A General Approach for Orthogonal 4-Tap Integer Multiwavelet Transforms
An algorithm for orthogonal 4-tap integer multiwavelet transforms is proposed. We compute the singular value decomposition (SVD) of block recursive matrices of transform matrix, and then transform matrix can be rewritten in a product of two block diagonal matrices and a permutation matrix. Furthermo...
Gespeichert in:
| Veröffentlicht in: | Mathematical Problems in Engineering 2010-01, Vol.2010 (1), p.438-449-025 |
|---|---|
| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 449-025 |
|---|---|
| container_issue | 1 |
| container_start_page | 438 |
| container_title | Mathematical Problems in Engineering |
| container_volume | 2010 |
| creator | Jing, Mingli Huang, Hua Liu, Wuling Qi, Chun |
| description | An algorithm for orthogonal 4-tap integer multiwavelet transforms is proposed. We compute the singular value decomposition (SVD) of block recursive matrices of transform matrix, and then transform matrix can be rewritten in a product of two block diagonal matrices and a permutation matrix. Furthermore, we factorize the block matrix of block diagonal matrices into triangular elementary reversible matrices (TERMs), which map integers to integers by rounding arithmetic. The cost of factorizing block matrix into TERMs does not increase with the increase of the dimension of transform matrix, and the proposed algorithm is in-place calculation and without allocating auxiliary memory. Examples of integer multiwavelet transform using DGHM and CL are given, which verify that the proposed algorithm is an executable algorithm and outperforms the existing algorithm for orthogonal 4-tap integer multiwavelet transform. |
| doi_str_mv | 10.1155/2010/163758 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_855686596</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><airiti_id>P20161117002_201012_201703230019_201703230019_438_449_025</airiti_id><sourcerecordid>2287219251</sourcerecordid><originalsourceid>FETCH-LOGICAL-a437t-6bdb949d0da3882302dcac365bc02a891207a46c550012182dd1255f7005ae2a3</originalsourceid><addsrcrecordid>eNqF0M9LwzAUB_AiCs7pyX-geBGUuvfyq-lxDJ3CRA8TvIW3Nts6unYmncP_3swKohdPLwmf5OV9o-gc4QZRygEDhAEqnkp9EPVQKp5IFOlhWAMTCTL-ehydeL8CYChR96LxMB7b2jqq4uFm4xrKl_G8cfGTa5fNoqnDuUimtIkf6tYurIsft1Vb7ujdVraNp45qH_jan0ZHc6q8Pfuu_ejl7nY6uk8mT-OH0XCSkOBpm6hZMctEVkBBXGvGgRU55VzJWQ6MdIYMUhIqlxIAGWpWFMiknKcAkiwj3o8uu3fDX9-21rdmXfrcVhXVttl6o6VUWslMBXnxR66arQsD7ZECLQSDgK47lLvGe2fnZuPKNbkPg2D2kZp9pKaLNOirTi_LuqBd-Q9-7jCVrmzLn-7PQSlEDDOxrxv4VVLgIQ_A7PdGcG2EyAwwyT8BX0SIZA</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>856084420</pqid></control><display><type>article</type><title>A General Approach for Orthogonal 4-Tap Integer Multiwavelet Transforms</title><source>Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals</source><source>Wiley-Blackwell Open Access Titles</source><source>Alma/SFX Local Collection</source><creator>Jing, Mingli ; Huang, Hua ; Liu, Wuling ; Qi, Chun</creator><contributor>Luongo, Angelo</contributor><creatorcontrib>Jing, Mingli ; Huang, Hua ; Liu, Wuling ; Qi, Chun ; Luongo, Angelo</creatorcontrib><description>An algorithm for orthogonal 4-tap integer multiwavelet transforms is proposed. We compute the singular value decomposition (SVD) of block recursive matrices of transform matrix, and then transform matrix can be rewritten in a product of two block diagonal matrices and a permutation matrix. Furthermore, we factorize the block matrix of block diagonal matrices into triangular elementary reversible matrices (TERMs), which map integers to integers by rounding arithmetic. The cost of factorizing block matrix into TERMs does not increase with the increase of the dimension of transform matrix, and the proposed algorithm is in-place calculation and without allocating auxiliary memory. Examples of integer multiwavelet transform using DGHM and CL are given, which verify that the proposed algorithm is an executable algorithm and outperforms the existing algorithm for orthogonal 4-tap integer multiwavelet transform.