3D Data Denoising Using Combined Sparse Dictionaries
Directional multiscale representations such as shearlets and curvelets have gained increasing recognition in recent years as superior methods for the sparse representation of data. Thanks to their ability to sparsely encode images and other multidimensional data, transform-domain denoising algorithm...
Gespeichert in:
| Veröffentlicht in: | Mathematical modelling of natural phenomena 2013, Vol.8 (1), p.60-74 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 74 |
|---|---|
| container_issue | 1 |
| container_start_page | 60 |
| container_title | Mathematical modelling of natural phenomena |
| container_volume | 8 |
| creator | Easley, G. Labate, D. Negi, P. |
| description | Directional multiscale representations such as shearlets and curvelets have gained increasing recognition in recent years as superior methods for the sparse representation of data. Thanks to their ability to sparsely encode images and other multidimensional data, transform-domain denoising algorithms based on these representations are among the best performing methods currently available. As already observed in the literature, the performance of many sparsity-based data processing methods can be further improved by using appropriate combinations of dictionaries. In this paper, we consider the problem of 3D data denoising and introduce a denoising algorithm which uses combined sparse dictionaries. Our numerical demonstrations show that the realization of the algorithm which combines 3D shearlets and local Fourier bases provides highly competitive results as compared to other 3D sparsity-based denosing algorithms based on both single and combined dictionaries. |
| doi_str_mv | 10.1051/mmnp/20138104 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_1431078020</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>3067198361</sourcerecordid><originalsourceid>FETCH-LOGICAL-c342t-9aa3b7014a977e3778dddc0c084bd8afdc88f1132df30cd60c4bb92026ad28cc3</originalsourceid><addsrcrecordid>eNpFkE1LAzEQhoMoWGqP3hc8r51k0iR7lK5fUPBQq8eQTbKS6n6YbEH_vVvrxxxmLg_zvjyEnFO4pLCg86Zp-zkDiooCPyITKgXkggI9JhMoJOYL5OqUzFLawjhIOQJMCMcyK81gstK3XUihfck233vZNVVovcvWvYnJZ2WwQ-haE4NPZ-SkNm_Jz37ulGxurh-Xd_nq4fZ-ebXKLXI25IUxWEmg3BRSepRSOecsWFC8csrUzipVU4rM1QjWCbC8qgoGTBjHlLU4JReHv33s3nc-DXrb7WI7RuqxPgWpgMFI5QfKxi6l6Gvdx9CY-Kkp6L0bvXejf9388yEN_uMPNvFVC4lyoRU863VZPCkQQiN-AU6MZHI</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1431078020</pqid></control><display><type>article</type><title>3D Data Denoising Using Combined Sparse Dictionaries</title><source>Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals</source><source>Cambridge Journals</source><creator>Easley, G. ; Labate, D. ; Negi, P.</creator><contributor>Damanik, David ; Wang, Yang ; Vougalter, Vitali ; Wong, Man Wah ; Iosevich, Alex ; Finkelshtein, Andrei Martinez</contributor><creatorcontrib>Easley, G. ; Labate, D. ; Negi, P. ; Damanik, David ; Wang, Yang ; Vougalter, Vitali ; Wong, Man Wah ; Iosevich, Alex ; Finkelshtein, Andrei Martinez</creatorcontrib><description>Directional multiscale representations such as shearlets and curvelets have gained increasing recognition in recent years as superior methods for the sparse representation of data. Thanks to their ability to sparsely encode images and other multidimensional data, transform-domain denoising algorithms based on these representations are among the best performing methods currently available. As already observed in the literature, the performance of many sparsity-based data processing methods can be further improved by using appropriate combinations of dictionaries. In this paper, we consider the problem of 3D data denoising and introduce a denoising algorithm which uses combined sparse dictionaries. Our numerical demonstrations show that the realization of the algorithm which combines 3D shearlets and local Fourier bases provides highly competitive results as compared to other 3D sparsity-based denosing algorithms based on both single and combined dictionaries.