大葉大學圖書館 |

Multivariate wavelet frames[electronic resource] /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
杜威分類號:	515.2433
書名/作者:	Multivariate wavelet frames/ by Maria Skopina, Aleksandr Krivoshein, Vladimir Protasov.
作者:	Skopina, Maria.
其他作者:	Krivoshein, Aleksandr.
出版者:	Singapore : : Springer Singapore :, 2016.
面頁冊數:	xiii, 248 p. : : ill., digital ;; 24 cm.
Contained By:	Springer eBooks
標題:	Multivariate analysis.
標題:	Wavelets (Mathematics)
標題:	Mathematics.
標題:	Fourier Analysis.
標題:	Functional Analysis.
標題:	Applications of Mathematics.
標題:	Signal, Image and Speech Processing.
ISBN:	9789811032059
ISBN:	9789811032042
內容註:	Chapter 1. Bases and Frames in Hilbert Spaces -- Chapter 2. MRA-based Wavelet Bases and Frames -- Chapter 3. Construction of Wavelet Frames -- Chapter 4. Frame-like Wavelet Expansions -- Chapter 5. Symmetric Wavelets -- Chapter 6. Smoothness of Wavelets -- Chapter 7. Special Questions.
摘要、提要註:	This book presents a systematic study of multivariate wavelet frames with matrix dilation, in particular, orthogonal and bi-orthogonal bases, which are a special case of frames. Further, it provides algorithmic methods for the construction of dual and tight wavelet frames with a desirable approximation order, namely compactly supported wavelet frames, which are commonly required by engineers. It particularly focuses on methods of constructing them. Wavelet bases and frames are actively used in numerous applications such as audio and graphic signal processing, compression and transmission of information. They are especially useful in image recovery from incomplete observed data due to the redundancy of frame systems. The construction of multivariate wavelet frames, especially bases, with desirable properties remains a challenging problem as although a general scheme of construction is well known, its practical implementation in the multidimensional setting is difficult. Another important feature of wavelet is symmetry. Different kinds of wavelet symmetry are required in various applications, since they preserve linear phase properties and also allow symmetric boundary conditions in wavelet algorithms, which normally deliver better performance. The authors discuss how to provide H-symmetry, where H is an arbitrary symmetry group, for wavelet bases and frames. The book also studies so-called frame-like wavelet systems, which preserve many important properties of frames and can often be used in their place, as well as their approximation properties. The matrix method of computing the regularity of refinable function from the univariate case is extended to multivariate refinement equations with arbitrary dilation matrices. This makes it possible to find the exact values of the Holder exponent of refinable functions and to make a very refine analysis of their moduli of continuity.
電子資源:	http://dx.doi.org/10.1007/978-981-10-3205-9

Multivariate wavelet frames[electronic resource] /
Skopina, Maria.

Multivariate wavelet frames[electronic resource] /by Maria Skopina, Aleksandr Krivoshein, Vladimir Protasov. - Singapore :Springer Singapore :2016. - xiii, 248 p. :ill., digital ;24 cm. - Industrial and applied mathematics,2364-6837. - Industrial and applied mathematics..

Chapter 1. Bases and Frames in Hilbert Spaces -- Chapter 2. MRA-based Wavelet Bases and Frames -- Chapter 3. Construction of Wavelet Frames -- Chapter 4. Frame-like Wavelet Expansions -- Chapter 5. Symmetric Wavelets -- Chapter 6. Smoothness of Wavelets -- Chapter 7. Special Questions.

This book presents a systematic study of multivariate wavelet frames with matrix dilation, in particular, orthogonal and bi-orthogonal bases, which are a special case of frames. Further, it provides algorithmic methods for the construction of dual and tight wavelet frames with a desirable approximation order, namely compactly supported wavelet frames, which are commonly required by engineers. It particularly focuses on methods of constructing them. Wavelet bases and frames are actively used in numerous applications such as audio and graphic signal processing, compression and transmission of information. They are especially useful in image recovery from incomplete observed data due to the redundancy of frame systems. The construction of multivariate wavelet frames, especially bases, with desirable properties remains a challenging problem as although a general scheme of construction is well known, its practical implementation in the multidimensional setting is difficult. Another important feature of wavelet is symmetry. Different kinds of wavelet symmetry are required in various applications, since they preserve linear phase properties and also allow symmetric boundary conditions in wavelet algorithms, which normally deliver better performance. The authors discuss how to provide H-symmetry, where H is an arbitrary symmetry group, for wavelet bases and frames. The book also studies so-called frame-like wavelet systems, which preserve many important properties of frames and can often be used in their place, as well as their approximation properties. The matrix method of computing the regularity of refinable function from the univariate case is extended to multivariate refinement equations with arbitrary dilation matrices. This makes it possible to find the exact values of the Holder exponent of refinable functions and to make a very refine analysis of their moduli of continuity.

