This paper systematically studies the well-known Mexican hat wavelet (MHW) on manifold
geometry, including its derivation, properties, transforms, and applications. The MHW is …

Given a two-dimensional smooth manifold M and a bijective projection p from M on a fixed
plane (or a subset of that plane), we explore systematically how a wavelet transform (WT) on …

We review the coherent state (or group-theoretical) construction of the continuous wavelet
transform (CWT) on the two-sphere. Next, we describe the construction of a CWT on the …

We present a method for constructing wavelet bases on the unit sphere S 2 of R 3, using the
radial projection and an inner product associated to a convex polyhedron having the origin …

The prospects of atomic structure imaging with the continuous spherical wavelet transform
(CSWT) as applied to white beam x-ray fluorescence holograms (XFH) are discussed …

The X-ray bone images are extensively used by the medical practitioners to detect the
minute fractures as they are painless and economical compared to other image modalities …

Wavelets can be interpreted as coherent states and this group theoretic approach is very
successful. Unfortunately, this approach fails on spheres and other manifolds. In this paper …

From Design Methods and Generation Schemes to State-of-the-Art Applications Wavelets
are powerful tools for functional analysis and geometry processing, enabling researchers to …

In a first part, we discuss several properties that seem desirable for any type of wavelet, such
as smoothness, orthogonality, local support, Riesz stability, or vanishing moments. Then we …

On the basis of sampling approximation for a function defined on a bounded interval by
combining Coiflet‐type wavelet expansion and technique of boundary extension, a space …