</description><identifier>ISSN: 1024-123X</identifier><identifier>EISSN: 1563-5147</identifier><identifier>DOI: 10.1155/2010/163758</identifier><language>eng</language><publisher>New York: Hindawi Limiteds</publisher><subject>Algorithms ; Blocking ; Data compression ; Engineering ; Integers ; Mathematical analysis ; Mathematical models ; Matrices ; Matrix methods ; Numbers ; Permutations ; Recursive ; Singular value decomposition ; Studies ; Transformations (mathematics) ; Transforms ; Wavelet transforms</subject><ispartof>Mathematical Problems in Engineering, 2010-01, Vol.2010 (1), p.438-449-025</ispartof><rights>Copyright © 2010</rights><rights>Copyright © 2010 Mingli Jing et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-a437t-6bdb949d0da3882302dcac365bc02a891207a46c550012182dd1255f7005ae2a3</citedby><cites>FETCH-LOGICAL-a437t-6bdb949d0da3882302dcac365bc02a891207a46c550012182dd1255f7005ae2a3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><contributor>Luongo, Angelo</contributor><creatorcontrib>Jing, Mingli</creatorcontrib><creatorcontrib>Huang, Hua</creatorcontrib><creatorcontrib>Liu, Wuling</creatorcontrib><creatorcontrib>Qi, Chun</creatorcontrib><title>A General Approach for Orthogonal 4-Tap Integer Multiwavelet Transforms</title><title>Mathematical Problems in Engineering</title><description>An algorithm for orthogonal 4-tap integer multiwavelet transforms is proposed. We compute the singular value decomposition (SVD) of block recursive matrices of transform matrix, and then transform matrix can be rewritten in a product of two block diagonal matrices and a permutation matrix. Furthermore, we factorize the block matrix of block diagonal matrices into triangular elementary reversible matrices (TERMs), which map integers to integers by rounding arithmetic. The cost of factorizing block matrix into TERMs does not increase with the increase of the dimension of transform matrix, and the proposed algorithm is in-place calculation and without allocating auxiliary memory. Examples of integer multiwavelet transform using DGHM and CL are given, which verify that the proposed algorithm is an executable algorithm and outperforms the existing algorithm for orthogonal 4-tap integer multiwavelet transform.</description><subject>Algorithms</subject><subject>Blocking</subject><subject>Data compression</subject><subject>Engineering</subject><subject>Integers</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>Matrices</subject><subject>Matrix methods</subject><subject>Numbers</subject><subject>Permutations</subject><subject>Recursive</subject><subject>Singular value decomposition</subject><subject>Studies</subject><subject>Transformations (mathematics)</subject><subject>Transforms</subject><subject>Wavelet transforms</subject><issn>1024-123X</issn><issn>1563-5147</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2010</creationdate><recordtype>article</recordtype><sourceid>RHX</sourceid><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><recordid>eNqF0M9LwzAUB_AiCs7pyX-geBGUuvfyq-lxDJ3CRA8TvIW3Nts6unYmncP_3swKohdPLwmf5OV9o-gc4QZRygEDhAEqnkp9EPVQKp5IFOlhWAMTCTL-ehydeL8CYChR96LxMB7b2jqq4uFm4xrKl_G8cfGTa5fNoqnDuUimtIkf6tYurIsft1Vb7ujdVraNp45qH_jan0ZHc6q8Pfuu_ejl7nY6uk8mT-OH0XCSkOBpm6hZMctEVkBBXGvGgRU55VzJWQ6MdIYMUhIqlxIAGWpWFMiknKcAkiwj3o8uu3fDX9-21rdmXfrcVhXVttl6o6VUWslMBXnxR66arQsD7ZECLQSDgK47lLvGe2fnZuPKNbkPg2D2kZp9pKaLNOirTi_LuqBd-Q9-7jCVrmzLn-7PQSlEDDOxrxv4VVLgIQ_A7PdGcG2EyAwwyT8BX0SIZA</recordid><startdate>20100101</startdate><enddate>20100101</enddate><creator>Jing, Mingli</creator><creator>Huang, Hua</creator><creator>Liu, Wuling</creator><creator>Qi, Chun</creator><general>Hindawi Limiteds</general><general>Hindawi Publishing Corporation</general><general>Hindawi Limited</general><scope>188</scope><scope>RHU</scope><scope>RHW</scope><scope>RHX</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7TB</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>CWDGH</scope><scope>DWQXO</scope><scope>FR3</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>KR7</scope><scope>L6V</scope><scope>M7S</scope><scope>P5Z</scope><scope>P62</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope></search><sort><creationdate>20100101</creationdate><title>A General Approach for Orthogonal 4-Tap Integer Multiwavelet Transforms</title><author>Jing, Mingli ; Huang, Hua ; Liu, Wuling ; Qi, Chun</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a437t-6bdb949d0da3882302dcac365bc02a891207a46c550012182dd1255f7005ae2a3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2010</creationdate><topic>Algorithms</topic><topic>Blocking</topic><topic>Data