Related papers: Wavelets and wavelet-like transforms on the sphere…
We summarise the construction of exact axisymmetric scale-discretised wavelets on the sphere and on the ball. The wavelet transform on the ball relies on a novel 3D harmonic transform called the Fourier-Laguerre transform which combines the…
In recent years, a rapidly growing literature has focussed on the construction of wavelet systems to analyze functions defined on the sphere. Our purpose in this paper is to generalize these constructions to situations where sections of…
A new construction of a directional continuous wavelet analysis on the sphere is derived herein. We adopt the harmonic scaling idea for the spherical dilation operator recently proposed by Sanz et al. but extend the analysis to a more…
In the present paper, a construction of spin weighted spherical wavelets is presented. It is based on approximate identities, the wavelets are defined for a continuous set of parameters, and the wavelet transform is invertible directly by…
The analysis of gravitational-wave (GW) signals is one of the most challenging application areas of signal processing. Wavelet transforms are specially helpful in detecting and analyzing GW transients and several analysis pipelines are…
Recent work introduced a unified framework for steerable and directional wavelets in two and three dimensions that ensures many desirable properties, such as a multi-scale structure, fast transforms, and a flexible angular localization. We…
We construct spherical wavelets based on approximate identities that are directional, i.e. not rotation-invariant, and have an adaptive angular selectivity. The problem of how to find a proper representation of distinct kinds of details of…
A new method is presented for the construction of a natural continuous wavelet transform on the sphere. It incorporates the analysis and synthesis with the same wavelet and the definition of translations and dilations on the sphere through…
Classical multiscale analysis based on wavelets has a number of successful applications, e.g. in data compression, fast algorithms, and noise removal. Wavelets, however, are adapted to point singularities, and many phenomena in several…
We present spatial-Slepian transform~(SST) for the representation of signals on the sphere to support localized signal analysis. We use well-optimally concentrated Slepian functions, obtained by solving the Slepian spatial-spectral…
Graphite is an example of a layered material that can be bent to form fullerenes which promise important applications in electronic nanodevices. The spheroidal geometry of a slightly elliptically deformed sphere was used as a possible…
This chapter is dedicated to recent developments in the field of wavelet analysis for scattered data. We introduce the concept of samplets, which are signed measures of wavelet type and may be defined on sets of arbitrarily distributed data…
Compared with the traditional spherical harmonics, the spherical needlets are a new generation of spherical wavelets that possess several attractive properties. Their double localization in both spatial and frequency domains empowers them…
Analysis on the unit sphere $\mathbb{S}^{2}$ found many applications in seismology, weather prediction, astrophysics, signal analysis, crystallography, computer vision, computerized tomography, neuroscience, and statistics. In the last two…
We construct spherical vector bases that are bandlimited and spatially concentrated, or, alternatively, spacelimited and spectrally concentrated, suitable for the analysis and representation of real-valued vector fields on the surface of…
Wavelets, known to be useful in non-linear multi-scale processes and in multi-resolution analysis, are shown to have a q-deformed algebraic structure. The translation and dilation operators of the theory associate with any scaling equation…
This work is concerned with the study of the adaptivity properties of nonparametric regression estimators over the $d$-dimensional sphere within the global thresholding framework. The estimators are constructed by means of a form of…
In this article, we present a space-frequency theory for spherical harmonics based on the spectral decomposition of a particular space-frequency operator. The presented theory is closely linked to the theory of ultraspherical polynomials on…
Here we present a method of constructing steerable wavelet frames in $L_2(\mathbb{R}^d)$ that generalizes and unifies previous approaches, including Simoncelli's pyramid and Riesz wavelets. The motivation for steerable wavelets is the need…
In this paper we propose a new wavelet transform applicable to functions defined on graphs, high dimensional data and networks. The proposed method generalizes the Haar-like transform proposed in [1], and it is defined via a hierarchical…