Tight Wavelet Frames Generated by Three Symmetric B-spline Functions with High Vanishing Moments
نویسندگان
چکیده
In this note, we show that one can derive from any B-spline function of order m (m ∈ N) an MRA tight wavelet frame in L2(R) that is generated by the dyadic dilates and integer shifts of three compactly supported real-valued symmetric wavelet functions with vanishing moments of the highest possible order m.
منابع مشابه
Framelets with Many Vanishing Moments
We study tight wavelet frames associated with given refinable functions which are obtained with the unitary extension principles. All possible polynomial symbols generating refinable functions and admitting framelets with a given number of vanishing moments are found. We also consider constructions of (anti)symmetric framelets generated by a symmetric refinable function. We give a few examples ...
متن کاملTight and sibling frames originated from discrete splines
We present a new family of frames, which are generated by perfect reconstruction filter banks. The filter banks are based on the discrete interpolatory splines and are related to Butterworth filters. Each filter bank comprises one interpolatory symmetric low-pass filter, one band-pass and one high-pass filters. In the sibling frames case, all the filters are linear phase and generate symmetric ...
متن کاملPairs of Dual Wavelet Frames from Any Two Refinable Functions
Starting from any two compactly supported refinable functions in L2(R) with dilation factor d, we show that it is always possible to construct 2d wavelet functions with compact support such that they generate a pair of dual d-wavelet frames in L2(R). Moreover, the number of vanishing moments of each of these wavelet frames is equal to the approximation order of the dual MRA; this is the highest...
متن کاملSymmetric Mra Tight Wavelet Frames with Three Generators and High Vanishing Moments
Let φ be a compactly supported symmetric real-valued refinable function in L2(R) with a finitely supported symmetric real-valued mask on Z. Under the assumption that the shifts of φ are stable, in this paper we prove that one can always construct three wavelet functions ψ, ψ and ψ such that (i) All the wavelet functions ψ, ψ and ψ are compactly supported, real-valued and finite linear combinati...
متن کاملCompactly supported tight and sibling frames with maximum vanishing moments
The notion of vanishing-moment recovery (VMR) functions is introduced in this paper for the construction of compactly supported tight frames with two generators having the maximum order of vanishing moments as determined by the given refinable function, such as the mth order cardinal B-spline Nm. Tight frames are also extended to “sibling frames” to allow additional properties, such as symmetry...
متن کامل