: 2004 ident: ref_57 article-title: An Algorithm for Total Variation Minimization and Applications publication-title: J. Math. Imaging Vis. doi: 10.1023/B:JMIV.0000011321.19549.88 – volume: 41 start-page: 613 year: 1995 ident: ref_12 article-title: De-noising by soft-thresholding publication-title: IEEE Trans. Inf. Theory doi: 10.1109/18.382009 – volume: 60 start-page: 259 year: 1992 ident: ref_10 article-title: Nonlinear total variation based noise removal algorithms publication-title: Phys. D Nonlinear Phenom. doi: 10.1016/0167-2789(92)90242-F – volume: 34 start-page: 584 year: 2006 ident: ref_51 article-title: Adapting to unknown sparsity by controlling the false discovery rate publication-title: Ann. Stat. doi: 10.1214/009053606000000074 – ident: ref_18 doi: 10.1007/978-3-319-41589-5 – volume: 26 start-page: 3142 year: 2017 ident: ref_72 article-title: Beyond a Gaussian denoiser: Residual learning of deep CNN for image denoising publication-title: IEEE Trans. Image Process. doi: 10.1109/TIP.2017.2662206 – ident: ref_24 doi: 10.1007/978-3-319-18461-6 – volume: 454 start-page: 891 year: 2017 ident: ref_20 article-title: Analytical aspects of spatially adapted total variation regularisation publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2017.05.025 – volume: 35 start-page: 454 year: 1991 ident: ref_44 article-title: On a Problem of Adaptive Estimation in Gaussian White Noise publication-title: Theory Probab. Appl. doi: 10.1137/1135065 – volume: 28 start-page: 922 year: 2000 ident: ref_7 article-title: Maximum likelihood estimation of smooth monotone and unimodal densities publication-title: Ann. Stat. doi: 10.1214/aos/1015952005 – volume: 35 start-page: 2313 year: 2007 ident: ref_15 article-title: The Dantzig selector: Statistical estimation when p is much larger than n publication-title: Ann. Stat. |
| SSID | ssj0065961 |
| Score | 2.1969957 |
| Snippet | Many modern statistically efficient methods come with tremendous computational challenges, often leading to large-scale optimisation problems. In this work, we... |
| SourceID | doaj proquest crossref |
| SourceType | Open Website Aggregation Database Enrichment Source Index Database |
| StartPage | 296 |
| SubjectTerms | Algorithms Constraints Dictionaries Estimators Fines & penalties image denoising MIND estimator Minimax technique multiscale methods Noise reduction non-smooth large-scale optimisation Nonparametric statistics Optimization Random variables Regression analysis Signal reconstruction Smoothness Statistical analysis Statistical methods variational estimation |
