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Nonhomogeneous wavelet systems in high dimensions

2019-08-23 15:01

Oct 20, 2011 We shall see that nonhomogeneous wavelet systems naturally link many aspects of wavelet analysis together. There are two fundamental issues of the basic theory of wavelets and framelets: frequencybased nonhomogeneous dual framelets in the distribution space and stability of nonhomogeneous wavelet systems in a general function space.Read the latest articles of Applied and Computational Harmonic Analysis at ScienceDirect. com, Elseviers leading platform of peerreviewed scholarly literature select article Nonhomogeneous wavelet systems in high dimensions. Research article Open archive Nonhomogeneous wavelet systems in high dimensions. Bin Han. Pages Download PDF. nonhomogeneous wavelet systems in high dimensions

Moreover, such nonhomogeneous tight wavelet frames are associated with filter banks and can be modified to achieve directionality in high dimensions. Our analysis of nonhomogeneous wavelet systems employs a notion of frequencybased nonhomogeneous wavelet systems in

Bin Han, Nonhomogeneous wavelet systems in high dimensions, Applied and Computational Harmonic Analysis, Vol. 32 (2012), Issue 2, . Bin Han, Gitta Kutyniok, and Zuowei Shen, Adaptive multiresolution analysis structures and shearlet systems, SIAM Journal on Numerical Analysis, Vol. 49 (2011), . open archive. Continuing the lines developed in Han (2010) [20, in this paper we study nonhomogeneous wavelet systems in high dimensions. It is of interest to study a wavelet system with a minimum number of generators. It has been shown in Dai et al. nonhomogeneous wavelet systems in high dimensions Homogeneous wavelets and framelets have been extensively investigated in the classical theory of wavelets and they are often constructed from refinable functions via the multiresolution analysis. On the other hand, nonhomogeneous wavelets and framelets enjoy many desirable theoretical properties and are often intrinsically linked to the refinable structure and multiresolution analysis.

Moreover, such nonhomogeneous tight wavelet frames are associated with filter banks and can be modified to achieve directionality in high dimensions. Our analysis of nonhomogeneous wavelet systems employs a notion of frequencybased nonhomogeneous wavelet systems in nonhomogeneous wavelet systems in high dimensions In this paper, we shall discuss recent developments in the basic theory of wavelets and framelets within the framework of nonhomogeneous wavelet systems in a natural and simple way. Nonhomogeneous Wavelet Systems in High Dimensions. Affine systems of the type (1. 6) for wavelet frames in R d have been studied in [31, 32 and later extended to affine shear systems in [34, 58, 59. Many authors have studied the construction of wavelets or wavelet frames (2012) Nonhomogeneous wavelet systems in high dimensions. Applied and Computational Harmonic Analysis 32: 2, .

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