Compactly Supported Multivariate Wavelet Frames Obtained by Convolution

Compactly Supported Multivariate, Pairs of Dual Wavelet Frames Obtained by Convolution

In this paper, we present a construction of compactly supported multivariate pairs of dual wavelet frames. The approach is based on the convolution of two refinable distributions. We obtain smooth wavelets with any preassigned number of vanishing moments. Their underlying refinable function is fundamental. In the examples, we obtain symmetric wavelets with small support from optimal refinable f...

Construction of Compactly Supported Nonseparable Orthogonal Wavelets of L^2(R^n)

Wavelet Bi-frames with few Generators from Multivariate Refinable Functions

Using results on syzygy modules over a multivariate polynomial ring, we are able to construct compactly supported wavelet bi-frames with few generators from almost any pair of compactly supported multivariate refinable functions. In our examples, we focus on wavelet bi-frames whose primal and dual wavelets are both derived from one box spline function. Our wavelet bi-frames have fewer generator...

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...

Dual Multiwavelet Frames with High Balancing Order and Compact Fast Frame Transform

An interesting method called Oblique Extension Principle (OEP) has been proposed in the literature for constructing compactly supported MRA tight and dual wavelet frames with high vanishing moments and high frame approximation orders. Many compactly supported MRA wavelet frames have been recently constructed from scalar refinable functions via OEP. Despite the great flexibility and popularity o...