For a given symmetric refinable mask obeying the sum rule of order n, an explicit method is suggested for the construction of mutually symmetric almost frame-like wavelet system providing approximation order n. A transformation based on the lifting scheme is described that allows to improve almost frame-like wavelets up to dual wavelet frames and preserve other properties. A direct method for the construction of dual wavelet frames providing approximation order n and mutual symmetry properties is also discussed. For an abelian symmetry group a technique providing the -symmetry property for each wavelet function is given for the above three methods.
|Translated title of the contribution||От фреймоподобных систем к фреймам всплесков с сохранением аппроксимационных свойств и симметрии|
|Journal||Applied Mathematics and Computation|
|Early online date||31 Oct 2018|
|Publication status||Published - 1 Mar 2019|
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