We discuss wavelet frames constructed via multiresolution analysis (MRA), with emphasis
on tight wavelet frames. In particular, we establish general principles and specific algorithms …

This collection of lecture notes is based on a series of lectures presented by the authors at
the Institute for Advanced Studies/Park City Mathematics 2010 Summer Program on “The …

The first type of pseudo-splines were introduced in [I. Daubechies, B. Han, A. Ron, Z. Shen,
Framelets: MRA-based constructions of wavelet frames, Appl. Comput. Harmon. Anal. 14 …

One of the major driven forces in the area of applied and computational harmonic analysis
over the last decade or longer is the development of redundant systems that have sparse …

The notion of a frame multiresolution analysis (FMRA) is formulated. An FMRA is a natural
extension to affine frames of the classical notion of a multiresolution analysis (MRA). The …

The objective of this paper is to establish a complete characterization of tight frames, and
particularly of orthonormal wavelets, for an arbitrary dilation factor a> 1, that are generated …

A variety of methods have been proposed for the construction of wavelets. Among others,
notable contributions have been made by Battle, Daubechies, Lemarié, Mallat, Meyer, and …

After reviewing the basic ideas of frame theory from a functional analysis point of view, we
discuss two approaches for the construction of (affine) wavelet frames. The theory of Frame …

Starting from any two compactly supported refinable functions in L 2 (R) with dilation factor d,
we show that it is always possible to construct 2d wavelet functions with compact support …

It is well known that in applied and computational mathematics, cardinal B-splines play an
important role in geometric modeling (in computeraided geometric design), statistical data …