國立虎尾科技大學 |

Multivariate wavelet frames

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Multivariate wavelet frames/ by Maria Skopina, Aleksandr Krivoshein, Vladimir Protasov.
Author:	Skopina, Maria.
other author:	Krivoshein, Aleksandr.
Published:	Singapore :Springer Singapore : : 2016.,
Description:	xiii, 248 p. :ill., digital ; : 24 cm.;
Contained By:	Springer eBooks
Subject:	Multivariate analysis. -
Online resource:	http://dx.doi.org/10.1007/978-981-10-3205-9
ISBN:	9789811032059

Multivariate wavelet frames
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:

577402
Multivariate analysis.

LC Class. No.: QA403.3

Dewey Class. No.: 515.2433

Multivariate wavelet frames
LDR:03213nam a2200325 a 4500 001 869379
003 DE-He213
005 20170202155957.0
006 m d
007 cr nn 008maaau
008 170828s2016 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 1117543
245 1 0 $a Multivariate wavelet frames $h [electronic resource] / $c by Maria Skopina, Aleksandr Krivoshein, Vladimir Protasov.
260 $a Singapore : $c 2016. $b Springer Singapore : $b Imprint: Springer,
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 577402
650 0 $a Wavelets (Mathematics) $3 528163
650 1 4 $a Mathematics. $3 527692
650 2 4 $a Fourier Analysis. $3 672627
650 2 4 $a Functional Analysis. $3 672166
650 2 4 $a Applications of Mathematics. $3 669175
650 2 4 $a Signal, Image and Speech Processing. $3 670837
700 1 $a Krivoshein, Aleksandr. $3 1117544
700 1 $a Protasov, Vladimir. $3 1117545
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer eBooks
830 0 $a Industrial and applied mathematics. $3 1070535
856 4 0 $u http://dx.doi.org/10.1007/978-981-10-3205-9
950 $a Mathematics and Statistics (Springer-11649)