ISBN: 9789811032059

Standard No.: 10.1007/978-981-10-3205-9doiSubjects--Topical Terms:

182818
Multivariate analysis.

LC Class. No.: QA403.3

Dewey Class. No.: 515.2433

Multivariate wavelet frames[electronic resource] /
LDR:03213nam a2200325 a 4500 001 477367
003 DE-He213
005 20170202155957.0
006 m d
007 cr nn 008maaau
008 181208s2016 si s 0 eng d
020 $a 9789811032059 $q (electronic bk.)
020 $a 9789811032042 $q (paper)
024 7 $a 10.1007/978-981-10-3205-9 $2 doi
035 $a 978-981-10-3205-9
040 $a GP $c GP
041 0 $a eng
050 4 $a QA403.3
072 7 $a PBKF $2 bicssc
072 7 $a MAT034000 $2 bisacsh
082 0 4 $a 515.2433 $2 23
090 $a QA403.3 $b .S628 2016
100 1 $a Skopina, Maria. $3 688881
245 1 0 $a Multivariate wavelet frames $h [electronic resource] / $c by Maria Skopina, Aleksandr Krivoshein, Vladimir Protasov.
260 $a Singapore : $b Springer Singapore : $b Imprint: Springer, $c 2016.
300 $a xiii, 248 p. : $b ill., digital ; $c 24 cm.
490 1 $a Industrial and applied mathematics, $x 2364-6837
505 0 $a Chapter 1. Bases and Frames in Hilbert Spaces -- Chapter 2. MRA-based Wavelet Bases and Frames -- Chapter 3. Construction of Wavelet Frames -- Chapter 4. Frame-like Wavelet Expansions -- Chapter 5. Symmetric Wavelets -- Chapter 6. Smoothness of Wavelets -- Chapter 7. Special Questions.
520 $a This book presents a systematic study of multivariate wavelet frames with matrix dilation, in particular, orthogonal and bi-orthogonal bases, which are a special case of frames. Further, it provides algorithmic methods for the construction of dual and tight wavelet frames with a desirable approximation order, namely compactly supported wavelet frames, which are commonly required by engineers. It particularly focuses on methods of constructing them. Wavelet bases and frames are actively used in numerous applications such as audio and graphic signal processing, compression and transmission of information. They are especially useful in image recovery from incomplete observed data due to the redundancy of frame systems. The construction of multivariate wavelet frames, especially bases, with desirable properties remains a challenging problem as although a general scheme of construction is well known, its practical implementation in the multidimensional setting is difficult. Another important feature of wavelet is symmetry. Different kinds of wavelet symmetry are required in various applications, since they preserve linear phase properties and also allow symmetric boundary conditions in wavelet algorithms, which normally deliver better performance. The authors discuss how to provide H-symmetry, where H is an arbitrary symmetry group, for wavelet bases and frames. The book also studies so-called frame-like wavelet systems, which preserve many important properties of frames and can often be used in their place, as well as their approximation properties. The matrix method of computing the regularity of refinable function from the univariate case is extended to multivariate refinement equations with arbitrary dilation matrices. This makes it possible to find the exact values of the Holder exponent of refinable functions and to make a very refine analysis of their moduli of continuity.
650 0 $a Multivariate analysis. $3 182818
650 0 $a Wavelets (Mathematics) $3 393849
650 1 4 $a Mathematics. $3 172349
650 2 4 $a Fourier Analysis. $3 463928
650 2 4 $a Functional Analysis. $3 464114
650 2 4 $a Applications of Mathematics. $3 463820
650 2 4 $a Signal, Image and Speech Processing. $3 463860
700 1 $a Krivoshein, Aleksandr. $3 688882
700 1 $a Protasov, Vladimir. $3 688883
710 2 $a SpringerLink (Online service) $3 463450
773 0 $t Springer eBooks
830 0 $a Industrial and applied mathematics. $3 636423
856 4 0 $u http://dx.doi.org/10.1007/978-981-10-3205-9
950 $a Mathematics and Statistics (Springer-11649)