Compactly Supported Tight and Sibling Frames Based on Generalized Bernstein Polynomials

Compactly 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...

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

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...