Semi-Local Scaling Exponent Estimation With Box-Penalty Constraints and Total-Variation Regularization
We here establish and exploit the result that 2D isotropic self-similar fields beget quasi-decorrelated wavelet coefficients and that the resulting localised log sample second moment statistic is asymptotically normal. This leads to the development of a semi-local scaling exponent estimation framewo...
Gespeichert in:
| Veröffentlicht in: | IEEE transactions on image processing 2016-07, Vol.25 (7), p.3167-3181 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext bestellen |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 3181 |
|---|---|
| container_issue | 7 |
| container_start_page | 3167 |
| container_title | IEEE transactions on image processing |
| container_volume | 25 |
| creator | Nelson, J. D. B. Nafornita, C. Isar, A. |
| description | We here establish and exploit the result that 2D isotropic self-similar fields beget quasi-decorrelated wavelet coefficients and that the resulting localised log sample second moment statistic is asymptotically normal. This leads to the development of a semi-local scaling exponent estimation framework with optimally modified weights. Furthermore, recent interest in penalty methods for least square problems and generalized Lasso for scaling exponent estimation inspires the simultaneous incorporation of both bounding box constraints and total variation smoothing into an iteratively reweighted least-square estimator framework. Numerical results on fractional Brownian fields with global and piecewise constant, semi-local Hurst parameters illustrate the benefits of the new estimators. |
| doi_str_mv | 10.1109/TIP.2016.2551365 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_RIE</sourceid><recordid>TN_cdi_crossref_primary_10_1109_TIP_2016_2551365</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><ieee_id>7448417</ieee_id><sourcerecordid>1826675992</sourcerecordid><originalsourceid>FETCH-LOGICAL-c380t-607c3df2715e4ae340d5adc0d853c27a132779774aa6cf918cbb7bda682d96883</originalsourceid><addsrcrecordid>eNqNkc1vEzEQxS0EoqVwR0JCK3HhssHjr7GPEAWoFImKBjiuHK-3uNrY6dortfz1uCT0wImLx6P5vdHoPUJeAl0AUPNuc36xYBTUgkkJXMlH5BSMgJZSwR7XP5XYIghzQp7lfE0pCAnqKTlhSBFAmVMyXPpdaNfJ2bG5rE-IV83qdp-ij6VZ5RJ2toQUmx-h_Gw-pNv2wkc7lrtmmWIukw2x5MbGvtmkYsf2u53CQfDVX81j7X79aZ-TJ4Mds39xrGfk28fVZvm5XX_5dL58v24d17S0iqLj_cAQpBfWc0F7aXtHey25Y2iBM0SDKKxVbjCg3XaL294qzXqjtOZn5O1h735KN7PPpduF7Pw42ujTnDvQTCmUxrD_QKGeIzXjFX3zD3qd5qn6UCk01UqJEitFD5SbUs6TH7r9VO2b7jqg3X1cXY2ru4-rO8ZVJa-Pi-ftzvcPgr_5VODVAQje-4cxCqEFIP8NiTGYYg</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1790715757</pqid></control><display><type>article</type><title>Semi-Local Scaling Exponent Estimation With Box-Penalty Constraints and Total-Variation Regularization</title><source>IEEE Electronic Library (IEL)</source><creator>Nelson, J. D. B. ; Nafornita, C. ; Isar, A.</creator><creatorcontrib>Nelson, J. D. B. ; Nafornita, C. ; Isar, A.</creatorcontrib><description>We here establish and exploit the result that 2D isotropic self-similar fields beget quasi-decorrelated wavelet coefficients and that the resulting localised log sample second moment statistic is asymptotically normal. This leads to the development of a semi-local scaling exponent estimation framework with optimally modified weights. Furthermore, recent interest in penalty methods for least square problems and generalized Lasso for scaling exponent estimation inspires the simultaneous incorporation of both bounding box constraints and total variation smoothing into an iteratively reweighted least-square estimator framework. Numerical results on fractional Brownian fields with global and piecewise constant, semi-local Hurst parameters illustrate the benefits of the new estimators.