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We introduce one- and two-dimensional `exponential shapelets': orthonormal basis functions that efficiently model isolated features in data. They are built from eigenfunctions of the quantum mechanical hydrogen atom, and inherit mathematics…
The empirical wavelet transform is an adaptive multiresolution analysis tool based on the idea of building filters on a data-driven partition of the Fourier domain. However, existing 2D extensions are constrained by the shape of the…
In this paper we propose spectral tools based on non-decimated complex wavelet transforms implemented by their matrix formulation. This non-decimated complex wavelet spectra utilizes both real and imaginary parts of complex-valued wavelet…
The quadratic phase Fourier transform has gained much popularity in recent years because of its applications in image and signal processing. However, the QPFT is inadequate for localizing the quadratic phase spectrum which is required in…
We describe and study geometric properties of discrete circular and spherical means of directional derivatives of functions, as well as discrete approximations of higher order differential operators. For an arbitrary dimension we present a…
In this paper we show that certain trigonometric polynomial shearlets which are special cases of directional de la Vall\'{e}e Poussin type wavelets are able to detect singularities along boundary curves of periodic characteristic functions.…
This work introduces Differential Wavelet Amplifier (DWA), a drop-in module for wavelet-based image Super-Resolution (SR). DWA invigorates an approach recently receiving less attention, namely Discrete Wavelet Transformation (DWT). DWT…
Using the fact that every worldsheet is ruled by two (light-cone) copies of worldlines, the recent classification of off-shell supermultiplets of N-extended worldline supersymmetry is extended to construct standard off-shell and also…
Orthogonal wavelet transforms are a cornerstone of modern signal and image denoising because they combine multiscale representation, energy preservation, and perfect reconstruction. In this paper, we show that these advantages can be…
Recently introduced inpainting algorithms using a combination of applied harmonic analysis and compressed sensing have turned out to be very successful. One key ingredient is a carefully chosen representation system which provides…
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…
Due to the emergence of new high resolution numerical weather prediction (NWP) models and the availability of new or more reliable remote sensing data, the importance of efficient spatial verification techniques is growing. Wavelet…
Deep kernel processes are a recently introduced class of deep Bayesian models that have the flexibility of neural networks, but work entirely with Gram matrices. They operate by alternately sampling a Gram matrix from a distribution over…
A family of orthonormal bases of ultrametric wavelets in the space of quadratically integrable with respect to arbitrary measure functions on general (up to some topological restrictions) ultrametric space is introduced. Pseudodifferential…
In this paper we present a general approach to multivariate periodic wavelets generated by scaling functions of de la Vall\'ee Poussin type. These scaling functions and their corresponding wavelets are determined by their Fourier…
We give explicit polynomial-sized (in $n$ and $k$) semidefinite representations of the hyperbolicity cones associated with the elementary symmetric polynomials of degree $k$ in $n$ variables. These convex cones form a family of…
Spectral representations of the dilation and translation operators on $L^2({\mathbb R})$ are built through appropriate bases. Orthonormal wavelets and multiresolution analysis are then described in terms of rigid operator-valued functions…
Pursuing a continuous visual representation that offers flexible frequency modulation and fast rendering speed has recently garnered increasing attention in the fields of 3D vision and graphics. However, existing representations often rely…
Several variants of Convolutional Neural Networks (CNN) have been developed for Magnetic Resonance (MR) image reconstruction. Among them, U-Net has shown to be the baseline architecture for MR image reconstruction. However, sub-sampling is…
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…