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Multivariate wavelet frames

Skopina, Maria.

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Multivariate wavelet frames

Record Type:	Electronic resources : 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.
[NT 15003449]:	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.
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:

517467
Multivariate analysis.

LC Class. No.: QA403.3

Dewey Class. No.: 515.2433

Multivariate wavelet frames
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100 1 $a Skopina, Maria. $3 3210124
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 517467
650 0 $a Wavelets (Mathematics) $3 532597
650 1 4 $a Mathematics. $3 515831
650 2 4 $a Fourier Analysis. $3 891095
650 2 4 $a Functional Analysis. $3 893943
650 2 4 $a Applications of Mathematics. $3 890893
650 2 4 $a Signal, Image and Speech Processing. $3 891073
700 1 $a Krivoshein, Aleksandr. $3 3210125
700 1 $a Protasov, Vladimir. $3 3210126
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer eBooks
830 0 $a Industrial and applied mathematics. $3 2165673
856 4 0 $u http://dx.doi.org/10.1007/978-981-10-3205-9
950 $a Mathematics and Statistics (Springer-11649)