Discrete affine systems are obtained by applying dilations to a given shift-invariant system.
The complicated structure of the affine system is due, first and foremost, to the fact that it is …

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

During the last several years, frames have become increasingly popular; they have
appeared in a large number of applications, and several concrete constructions of frames of …

As a rapidly growing, multidisciplinary field of mathematics, wavelet theory provides the
major mathematical multiscale representation for analyzing functions/data and has …

As the use of virtual and augmented reality applications becomes more common, the need
to fully understand how observers perceive spatial relationships grows more critical. One of …

Using the range function approach to shift invariant spaces in L2 (R n) we give a simple
characterization of frames and Riesz families generated by shifts of a countable set of …

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 …

Graph representation learning has many real-world applications, from self-driving LiDAR,
3D computer vision to drug repurposing, protein classification, social networks analysis. An …

In the past few decades, mathematics based approaches have been widely adopted in
various image restoration problems; the partial differential equation (PDE) based approach …

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 …