</description><identifier>ISSN: 0973-5348</identifier><identifier>EISSN: 1760-6101</identifier><identifier>DOI: 10.1051/mmnp/20138104</identifier><language>eng</language><publisher>Les Ulis: EDP Sciences</publisher><subject>3-D graphics ; 42C15 ; 42C40 ; Algorithms ; curvelets ; denoising ; Fourier transforms ; nonlinear approximations ; pursuit algorithms ; shearlets ; sparse approximations ; wavelets</subject><ispartof>Mathematical modelling of natural phenomena, 2013, Vol.8 (1), p.60-74</ispartof><rights>EDP Sciences, 2013</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c342t-9aa3b7014a977e3778dddc0c084bd8afdc88f1132df30cd60c4bb92026ad28cc3</citedby><cites>FETCH-LOGICAL-c342t-9aa3b7014a977e3778dddc0c084bd8afdc88f1132df30cd60c4bb92026ad28cc3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,4022,27922,27923,27924</link.rule.ids></links><search><contributor>Damanik, David</contributor><contributor>Wang, Yang</contributor><contributor>Vougalter, Vitali</contributor><contributor>Wong, Man Wah</contributor><contributor>Iosevich, Alex</contributor><contributor>Finkelshtein, Andrei Martinez</contributor><creatorcontrib>Easley, G.</creatorcontrib><creatorcontrib>Labate, D.</creatorcontrib><creatorcontrib>Negi, P.</creatorcontrib><title>3D Data Denoising Using Combined Sparse Dictionaries</title><title>Mathematical modelling of natural phenomena</title><description>Directional multiscale representations such as shearlets and curvelets have gained increasing recognition in recent years as superior methods for the sparse representation of data. Thanks to their ability to sparsely encode images and other multidimensional data, transform-domain denoising algorithms based on these representations are among the best performing methods currently available. As already observed in the literature, the performance of many sparsity-based data processing methods can be further improved by using appropriate combinations of dictionaries. In this paper, we consider the problem of 3D data denoising and introduce a denoising algorithm which uses combined sparse dictionaries. Our numerical demonstrations show that the realization of the algorithm which combines 3D shearlets and local Fourier bases provides highly competitive results as compared to other 3D sparsity-based denosing algorithms based on both single and combined dictionaries.</description><subject>3-D graphics</subject><subject>42C15</subject><subject>42C40</subject><subject>Algorithms</subject><subject>curvelets</subject><subject>denoising</subject><subject>Fourier transforms</subject><subject>nonlinear approximations</subject><subject>pursuit algorithms</subject><subject>shearlets</subject><subject>sparse approximations</subject><subject>wavelets</subject><issn>0973-5348</issn><issn>1760-6101</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2013</creationdate><recordtype>article</recordtype><recordid>eNpFkE1LAzEQhoMoWGqP3hc8r51k0iR7lK5fUPBQq8eQTbKS6n6YbEH_vVvrxxxmLg_zvjyEnFO4pLCg86Zp-zkDiooCPyITKgXkggI9JhMoJOYL5OqUzFLawjhIOQJMCMcyK81gstK3XUihfck233vZNVVovcvWvYnJZ2WwQ-haE4NPZ-SkNm_Jz37ulGxurh-Xd_nq4fZ-ebXKLXI25IUxWEmg3BRSepRSOecsWFC8csrUzipVU4rM1QjWCbC8qgoGTBjHlLU4JReHv33s3nc-DXrb7WI7RuqxPgWpgMFI5QfKxi6l6Gvdx9CY-Kkp6L0bvXejf9388yEN_uMPNvFVC4lyoRU863VZPCkQQiN-AU6MZHI</recordid><startdate>2013</startdate><enddate>2013</enddate><creator>Easley, G.</creator><creator>Labate, D.</creator><creator>Negi, P.</creator><general>EDP Sciences</general><scope>BSCLL</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7QF</scope><scope>7QO</scope><scope>7QQ</scope><scope>7SC</scope><scope>7SE</scope><scope>7SP</scope><scope>7SR</scope><scope>7TA</scope><scope>7TB</scope><scope>7TK</scope><scope>7U5</scope><scope>8BQ</scope><scope>8FD</scope><scope>F28</scope><scope>FR3</scope><scope>H8D</scope><scope>H8G</scope><scope>JG9</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>P64</scope></search><sort><creationdate>2013</creationdate><title>3D Data Denoising Using Combined Sparse Dictionaries</title><author>Easley, G. ; Labate, D. ; Negi, P.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c342t-9aa3b7014a977e3778dddc0c084bd8afdc88f1132df30cd60c4bb92026ad28cc3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2013</creationdate><topic>3-D graphics</topic><topic>42C15</topic><topic>42C40</topic><topic>Algorithms</topic><topic>curvelets</topic><topic>denoising</topic><topic>Fourier transforms</topic><topic>nonlinear approximations</topic><topic>pursuit algorithms</topic><topic>shearlets</topic><topic>sparse approximations</topic><topic>wavelets</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Easley, G.