| SummonAdditionalLinks | – databaseName: Engineering Database dbid: M7S link: http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV27TsMwFLWgMLBQnqJQkIUYWKLm5ThhQQVRMaAK8VK3yLm2y9AmpS18P9euU5BALKyxlVg59vU9fpxDyJnWARQyDDykyNpD_oVxMOXKE4DJeJFgwiEt0ne8308Hg-zeLbjN3LHKOibaQC0rMGvkHaN7xnE2jf3LyZtnXKPM7qqz0Fgla0YlIbBH9x7rSJywLAkWakIRUvuOMNIyfmj0-b_NQVaq_0ckttNLr_nfhm2RTZdY0u6iJ2yTFVXukGZt2kDdGN4l_Rdkx24FkNrrtzOESdF-VRoZ8LFx2AL6oIaLA7LlBe2Ohvi9-et4RkUpqdUTHrsrS-Ueee7dPF3fes5UwYOIpXNPsRTbC6ngGpALgeYyk1opH4JUIFdLChnFQjLhQxQJGSu_YFKFKs64kpni0T5plFWpDghl3IcQ3wQai5EWZYUw9lRM80IxCaJFzuvfnINTHDfGF6McmYdBJF8i0iKny6qThczGb5WuDFbLCkYZ2z6opsPcDbQ8YQIDPCsCJXWcRbIwnu7YFQLQEjCZapF2DWPuhuss_8Lw8O_iI7IRGsJtLyO2SWM-fVfHZB0-EKzpie19nzli5o4 priority: 102 providerName: ProQuest |
| Title | Variational Multiscale Nonparametric Regression: Algorithms and Implementation |
| URI | https://www.proquest.com/docview/2461739940 https://doaj.org/article/65a8765b1edf493db90820651cfdc028 |
| Volume | 13 |
| WOSCitedRecordID | wos000593022100001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVAON databaseName: DOAJ Directory of Open Access Journals customDbUrl: eissn: 1999-4893 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0065961 issn: 1999-4893 databaseCode: DOA dateStart: 20080101 isFulltext: true titleUrlDefault: https://www.doaj.org/ providerName: Directory of Open Access Journals – providerCode: PRVHPJ databaseName: ROAD: Directory of Open Access Scholarly Resources customDbUrl: eissn: 1999-4893 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0065961 issn: 1999-4893 databaseCode: M~E dateStart: 20080101 isFulltext: true titleUrlDefault: https://road.issn.org providerName: ISSN International Centre – providerCode: PRVPQU databaseName: Computer Science Database customDbUrl: eissn: 1999-4893 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0065961 issn: 1999-4893 databaseCode: K7- dateStart: 20080301 isFulltext: true titleUrlDefault: http://search.proquest.com/compscijour providerName: ProQuest – providerCode: PRVPQU databaseName: Engineering Database (Proquest) customDbUrl: eissn: 1999-4893 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0065961 issn: 1999-4893 databaseCode: M7S dateStart: 20080301 isFulltext: true titleUrlDefault: http://search.proquest.com providerName: ProQuest – providerCode: PRVPQU databaseName: ProQuest Central customDbUrl: eissn: 1999-4893 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0065961 issn: 1999-4893 databaseCode: BENPR dateStart: 20080301 isFulltext: true titleUrlDefault: https://www.proquest.com/central providerName: ProQuest – providerCode: PRVPQU databaseName: Publicly Available Content Database customDbUrl: eissn: 1999-4893 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0065961 issn: 1999-4893 databaseCode: PIMPY dateStart: 20080301 isFulltext: true titleUrlDefault: http://search.proquest.com/publiccontent providerName: ProQuest |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV07T8MwELYQMLDwRhRKZSEGlqh5OY7ZWtQKBERReahMkeNHGdoUtYWR3845capKILGweIhPSXQX390X2d-H0IXWnsil7zkAkbUD-AvyYEyVwwU043kEDYcsI31PkyQeDlm6IvVl9oRV9MCV49oR4bBgSe4pqUMWyNxodEPd9ISWAoqjyb4uZTWYqnJwRFjkVTxCAYD6NjekMq5vmPlXqk9J0v8jB5eFpb-Ltm1HiDvVm-yhNVXso51abQHbxXeAkheAtfbXHS7Pzc7Bvwon08Lwd0-MNJbAAzWqdrYWV7gzHk0B-79N5pgXEpdEwBN71qg4RM_93tP1jWPVEBwRkHjhKBJDtyFiTrUAECM0lUxqpVzhxRxAVpTLIOSScFcEAZehcnMila9CRpVkigZHaL2YFuoYYUJd4cOdhIZpwDMs50ZXimiaKyIFb6DL2kuZsFThRrFinAFkMA7Nlg5toPOl6XvFj_GbUde4emlgKK3LCxDozAY6-yvQDdSsA5XZdTbPDBsehR4rdE_-4xmnaMs3eLo8a9hE64vZhzpDm-ITQjproY1uL0kHrfJTg_GOOi2zV_TRjF89mE9vH9LXb3l83nc |
| linkProvider | Directory of Open Access Journals |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1Nb9QwEB2VggQXyqfYUsBCIHGJmsRxnCAhVD6qVrtECBXUW-rY4-XQzba7C4g_xW9kxkkWJBC3HrjGliVnXt7MOJ55AE-8T2zj0iSiFNlHlH8RDxYaI2MpGG9yCjhcsPREV1VxfFy-34AfQy0MX6scODEQtZtbPiPf5b5nmrxpFr88O49YNYr_rg4SGh0sxvj9G6VsyxeHb8i-T9N0_-3R64OoVxWIrFTFKkJV0Eq2MNpbSgas1650HjG2SWEoWckbJzPjlImtlMZlGDfKYYpZqdGVqCWtewkuZ7LQ_F2NdTQwf67KPOm6F0lZxruGW9nEKesB_ObzgjTAH8wf3Nn-1v_2Im7A9T5wFnsd0m_CBra3YGsQpRA9R92G6hNl__0JpwjlxUuCIYpq3nKb8xkriFnxAafdBeD2udg7ndL-Vp9nS2FaJ0K_5FlfktXegY8Xsqu7sNnOW7wHQunYprSS9TRMaV_ZGJbfUl43qJw1I3g2mLW2fUd1FvY4rSmzYgTUawSM4PF66lnXRuRvk14xNtYTuPN3eDBfTOueSOpcGXJgqknQ-ayUrmHNeoJeYr2zFCyOYGeATd3T0bL-hZntfw8_gqsHR-8m9eSwGt-HaykfLoTCyx3YXC2-4AO4Yr-S4RYPA_IFnFw0wn4CAbhGfA |
| linkToPdf | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1bi9QwFD6ssyK-uF5xdNUgCr6U6S1NK4isroPDrmUQlfWppicnsws7nXVmVPxr_jpP2nQUFN_2wdc2BNLz5VzSnO8DeGRthLWJo4BLZBtw_cV-MFcUaORkvM444TCtpQ9VWeZHR8V0C370vTDuWmXvE1tHbRbozshHjvdMcTRNw5H11yKm--PnZ58DpyDl_rT2chodRA7o-zcu31bPJvts68dxPH717uXrwCsMBJjIfB2QzHlWzLWyyIUBWmUKY4lCjHLNhUtWmyTVRuoQk0SblMJaGoopLRSZglTC816AbU7J03gA29PJm-nHPg5kssiijssoSYpwpB2xTRg7dYDfImArFPBHHGiD23jnf_4sV-GKT6nFXrcHrsEWNddhp5erEN573YDyg16e-LNP0TYerxigJMpF4wjQ505bDMVbmnVXg5unYu90xutbH89XQjdGtEzKc9-s1dyE9-eyqlswaBYN3QYhVYgxz4SWX3NBWNTaCXNJq2qSBvUQnvQmrtBzrTvJj9OKay6HhmqDhiE83Aw96whG_jbohcPJZoDjBG8fLJazyruYKpOaQ5usIzI2LRJTOzV7hmGE1iCnkUPY7SFUeUe1qn7h586_Xz-ASwys6nBSHtyFy7E7dWg7MndhsF5-oXtwEb-y3Zb3_TYQ8Om8IfYTkOVQ_Q |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Variational+Multiscale+Nonparametric+Regression%3A+Algorithms+and+Implementation&rft.jtitle=Algorithms&rft.au=del+Alamo%2C+Miguel&rft.au=Li%2C+Housen&rft.au=Munk%2C+Axel&rft.au=Werner%2C+Frank&rft.date=2020-11-01&rft.issn=1999-4893&rft.eissn=1999-4893&rft.volume=13&rft.issue=11&rft.spage=296&rft_id=info:doi/10.3390%2Fa13110296&rft.externalDBID=n%2Fa&rft.externalDocID=10_3390_a13110296 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1999-4893&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1999-4893&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1999-4893&client=summon |