2026-09-19T06:30:50Zhttps://dspace.mit.edu/server/oai/request

oai:dspace.mit.edu:1721.1/379372022-01-13T07:54:29Zcom_1721.1_7582com_1721.1_7581col_1721.1_131023

Vivek K. Goyal. Ba, Demba Elimane Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science. Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science 2007-07-18T13:12:58Z 2007-07-18T13:12:58Z 2006 2006 http://hdl.handle.net/1721.1/37937 143847707 Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006. Includes bibliographical references (p. 51-52). In conventional transform coding, the importance of preserving desirable quantization partition cell shapes prevents one from considering the use of a nonlinear change of variables. If no linear transformation of a given source would yield independent components, this means having to encode it at a rate higher than its entropy, i.e. suboptimally. This thesis proposes a new transform coding technique where the source samples are first uniformly scalar quantized and then transformed with an integer-to-integer approximation to a nonlinear transformation that would give independent components. In particular, we design a family of integer-to-integer approximations to the Cartesian-to-polar transformation and analyze its behavior for high rate transform coding. Among the benefits of such an approach is the ability to achieve redundancy reduction beyond decorrelation without limitation to orthogonal linear transformations of the original variables. A high resolution analysis is given, and for source models inspired by a sensor network application and by image compression, simulations show improvements over conventional transform coding. A comparison to state-of-the-art entropy-coded polar quantization techniques is also provided. by Demba Elimane Ba. S.M. 52 p. eng Massachusetts Institute of Technology M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582 Electrical Engineering and Computer Science. Nonlinear transform coding with lossless polar coordinates Thesis application/pdf false Publication unknown unknown <Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="3fb3ef67-1891-4fd8-9a85-f72524d0d488"> <Type xmlns="https://www.openaire.eu/cerif-profile/vocab/COAR_Publication_Types">http://purl.org/coar/resource_type/c_1843</Type> <Language>eng</Language> <Title>Nonlinear transform coding with lossless polar coordinates</Title> <PublishedIn> <Publication> </Publication> </PublishedIn> <PublicationDate>2006</PublicationDate> <Authors> <Author> <DisplayName>Ba, Demba Elimane</DisplayName> <Affiliation> <OrgUnit> </OrgUnit> </Affiliation> </Author> </Authors> <Editors> </Editors> <Publishers> <Publisher> <DisplayName>Massachusetts Institute of Technology</DisplayName> <OrgUnit /> </Publisher> </Publishers> <License>http://dspace.mit.edu/handle/1721.1/7582</License> <Keyword>Electrical Engineering and Computer Science.</Keyword> <Abstract>In conventional transform coding, the importance of preserving desirable quantization partition cell shapes prevents one from considering the use of a nonlinear change of variables. If no linear transformation of a given source would yield independent components, this means having to encode it at a rate higher than its entropy, i.e. suboptimally. This thesis proposes a new transform coding technique where the source samples are first uniformly scalar quantized and then transformed with an integer-to-integer approximation to a nonlinear transformation that would give independent components. In particular, we design a family of integer-to-integer approximations to the Cartesian-to-polar transformation and analyze its behavior for high rate transform coding. Among the benefits of such an approach is the ability to achieve redundancy reduction beyond decorrelation without limitation to orthogonal linear transformations of the original variables. A high resolution analysis is given, and for source models inspired by a sensor network application and by image compression, simulations show improvements over conventional transform coding. A comparison to state-of-the-art entropy-coded polar quantization techniques is also provided.</Abstract> <Access xmlns="http://purl.org/coar/access_right" > </Access> </Publication>