Construction of multivariate compactly supported tight wavelet frames

Construction of Multivariate Compactly Supported Tight Wavelet Frames

Two simple constructive methods are presented to compute compactly supported tight wavelet frames for any given refinable function whose mask satisfies the QMF or sub-QMF conditions in the multivariate setting. We use one of our constructive methods in order to find tight wavelet frames associated with multivariate box splines, e.g., bivariate box splines on a three or four directional mesh. Mo...

Construction of compactly Supported Conjugate Symmetric Complex Tight Wavelet Frames

Two algorithms for constructing a class of compactly supported complex tight wavelet frames with conjugate symmetry are provided. Firstly, based on a given complex refinable function φ, an explicit formula for constructing complex tight wavelet frames is presented. If the given complex refinable function φ is compactly supported conjugate symmetric, then we prove that there exists a compactly s...

Construction of Compactly Supported Tight Wavelets Frames

Tight compactly supported wavelet frames of arbitrarily high smoothness

Based on the method for constructing tight wavelet frames of [RS2], we show that one can construct, for any dilation matrix, and in any spatial dimension, tight wavelet frames generated by compactly supported functions with arbitrarily high smoothness. AMS (MOS) Subject Classifications: Primary 42C15, Secondary 42C30

Some Smooth Compactly Supported Tight Wavelet Frames with Vanishing Moments

Let A ∈ Rd×d, d ≥ 1 be a dilation matrix with integer entries and | detA| = 2. We construct several families of compactly supported Parseval framelets associated to A having any desired number of vanishing moments. The first family has a single generator and its construction is based on refinable functions associated to Daubechies low pass filters and a theorem of Bownik. For the construction o...