</description><identifier>ISSN: 1057-7149</identifier><identifier>EISSN: 1941-0042</identifier><identifier>DOI: 10.1109/TIP.2016.2551365</identifier><identifier>PMID: 27071169</identifier><identifier>CODEN: IIPRE4</identifier><language>eng</language><publisher>United States: IEEE</publisher><subject>Asymptotic properties ; Constants ; Estimation ; Estimators ; Exponents ; Image reconstruction ; Least squares method ; Mathematical models ; Noise reduction ; Robustness ; Self-similarity ; Statistical methods ; Wavelet domain ; Wavelet transforms</subject><ispartof>IEEE transactions on image processing, 2016-07, Vol.25 (7), p.3167-3181</ispartof><rights>Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2016</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c380t-607c3df2715e4ae340d5adc0d853c27a132779774aa6cf918cbb7bda682d96883</citedby><cites>FETCH-LOGICAL-c380t-607c3df2715e4ae340d5adc0d853c27a132779774aa6cf918cbb7bda682d96883</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/7448417$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>314,776,780,792,27901,27902,54733</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/7448417$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc><backlink>$$Uhttps://www.ncbi.nlm.nih.gov/pubmed/27071169$$D View this record in MEDLINE/PubMed$$Hfree_for_read</backlink></links><search><creatorcontrib>Nelson, J. D. B.</creatorcontrib><creatorcontrib>Nafornita, C.</creatorcontrib><creatorcontrib>Isar, A.</creatorcontrib><title>Semi-Local Scaling Exponent Estimation With Box-Penalty Constraints and Total-Variation Regularization</title><title>IEEE transactions on image processing</title><addtitle>TIP</addtitle><addtitle>IEEE Trans Image Process</addtitle><description>We here establish and exploit the result that 2D isotropic self-similar fields beget quasi-decorrelated wavelet coefficients and that the resulting localised log sample second moment statistic is asymptotically normal. This leads to the development of a semi-local scaling exponent estimation framework with optimally modified weights. Furthermore, recent interest in penalty methods for least square problems and generalized Lasso for scaling exponent estimation inspires the simultaneous incorporation of both bounding box constraints and total variation smoothing into an iteratively reweighted least-square estimator framework. Numerical results on fractional Brownian fields with global and piecewise constant, semi-local Hurst parameters illustrate the benefits of the new estimators.</description><subject>Asymptotic properties</subject><subject>Constants</subject><subject>Estimation</subject><subject>Estimators</subject><subject>Exponents</subject><subject>Image reconstruction</subject><subject>Least squares method</subject><subject>Mathematical models</subject><subject>Noise reduction</subject><subject>Robustness</subject><subject>Self-similarity</subject><subject>Statistical methods</subject><subject>Wavelet domain</subject><subject>Wavelet transforms</subject><issn>1057-7149</issn><issn>1941-0042</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNqNkc1vEzEQxS0EoqVwR0JCK3HhssHjr7GPEAWoFImKBjiuHK-3uNrY6dortfz1uCT0wImLx6P5vdHoPUJeAl0AUPNuc36xYBTUgkkJXMlH5BSMgJZSwR7XP5XYIghzQp7lfE0pCAnqKTlhSBFAmVMyXPpdaNfJ2bG5rE-IV83qdp-ij6VZ5RJ2toQUmx-h_Gw-pNv2wkc7lrtmmWIukw2x5MbGvtmkYsf2u53CQfDVX81j7X79aZ-TJ4Mds39xrGfk28fVZvm5XX_5dL58v24d17S0iqLj_cAQpBfWc0F7aXtHey25Y2iBM0SDKKxVbjCg3XaL294qzXqjtOZn5O1h735KN7PPpduF7Pw42ujTnDvQTCmUxrD_QKGeIzXjFX3zD3qd5qn6UCk01UqJEitFD5SbUs6TH7r9VO2b7jqg3X1cXY2ru4-rO8ZVJa-Pi-ftzvcPgr_5VODVAQje-4cxCqEFIP8NiTGYYg</recordid><startdate>20160701</startdate><enddate>20160701</enddate><creator>Nelson, J. D. B.</creator><creator>Nafornita, C.</creator><creator>Isar, A.</creator><general>IEEE</general><general>The Institute of Electrical and Electronics Engineers, Inc. (IEEE)</general><scope>97E</scope><scope>RIA</scope><scope>RIE</scope><scope>NPM</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7SP</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>F28</scope><scope>FR3</scope><scope>7X8</scope></search><sort><creationdate>20160701</creationdate><title>Semi-Local Scaling Exponent Estimation With Box-Penalty Constraints and Total-Variation Regularization</title><author>Nelson, J. D. B. ; Nafornita, C. ; Isar, A.