Related papers: S2LET: A code to perform fast wavelet analysis on …
In a recent paper, we analyzed the properties of a new kind of spherical wavelets (called needlets) for statistical inference procedures on spherical random fields; the investigation was mainly motivated by applications to cosmological…
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…
We present Wavemoth, an experimental open source code for computing scalar spherical harmonic transforms (SHTs). Such transforms are ubiquitous in astronomical data analysis. Our code performs substantially better than existing publicly…
Wavelet based algorithms in numerical analysis are similar to other transform methods in that vectors and operators are expanded into a basis and the computations take place in this new system of coordinates. However, due to the recursive…
This paper introduces the synchrosqueezed curvelet transform as an optimal tool for 2D mode decomposition of wavefronts or banded wave-like components. The synchrosqueezed curvelet transform consists of a generalized curvelet transform with…
Satellites mapping the spatial variations of the gravitational or magnetic fields of the Earth or other planets ideally fly on polar orbits, uniformly covering the entire globe. Thus, potential fields on the sphere are usually expressed in…
We present here a simple construction of a wavelet system for the three-dimensional ball, which we label \emph{Radial 3D Needlets}. The construction envisages a data collection environment where an observer located at the centre of the ball…
We present a self-consistent framework to perform the wavelet analysis of two-dimensional statistical distributions. The analysis targets the 2D probability density function (p.d.f.) of an input sample, in which each object is characterized…
We construct the spin flaglet transform, a wavelet transform to analyze spin signals in three dimensions. Spin flaglets can probe signal content localized simultaneously in space and frequency and, moreover, are separable so that their…
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…
The Easy Path Wavelet Transform is an adaptive transform for bivariate functions (in particular natural images) which has been proposed in [1]. It provides a sparse representation by finding a path in the domain of the function leveraging…
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…
Wavelets and their associated transforms are highly efficient when approximating and analyzing one-dimensional signals. However, multivariate signals such as images or videos typically exhibit curvilinear singularities, which wavelets are…
Discrete wavelet transform of finite-length signals must necessarily handle the signal boundaries. The state-of-the-art approaches treat such boundaries in a complicated and inflexible way, using special prolog or epilog phases. This holds…
This paper is concerned with density estimation of directional data on the sphere. We introduce a procedure based on thresholding on a new type of spherical wavelets called {\it needlets}. We establish a minimax result and prove its…
A fast algorithm for Antoine and Vandergheynst's (1998) directional continuous spherical wavelet transform (CSWT) is presented. Computational requirements are reduced by a factor of O(\sqrt{N}), when N is the number of pixels on the sphere.…
We construct an adaptive estimator of a density function on $d$ dimensional unit sphere $S^d$ ($d \geq 2 $), using a new type of spherical frames. The frames, or as we call them, stereografic wavelets are obtained by transforming a wavelet…
Coarse-to-fine schemes are widely used in traditional single-image motion deblur; however, in the context of deep learning, existing multi-scale algorithms not only require the use of complex modules for feature fusion of low-scale RGB…
Wavelet-based segmentation approaches are widely used for texture segmentation purposes because of their ability to characterize different textures. In this paper, we assess the influence of the chosen wavelet and propose to use the…
In this paper we analyze two-dimensional wavelet reconstructions from Fourier samples within the framework of generalized sampling. For this, we consider both separable compactly-supported wavelets and boundary wavelets. We prove that the…