Analysis of low bit rate image transform coding

Calculations based on high-resolution quantizations prove that the distortion rate D(R) of an image transform coding is proportional to 2/sup -2R/ when R is large enough. In wavelet and block cosine bases, we show that if R

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Veröffentlicht in:	IEEE transactions on signal processing 1998-04, Vol.46 (4), p.1027-1042
Hauptverfasser:	Mallat, S., Falzon, F.
Format:	Artikel
Sprache:	eng
Schlagworte:	Bit rate Entropy Image analysis Image coding Pixel Quantization Rate distortion theory Transform coding Wavelet analysis Wavelet transforms
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container_title	IEEE transactions on signal processing
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creator	Mallat, S. Falzon, F.
description	Calculations based on high-resolution quantizations prove that the distortion rate D(R) of an image transform coding is proportional to 2/sup -2R/ when R is large enough. In wavelet and block cosine bases, we show that if R
doi_str_mv	10.1109/78.668554
format	Article
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In wavelet and block cosine bases, we show that if R<1 bit/pixel, then D(R) varies like R/sup 1-2/spl gamma//, where /spl gamma/ remains of the order of 1 for most natural images. The improved performance of embedded codings in wavelet bases is analyzed. At low bit rates, we show that the compression performance of an orthonormal basis depends mostly on its ability to approximate images with a few nonzero vectors.</description><identifier>ISSN: 1053-587X</identifier><identifier>EISSN: 1941-0476</identifier><identifier>DOI: 10.1109/78.668554</identifier><identifier>CODEN: ITPRED</identifier><language>eng</language><publisher>IEEE</publisher><subject>Bit rate ; Entropy ; Image analysis ; Image coding ; Pixel ; Quantization ; Rate distortion theory ; Transform coding ; Wavelet analysis ; Wavelet transforms</subject><ispartof>IEEE transactions on signal processing, 1998-04, Vol.46 (4), p.1027-1042</ispartof><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c277t-84ddd1b99dc4ed7ca5c78188999f0f168bfe202776d769825d6c1edc11f4a6333</citedby><cites>FETCH-LOGICAL-c277t-84ddd1b99dc4ed7ca5c78188999f0f168bfe202776d769825d6c1edc11f4a6333</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/668554$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>314,776,780,792,27901,27902,54733</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/668554$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc></links><search><creatorcontrib>Mallat, S.</creatorcontrib><creatorcontrib>Falzon, F.</creatorcontrib><title>Analysis of low bit rate image transform coding</title><title>IEEE transactions on signal processing</title><addtitle>TSP</addtitle><description>Calculations based on high-resolution quantizations prove that the distortion rate D(R) of an image transform coding is proportional to 2/sup -2R/ when R is large enough. In wavelet and block cosine bases, we show that if R<1 bit/pixel, then D(R) varies like R/sup 1-2/spl gamma//, where /spl gamma/ remains of the order of 1 for most natural images. The improved performance of embedded codings in wavelet bases is analyzed. At low bit rates, we show that the compression performance of an orthonormal basis depends mostly on its ability to approximate images with a few nonzero vectors.</description><subject>Bit rate</subject><subject>Entropy</subject><subject>Image analysis</subject><subject>Image coding</subject><subject>Pixel</subject><subject>Quantization</subject><subject>Rate distortion theory</subject><subject>Transform coding</subject><subject>Wavelet analysis</subject><subject>Wavelet transforms</subject><issn>1053-587X</issn><issn>1941-0476</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1998</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNo90E1LAzEQBuAgCtbqwaunnAQP22Z2s_k4luIXFLwoeAvZZFJWtpuabJH-e1e2eJqBeXgZXkJugS0AmF5KtRBC1TU_IzPQHArGpTgfd1ZXRa3k5yW5yvmLMeBcixlZrnrbHXObaQy0iz-0aQea7IC03dkt0iHZPoeYdtRF3_bba3IRbJfx5jTn5OPp8X39Umzenl_Xq03hSimHQnHvPTRae8fRS2drJxUopbUOLIBQTcCSjVR4KbQqay8coHcAgVtRVdWc3E-5-xS_D5gHs2uzw66zPcZDNqXioIGxET5M0KWYc8Jg9ml8PR0NMPNXiZHKTJWM9m6yLSL-u9PxF4KQWqs</recordid><startdate>19980401</startdate><enddate>19980401</enddate><creator>Mallat, S.</creator><creator>Falzon, F.</creator><general>IEEE</general><scope>RIA</scope><scope>RIE</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>19980401</creationdate><title>Analysis of low bit rate image transform coding</title><author>Mallat, S. ; Falzon, F.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c277t-84ddd1b99dc4ed7ca5c78188999f0f168bfe202776d769825d6c1edc11f4a6333</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1998</creationdate><topic>Bit rate</topic><topic>Entropy</topic><topic>Image analysis</topic><topic>Image coding</topic><topic>Pixel</topic><topic>Quantization</topic><topic>Rate distortion theory</topic><topic>Transform coding</topic><topic>Wavelet analysis</topic><topic>Wavelet transforms</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Mallat, S.</creatorcontrib><creatorcontrib>Falzon, F.</creatorcontrib><collection>IEEE All-Society Periodicals Package (ASPP) 1998-Present</collection><collection>IEEE Electronic Library (IEL)</collection><collection>CrossRef</collection><collection>Computer and Information Systems 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><jtitle>IEEE transactions on signal processing</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Mallat, S.</au><au>Falzon, F.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Analysis of low bit rate image transform coding</atitle><jtitle>IEEE transactions on signal processing</jtitle><stitle>TSP</stitle><date>1998-04-01</date><risdate>1998</risdate><volume>46</volume><issue>4</issue><spage>1027</spage><epage>1042</epage><pages>1027-1042</pages><issn>1053-587X</issn><eissn>1941-0476</eissn><coden>ITPRED</coden><abstract>Calculations based on high-resolution quantizations prove that the distortion rate D(R) of an image transform coding is proportional to 2/sup -2R/ when R is large enough. In wavelet and block cosine bases, we show that if R<1 bit/pixel, then D(R) varies like R/sup 1-2/spl gamma//, where /spl gamma/ remains of the order of 1 for most natural images. The improved performance of embedded codings in wavelet bases is analyzed. At low bit rates, we show that the compression performance of an orthonormal basis depends mostly on its ability to approximate images with a few nonzero vectors.</abstract><pub>IEEE</pub><doi>10.1109/78.668554</doi><tpages>16</tpages></addata></record>
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subjects	Bit rate Entropy Image analysis Image coding Pixel Quantization Rate distortion theory Transform coding Wavelet analysis Wavelet transforms
title	Analysis of low bit rate image transform coding
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