compression</topic><topic>Engineering</topic><topic>Integers</topic><topic>Mathematical analysis</topic><topic>Mathematical models</topic><topic>Matrices</topic><topic>Matrix methods</topic><topic>Numbers</topic><topic>Permutations</topic><topic>Recursive</topic><topic>Singular value decomposition</topic><topic>Studies</topic><topic>Transformations (mathematics)</topic><topic>Transforms</topic><topic>Wavelet transforms</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Jing, Mingli</creatorcontrib><creatorcontrib>Huang, Hua</creatorcontrib><creatorcontrib>Liu, Wuling</creatorcontrib><creatorcontrib>Qi, Chun</creatorcontrib><collection>Airiti Library</collection><collection>Hindawi Publishing Complete</collection><collection>Hindawi Publishing Subscription Journals</collection><collection>Hindawi Publishing Open Access</collection><collection>CrossRef</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>Middle East & Africa Database</collection><collection>ProQuest Central Korea</collection><collection>Engineering Research Database</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer Science Database</collection><collection>Civil Engineering Abstracts</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>Publicly Available Content Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection><jtitle>Mathematical Problems in Engineering</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Jing, Mingli</au><au>Huang, Hua</au><au>Liu, Wuling</au><au>Qi, Chun</au><au>Luongo, Angelo</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A General Approach for Orthogonal 4-Tap Integer Multiwavelet Transforms</atitle><jtitle>Mathematical Problems in Engineering</jtitle><date>2010-01-01</date><risdate>2010</risdate><volume>2010</volume><issue>1</issue><spage>438</spage><epage>449-025</epage><pages>438-449-025</pages><issn>1024-123X</issn><eissn>1563-5147</eissn><abstract>An algorithm for orthogonal 4-tap integer multiwavelet transforms is proposed. We compute the singular value decomposition (SVD) of block recursive matrices of transform matrix, and then transform matrix can be rewritten in a product of two block diagonal matrices and a permutation matrix. Furthermore, we factorize the block matrix of block diagonal matrices into triangular elementary reversible matrices (TERMs), which map integers to integers by rounding arithmetic. The cost of factorizing block matrix into TERMs does not increase with the increase of the dimension of transform matrix, and the proposed algorithm is in-place calculation and without allocating auxiliary memory. Examples of integer multiwavelet transform using DGHM and CL are given, which verify that the proposed algorithm is an executable algorithm and outperforms the existing algorithm for orthogonal 4-tap integer multiwavelet transform.</abstract><cop>New York</cop><pub>Hindawi Limiteds</pub><doi>10.1155/2010/163758</doi><tpages>12</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1024-123X |
| ispartof | Mathematical Problems in Engineering, 2010-01, Vol.2010 (1), p.438-449-025 |
| issn | 1024-123X 1563-5147 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_855686596 |
| source | Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; Wiley-Blackwell Open Access Titles; Alma/SFX Local Collection |
| subjects | Algorithms Blocking Data compression Engineering Integers Mathematical analysis Mathematical models Matrices Matrix methods Numbers Permutations Recursive Singular value decomposition Studies Transformations (mathematics) Transforms Wavelet transforms |
| title | A General Approach for Orthogonal 4-Tap Integer Multiwavelet Transforms |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-05T16%3A16%3A39IST&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=A%20General%20Approach%20for%20Orthogonal%204-Tap%20Integer%20Multiwavelet%20Transforms&rft.jtitle=Mathematical%20Problems%20in%20Engineering&rft.au=Jing,%20Mingli&rft.date=2010-01-01&rft.volume=2010&rft.issue=1&rft.spage=438&rft.epage=449-025&rft.pages=438-449-025&rft.issn=1024-123X&rft.eissn=1563-5147&rft_id=info:doi/10.1155/2010/163758&rft_dat=%3Cproquest_cross%3E2287219251%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=856084420&rft_id=info:pmid/&rft_airiti_id=P20161117002_201012_201703230019_201703230019_438_449_025&rfr_iscdi=true |