</creatorcontrib><creatorcontrib>Labate, D.</creatorcontrib><creatorcontrib>Negi, P.</creatorcontrib><collection>Istex</collection><collection>CrossRef</collection><collection>Aluminium Industry Abstracts</collection><collection>Biotechnology Research Abstracts</collection><collection>Ceramic Abstracts</collection><collection>Computer and Information Systems Abstracts</collection><collection>Corrosion Abstracts</collection><collection>Electronics & Communications Abstracts</collection><collection>Engineered Materials Abstracts</collection><collection>Materials Business File</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Neurosciences Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>METADEX</collection><collection>Technology Research Database</collection><collection>ANTE: Abstracts in New Technology & Engineering</collection><collection>Engineering Research Database</collection><collection>Aerospace Database</collection><collection>Copper Technical Reference Library</collection><collection>Materials Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>Biotechnology and BioEngineering Abstracts</collection><jtitle>Mathematical modelling of natural phenomena</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Easley, G.</au><au>Labate, D.</au><au>Negi, P.</au><au>Damanik, David</au><au>Wang, Yang</au><au>Vougalter, Vitali</au><au>Wong, Man Wah</au><au>Iosevich, Alex</au><au>Finkelshtein, Andrei Martinez</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>3D Data Denoising Using Combined Sparse Dictionaries</atitle><jtitle>Mathematical modelling of natural phenomena</jtitle><date>2013</date><risdate>2013</risdate><volume>8</volume><issue>1</issue><spage>60</spage><epage>74</epage><pages>60-74</pages><issn>0973-5348</issn><eissn>1760-6101</eissn><abstract>Directional multiscale representations such as shearlets and curvelets have gained increasing recognition in recent years as superior methods for the sparse representation of data. Thanks to their ability to sparsely encode images and other multidimensional data, transform-domain denoising algorithms based on these representations are among the best performing methods currently available. As already observed in the literature, the performance of many sparsity-based data processing methods can be further improved by using appropriate combinations of dictionaries. In this paper, we consider the problem of 3D data denoising and introduce a denoising algorithm which uses combined sparse dictionaries. Our numerical demonstrations show that the realization of the algorithm which combines 3D shearlets and local Fourier bases provides highly competitive results as compared to other 3D sparsity-based denosing algorithms based on both single and combined dictionaries.</abstract><cop>Les Ulis</cop><pub>EDP Sciences</pub><doi>10.1051/mmnp/20138104</doi><tpages>15</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0973-5348 |
| ispartof | Mathematical modelling of natural phenomena, 2013, Vol.8 (1), p.60-74 |
| issn | 0973-5348 1760-6101 |
| language | eng |
| recordid | cdi_proquest_journals_1431078020 |
| source | Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; Cambridge Journals |
| subjects | 3-D graphics 42C15 42C40 Algorithms curvelets denoising Fourier transforms nonlinear approximations pursuit algorithms shearlets sparse approximations wavelets |
| title | 3D Data Denoising Using Combined Sparse Dictionaries |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-11T21%3A29%3A09IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=3D%20Data%20Denoising%20Using%20Combined%20Sparse%20Dictionaries&rft.jtitle=Mathematical%20modelling%20of%20natural%20phenomena&rft.au=Easley,%20G.&rft.date=2013&rft.volume=8&rft.issue=1&rft.spage=60&rft.epage=74&rft.pages=60-74&rft.issn=0973-5348&rft.eissn=1760-6101&rft_id=info:doi/10.1051/mmnp/20138104&rft_dat=%3Cproquest_cross%3E3067198361%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=1431078020&rft_id=info:pmid/&rfr_iscdi=true |