Related papers: Convolution Based Special Affine Wavelet Transform…
Inspired by recent interest in geometric deep learning, this work generalises the recently developed Slepian scale-discretised wavelets on the sphere to Riemannian manifolds. Through the sifting convolution, one may define translations and,…
The notion of wavelets is defined. It is briefly described {\it what} are wavelets, {\it how} to use them, {\it when} we do need them, {\it why} they are preferred and {\it where} they have been applied. Then one proceeds to the…
This paper studies the effects on Zernike coefficients of aperture scaling, translation and rotation, when a given aberrated wavefront is described on the Zernike polynomial basis. It proposes a new analytical method for computing the…
We study approximation properties generated by highly regular scaling functions and orthonormal wavelets. These properties are conveniently described in the framework of Gelfand-Shilov spaces. Important examples of multiresolution analyses…
In the present paper, details are given on the implementation of a wavelet-based analysis tailored to the processing of acoustical signals. The family of the suitable wavelets (`Reimann wavelets') are obtained in the time domain from a…
We propose the application of multiresolution transforms, such as wavelets (WT) and curvelets (CT), to the reconstruction of images of extended objects that have been acquired with adaptive optics (AO) systems. Such multichannel approaches…
Low-light image enhancement is a classical computer vision problem aiming to recover normal-exposure images from low-light images. However, convolutional neural networks commonly used in this field are good at sampling low-frequency local…
Domain-invariant representation learning is a powerful method for domain generalization. Previous approaches face challenges such as high computational demands, training instability, and limited effectiveness with high-dimensional data,…
Super-resolution (SR) refers to a combination of optical design and signal processing techniques jointly employed to obtain reconstructed wave-fronts at a higher-resolution from multiple low-resolution samples, overcoming the intrinsic…
The notion of group invariance helps neural networks in recognizing patterns and features under geometric transformations. Group convolutional neural networks enhance traditional convolutional neural networks by incorporating group-based…
We present an effective and efficient method that explores the properties of Transformers in the frequency domain for high-quality image deblurring. Our method is motivated by the convolution theorem that the correlation or convolution of…
In this paper, we describe Fourier-based Wave Front Sensors (WFS) as linear integral operators, characterized by their Kernel. In a first part, we derive the dependency of this quantity with respect to the WFS's optical parameters: pupil…
Face super-resolution aims to reconstruct a high-resolution face image from a low-resolution face image. Previous methods typically employ an encoder-decoder structure to extract facial structural features, where the direct downsampling…
In ground-based astronomy, Adaptive Optics (AO) is a pivotal technique, engineered to correct wavefront phase distortions and thereby enhance the quality of the observed images. Integral to an AO system is the wavefront sensor (WFS), which…
We propose the application of graphical convolution to the analysis of the resonance phenomenon. This time-domain approach encompasses both the finally attained periodic oscillations and the initial transient period. It also provides…
In this paper, we propose an end-to-end speech recognition network based on Nvidia's previous QuartzNet model. We try to promote the model performance, and design three components: (1) Multi-Resolution Convolution Module, replaces the…
We introduce a fast algorithm for generating long self-affine profiles. The algorithm, which is based on the fast wavelet transform, is faster than the conventional Fourier filtering algorithm. In addition to increased performance for large…
The standard chirplet transform (CT) with a chirp-modulated Gaussian window provides a valuable tool for analyzing linear chirp signals. The parameters present in the window determine the performance of the CT and play a vital role in…
We develop an exact wavelet transform on the three-dimensional ball (i.e. on the solid sphere), which we name the flaglet transform. For this purpose we first construct an exact transform on the radial half-line using damped Laguerre…
We describe the construction of a spherical wavelet analysis through the inverse stereographic projection of the Euclidean planar wavelet framework, introduced originally by Antoine and Vandergheynst and developed further by Wiaux et al.…