Related papers: Wavelet-based tools to analyze, filter, and recons…
In this paper, we have studied continuous fractional wavelet transform (CFrWT) in $n$-dimensional Euclidean space $\mathbb{R}^n$ with dilation parameter $\boldsymbol a=(a_{1},a_{2},\ldots,a_{n}),$ such that none of $a_{i}'s$ are zero.…
Some general remarks about integral transform approaches to response functions are made. Their advantage for calculating cross sections at energies in the continuum is stressed. In particular we discuss the class of kernels that allow…
The underlying mathematics of the wavelet formalism is a representation of the inhomogeneous Lorentz group or the affine group. Within the framework of wavelets, it is possible to define the ``window'' which allows us to introduce a…
With the increasing growth of technology and the entrance into the digital age, we have to handle a vast amount of information every time which often presents difficulties. So, the digital information must be stored and retrieved in an…
Like the continous shearlet transform and their relatives, discrete transformations based on the interplay between several filterbanks with anisotropic dilations provide a high potential to recover directed features in two and more…
In this paper we combine partial-wave (`modal') methods with a wavelet analysis of the CMB bispectrum. Our implementation exploits the advantages of both approaches to produce robust, reliable and efficient estimators which can constrain…
An exact solution of the homogeneous wave equation, which was found previously, is treated from the point of view of continuous wavelet analysis (CWA). If time is a fixed parameter, the solution represents a new multidimensional mother…
The wavelet transform, a family of orthonormal bases, is introduced as a technique for performing multiresolution analysis in statistical mechanics. The wavelet transform is a hierarchical technique designed to separate data sets into sets…
Biomedical signal classification presents unique challenges due to long sequences, complex temporal dynamics, and multi-scale frequency patterns that are poorly captured by standard transformer architectures. We propose WaveFormer, a…
The empirical wavelet transform is a data-driven time-scale representation consisting of an adaptive filter bank. Its robustness to data has made it the subject of intense developments and an increasing number of applications in the last…
Faraday tomography through broadband polarimetry can provide crucial information on magnetized astronomical objects, such as quasars, galaxies, or galaxy clusters. However, the limited wavelength coverage of the instruments requires that we…
Recent work introduced a unified framework for steerable and directional wavelets in two and three dimensions that ensures many desirable properties, such as a multi-scale structure, fast transforms, and a flexible angular localization. We…
Convolutional neural network (CNN), with ability of feature learning and nonlinear mapping, has demonstrated its effectiveness in prognostics and health management (PHM). However, explanation on the physical meaning of a CNN architecture…
We propose a class of spherical wavelet bases for the analysis of geophysical models and forthe tomographic inversion of global seismic data. Its multiresolution character allows for modeling with an effective spatial resolution that varies…
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…
We propose a novel method for constructing wavelet transforms of functions defined on the vertices of an arbitrary finite weighted graph. Our approach is based on defining scaling using the the graph analogue of the Fourier domain, namely…
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.…
In a preceding Letter (Opt. Lett. 32, 554 (2007)) we have proposed complex continuous wavelet transforms (CCWTs) and found Laguerre--Gaussian mother wavelets family. In this work we present the inversion formula and Parsval theorem for CCWT…
As the sensitivity and observing time of gravitational-wave detectors increase, a more diverse range of signals is expected to be observed from a variety of sources. Especially, long-lived gravitational-wave transients have received…
Accurate density estimation methodologies play an integral role in a variety of scientific disciplines, with applications including simulation models, decision support tools, and exploratory data analysis. In the past, histograms and kernel…