Abstract
For any dilation matrix with integer entries and , we construct a family of smooth compactly supported tight wavelet frames with three generators in . Our construction involves some compactly supported refinable functions, the oblique extension principle, and a slight generalization of a theorem of Lai and Stöckler. Estimates for the degrees of smoothness are given. With the exception of a polynomial whose coefficients must in general be computed by spectral factorization, the framelets are expressed in closed form in the frequency domain, in terms of elementary transcendental functions. By means of two examples we also show that for low degrees of smoothness the use of spectral factorization may be avoided.
Highlights
IntroductionBased on works by Ron and Shen and by Grochenig and Ron, Han [7] constructs compactly supported tight wavelet frames with degree of smoothness and vanishing moments of order as large as desired
Given a 2 × 2 dilation matrix A with integer entries, such that | det A| = 2, we construct smooth compactly supported tight framelets with three generators in L2(R2) associated to such a dilation, and with any desired degree of smoothness
We summarize the results we will use in our construction of tight framelets
Summary
Based on works by Ron and Shen and by Grochenig and Ron, Han [7] constructs compactly supported tight wavelet frames with degree of smoothness and vanishing moments of order as large as desired. Another method for constructing smooth compactly supported tight framelets was described in [8].
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