Related papers: Second-Generation Curvelets on the Sphere
We provide a detailed analysis of the obstruction (studied first by S. Durand and later by R. Yin and one of us) in the construction of multidirectional wavelet orthonormal bases corresponding to any admissible frequency partition in the…
Wavelet Transforms are a widely used technique for decomposing a signal into coefficient vectors that correspond to distinct frequency/scale bands while retaining time localization. This property enables an adaptive analysis of signals at…
Analysis of human sketches in deep learning has advanced immensely through the use of waypoint-sequences rather than raster-graphic representations. We further aim to model sketches as a sequence of low-dimensional parametric curves. To…
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…
We develop a sampling scheme on the sphere that permits accurate computation of the spherical harmonic transform and its inverse for signals band-limited at $L$ using only $L^2$ samples. We obtain the optimal number of samples given by the…
Some techniques for the study of intermittency by means of wavelet transforms, are presented on an example of synthetic turbulent signal. Several features of the turbulent field, that cannot be probed looking at standard structure function…
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…
Many scientific and engineering problems involving multi-physics span a wide range of scales. Understanding the interactions across these scales is essential for fully comprehending such complex problems. However, visualizing multivariate,…
In this article, we construct discrete tight frames for $L^2(\mathbb{S}^{d-1})$, $d\geq3$, which consist of localized polynomial wavelets with adjustable degrees of directionality. In contrast to the well studied isotropic case, these…
In statistical dimensionality reduction, it is common to rely on the assumption that high dimensional data tend to concentrate near a lower dimensional manifold. There is a rich literature on approximating the unknown manifold, and on…
Collaborative filtering is a popular approach in recommender systems, whose objective is to provide personalized item suggestions to potential users based on their purchase or browsing history. However, personalized recommendations require…
Order-independent transparency schemes rely on low-order approximations of transmittance as a function of depth. We introduce a new wavelet representation of this function and an algorithm for building and evaluating it efficiently on a…
In this paper, we propose a new redundant wavelet transform applicable to scalar functions defined on high dimensional coordinates, weighted graphs and networks. The proposed transform utilizes the distances between the given data points.…
We introduce a generalized attention mechanism for spherical domains, enabling Transformer architectures to natively process data defined on the two-dimensional sphere - a critical need in fields such as atmospheric physics, cosmology, and…
Second order spiral splines are $C^2$ unit-speed planar curves that can be used to interpolate a list $Y$ of $n+1$ points in $\R ^2$ at times specified in some list $T$, where $n\geq 2$. Asymptotic methods are used to develop a fast…
Many problems across computer vision and the natural sciences require the analysis of spherical data, for which representations may be learned efficiently by encoding equivariance to rotational symmetries. We present a generalized spherical…
We introduce a nonlocal vector calculus on the unit two-sphere using weakly singular integral operators. Within this framework, the operators are diagonalizable in terms of scalar and vector spherical harmonics, a property that facilitates…
We present a new method for the analysis of images, a fundamental task in observational astronomy. It is based on the linear decomposition of each object in the image into a series of localised basis functions of different shapes, which we…
We construct an algorithm for implementing the discrete wavelet transform by means of matrices in SO_2(R) for orthonormal compactly supported wavelets and matrices in SL_m(R), m > = 2, for compactly supported biorthogonal wavelets. We show…
As neural networks become able to generate realistic artificial images, they have the potential to improve movies, music, video games and make the internet an even more creative and inspiring place. Yet, the latest technology potentially…