Related papers: Slepian Scale-Discretised Wavelets on Manifolds
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…
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…
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…
In the domain of image-set based classification, a considerable advance has been made by representing original image sets as covariance matrices which typical lie in a Riemannian manifold. Specifically, it is a Symmetric Positive Definite…
Modeling information that resides on vertices of large graphs is a key problem in several real-life applications, ranging from social networks to the Internet-of-things. Signal Processing on Graphs and, in particular, graph wavelets can…
This article is devoted to developing a theory for effective kernel interpolation and approximation in a general setting. For a wide class of compact, connected $C^\infty$ Riemannian manifolds, including the important cases of spheres and…
Image deblurring is a classical computer vision problem that aims to recover a sharp image from a blurred image. To solve this problem, existing methods apply the Encode-Decode architecture to design the complex networks to make a good…
We introduce slant Riemannian maps from Riemannian manifolds to almost Hermitian manifolds as a generalization of slant immersions, invariant Riemannian maps and anti-invariant Riemannian maps. We give examples, obtain characterizations and…
In the chapter "Multiresolution Analysis on Compact Riemannian Manifolds" Isaac Pesenson describes multiscale analysis, sampling, interpolation and approximation of functions defined on manifolds. His main achievements are: construction on…
Stable fold maps are fundamental tools in a generalization of the theory of Morse functions on smooth manifolds and its application to studies of topological properties of smooth manifolds. Round fold maps were introduced as stable fold…
The symplectic Stiefel manifold, denoted by $\mathrm{Sp}(2p,2n)$, is the set of linear symplectic maps between the standard symplectic spaces $\mathbb{R}^{2p}$ and $\mathbb{R}^{2n}$. When $p=n$, it reduces to the well-known set of $2n\times…
Multiresolution analyses based upon interpolets, interpolating scaling functions introduced by Deslauriers and Dubuc, are particularly well-suited to physical applications because they allow exact recovery of the multiresolution…
Unoriented surface reconstruction is an important task in computer graphics and has extensive applications. Based on the compact support of wavelet and orthogonality properties, classic wavelet surface reconstruction achieves good and fast…
This article presents a novel resolution to the problem of spline interpolation versus least-squares fitting on smooth Riemannian manifolds utilizing the method of gradient flows of networks. This approach represents a contribution to both…
Spline interpolation is a widely used class of methods for solving interpolation problems by constructing smooth interpolants that minimize a regularized energy functional involving the Laplacian operator. While many existing approaches…
Tight framelets on a smooth and compact Riemannian manifold $\mathcal{M}$ provide a tool of multiresolution analysis for data from geosciences, astrophysics, medical sciences, etc. This work investigates the construction, characterizations,…
We investigate the Slepian spatiospectral localization problem within subdomains of the $d$-dimensional ball. Opposed to the more classical setups of the Euclidean space or the sphere, the ball lacks a standard or universally accepted…
In analogy with steerable wavelets, we present a general construction of adaptable tight wavelet frames, with an emphasis on scaling operations. In particular, the derived wavelets can be "dilated" by a procedure comparable to the operation…
We develop a method to estimate the power spectrum of a stochastic process on the sphere from data of limited geographical coverage. Our approach can be interpreted either as estimating the global power spectrum of a stationary process when…
The paper shows that under some mild conditions $n$-dimensional spherical wavelets derived from approximate identities build semi-continuous frames. Moreover, for sufficiently dense grids Poisson wavelets on $n$-dimensional spheres…