Combined Reduced-Rank Transform
We propose and justify a new approach to constructing optimal nonlinear transforms of random vectors. We show that the proposed transform improves such characteristics of rank-reduced transforms as compression ratio, accuracy of decompression and reduces required computational work. The proposed tra...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Datum: | 2006 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2006
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/146176 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Combined Reduced-Rank Transform / A. Torokhti, P. Howlett // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 47 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862546434345140224 |
|---|---|
| author | Torokhti, A. Howlett, P. |
| author_facet | Torokhti, A. Howlett, P. |
| citation_txt | Combined Reduced-Rank Transform / A. Torokhti, P. Howlett // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 47 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We propose and justify a new approach to constructing optimal nonlinear transforms of random vectors. We show that the proposed transform improves such characteristics of rank-reduced transforms as compression ratio, accuracy of decompression and reduces required computational work. The proposed transform Tp is presented in the form of a sum with p terms where each term is interpreted as a particular rank-reduced transform. Moreover, terms in Tp are represented as a combination of three operations Fk, Qk and φk with k = 1,...,p. The prime idea is to determine Fk separately, for each k = 1,...,p, from an associated rank-constrained minimization problem similar to that used in the Karhunen-Loève transform. The operations Qk andφk are auxiliary for finding Fk. The contribution of each term in Tp improves the entire transform performance. A corresponding unconstrained nonlinear optimal transform is also considered. Such a transform is important in its own right because it is treated as an optimal filter without signal compression. A rigorous analysis of errors associated with the proposed transforms is given.
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| first_indexed | 2025-11-25T10:17:53Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146176 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-25T10:17:53Z |
| publishDate | 2006 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Torokhti, A. Howlett, P. 2019-02-07T20:20:34Z 2019-02-07T20:20:34Z 2006 Combined Reduced-Rank Transform / A. Torokhti, P. Howlett // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 47 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 41A29 https://nasplib.isofts.kiev.ua/handle/123456789/146176 We propose and justify a new approach to constructing optimal nonlinear transforms of random vectors. We show that the proposed transform improves such characteristics of rank-reduced transforms as compression ratio, accuracy of decompression and reduces required computational work. The proposed transform Tp is presented in the form of a sum with p terms where each term is interpreted as a particular rank-reduced transform. Moreover, terms in Tp are represented as a combination of three operations Fk, Qk and φk with k = 1,...,p. The prime idea is to determine Fk separately, for each k = 1,...,p, from an associated rank-constrained minimization problem similar to that used in the Karhunen-Loève transform. The operations Qk andφk are auxiliary for finding Fk. The contribution of each term in Tp improves the entire transform performance. A corresponding unconstrained nonlinear optimal transform is also considered. Such a transform is important in its own right because it is treated as an optimal filter without signal compression. A rigorous analysis of errors associated with the proposed transforms is given. The first co-author is grateful to Oliver Capp´e for useful discussions related to the structure of the proposed transform. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Combined Reduced-Rank Transform Article published earlier |
| spellingShingle | Combined Reduced-Rank Transform Torokhti, A. Howlett, P. |
| title | Combined Reduced-Rank Transform |
| title_full | Combined Reduced-Rank Transform |
| title_fullStr | Combined Reduced-Rank Transform |
| title_full_unstemmed | Combined Reduced-Rank Transform |
| title_short | Combined Reduced-Rank Transform |
| title_sort | combined reduced-rank transform |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146176 |
| work_keys_str_mv | AT torokhtia combinedreducedranktransform AT howlettp combinedreducedranktransform |