Multivariate Wavelet Frames. 1st ed. 2016

種類:

電子ブック

責任表示:

by Maria Skopina, Aleksandr Krivoshein, Vladimir Protasov

出版情報:

Singapore : Springer Nature Singapore : Imprint: Springer, 2016

著者名:

• Skopina, Maria.
• Krivoshein, Aleksandr.
• Protasov, Vladimir.
• SpringerLink (Online service)

シリーズ名:

Industrial and Applied Mathematics ;

ISBN:

9789811032059 [981103205X]    

注記:

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

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