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c380t-607c3df2715e4ae340d5adc0d853c27a132779774aa6cf918cbb7bda682d96883</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><topic>Asymptotic properties</topic><topic>Constants</topic><topic>Estimation</topic><topic>Estimators</topic><topic>Exponents</topic><topic>Image reconstruction</topic><topic>Least squares method</topic><topic>Mathematical models</topic><topic>Noise reduction</topic><topic>Robustness</topic><topic>Self-similarity</topic><topic>Statistical methods</topic><topic>Wavelet domain</topic><topic>Wavelet transforms</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Nelson, J. D. B.</creatorcontrib><creatorcontrib>Nafornita, C.</creatorcontrib><creatorcontrib>Isar, A.</creatorcontrib><collection>IEEE All-Society Periodicals Package (ASPP) 2005-present</collection><collection>IEEE All-Society Periodicals Package (ASPP) 1998-Present</collection><collection>IEEE Electronic Library (IEL)</collection><collection>PubMed</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Electronics & Communications Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</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>ANTE: Abstracts in New Technology & Engineering</collection><collection>Engineering Research Database</collection><collection>MEDLINE - Academic</collection><jtitle>IEEE transactions on image processing</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Nelson, J. D. B.</au><au>Nafornita, C.</au><au>Isar, A.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Semi-Local Scaling Exponent Estimation With Box-Penalty Constraints and Total-Variation Regularization</atitle><jtitle>IEEE transactions on image processing</jtitle><stitle>TIP</stitle><addtitle>IEEE Trans Image Process</addtitle><date>2016-07-01</date><risdate>2016</risdate><volume>25</volume><issue>7</issue><spage>3167</spage><epage>3181</epage><pages>3167-3181</pages><issn>1057-7149</issn><eissn>1941-0042</eissn><coden>IIPRE4</coden><abstract>We here establish and exploit the result that 2D isotropic self-similar fields beget quasi-decorrelated wavelet coefficients and that the resulting localised log sample second moment statistic is asymptotically normal. This leads to the development of a semi-local scaling exponent estimation framework with optimally modified weights. Furthermore, recent interest in penalty methods for least square problems and generalized Lasso for scaling exponent estimation inspires the simultaneous incorporation of both bounding box constraints and total variation smoothing into an iteratively reweighted least-square estimator framework. Numerical results on fractional Brownian fields with global and piecewise constant, semi-local Hurst parameters illustrate the benefits of the new estimators.</abstract><cop>United States</cop><pub>IEEE</pub><pmid>27071169</pmid><doi>10.1109/TIP.2016.2551365</doi><tpages>15</tpages></addata></record> |
| fulltext | fulltext_linktorsrc |
| identifier | ISSN: 1057-7149 |
| ispartof | IEEE transactions on image processing, 2016-07, Vol.25 (7), p.3167-3181 |
| issn | 1057-7149 1941-0042 |
| language | eng |
| recordid | cdi_crossref_primary_10_1109_TIP_2016_2551365 |
| source | IEEE Electronic Library (IEL) |
| subjects | Asymptotic properties Constants Estimation Estimators Exponents Image reconstruction Least squares method Mathematical models Noise reduction Robustness Self-similarity Statistical methods Wavelet domain Wavelet transforms |
| title | Semi-Local Scaling Exponent Estimation With Box-Penalty Constraints and Total-Variation Regularization |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-05T10%3A36%3A20IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_RIE&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Semi-Local%20Scaling%20Exponent%20Estimation%20With%20Box-Penalty%20Constraints%20and%20Total-Variation%20Regularization&rft.jtitle=IEEE%20transactions%20on%20image%20processing&rft.au=Nelson,%20J.%20D.%20B.&rft.date=2016-07-01&rft.volume=25&rft.issue=7&rft.spage=3167&rft.epage=3181&rft.pages=3167-3181&rft.issn=1057-7149&rft.eissn=1941-0042&rft.coden=IIPRE4&rft_id=info:doi/10.1109/TIP.2016.2551365&rft_dat=%3Cproquest_RIE%3E1826675992%3C/proquest_RIE%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=1790715757&rft_id=info:pmid/27071169&rft_ieee_id=7448417&rfr_iscdi=true |