Tight frames of compactly supported multivariate multi-wavelets

Construction of Compactly Supported Tight Wavelets 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 multivariate compactly supported orthonormal wavelets

We propose a constructive method to find compactly supported orthonormal wavelets for any given compactly supported scaling function φ in the multivariate setting. For simplicity, we start with a standard dilation matrix 2I2×2 in the bivariate setting and show how to construct compactly supported functions ψ1, · · · , ψn with n > 3 such that {2ψj(2x − `, 2ky − m), k, `,m ∈ Z, j = 1, . . . , n} ...

Compactly Supported Tight Wavelet Frames and Orthonormal Wavelets of Exponential Decay with a General Dilation Matrix

Tight wavelet frames and orthonormal wavelet bases with a general dilation matrix have applications in many areas. In this paper, for any d × d dilation matrix M , we demonstrate in a constructive way that we can construct compactly supported tight M -wavelet frames and orthonormal M -wavelet bases in L2(R) of exponential decay, which are derived from compactly supported M -refinable functions,...

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