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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| Дата: | 2006 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2006
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/146176 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Combined Reduced-Rank Transform / A. Torokhti, P. Howlett // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 47 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-146176 |
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dspace |
| spelling |
irk-123456789-1461762019-02-08T01:24:19Z Combined Reduced-Rank Transform Torokhti, A. Howlett, P. 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. 2006 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/146176 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Torokhti, A. Howlett, P. |
| spellingShingle |
Torokhti, A. Howlett, P. Combined Reduced-Rank Transform Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Torokhti, A. Howlett, P. |
| author_sort |
Torokhti, A. |
| title |
Combined Reduced-Rank Transform |
| title_short |
Combined Reduced-Rank Transform |
| title_full |
Combined Reduced-Rank Transform |
| title_fullStr |
Combined Reduced-Rank Transform |
| title_full_unstemmed |
Combined Reduced-Rank Transform |
| title_sort |
combined reduced-rank transform |
| publisher |
Інститут математики НАН України |
| publishDate |
2006 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/146176 |
| citation_txt |
Combined Reduced-Rank Transform / A. Torokhti, P. Howlett // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 47 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT torokhtia combinedreducedranktransform AT howlettp combinedreducedranktransform |
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2023-05-20T17:24:02Z |
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2023-05-20T17:24:02Z |
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1796153208060510208 |