Related papers: On alternative wavelet reconstruction formula: a c…
For a given symmetric refinable mask obeying the sum rule of order $n$, an explicit method is suggested for the construction of mutually symmetric almost frame-like wavelet system providing approximation order $n$. A transformation based on…
Bayesian approaches are one of the primary methodologies to tackle an inverse problem in high dimensions. Such an inverse problem arises in hydrology to infer the permeability field given flow data in a porous media. It is common practice…
Wavelet estimators for a probability density f enjoy many good properties, however they are not "shape-preserving" in the sense that the final estimate may not be non-negative or integrate to unity. A solution to negativity issues may be to…
In the general context of complex data processing, this paper reviews a recent practical approach to the continuous wavelet formalism on the sphere. This formalism notably yields a correspondence principle which relates wavelets on the…
The Doppler shift is investigated in one-dimensional system with moving source. Theoretical findings are confirmed in numerical simulations of optical and acoustical waves propagation in simple metamaterial model, showing the reversed shift…
We establish a reproducing formula for the ridgelet transform on $\mathbb{R}^n$ in the framework of Banach lattices introduced in a recent paper by Nieraeth. Our approach is based on the $k$-plane Radon transform and a wavelet-type…
The act of measuring a physical signal or field suggests a generalization of the wavelet transform that turns out to be a windowed version of the Radon transform. A reconstruction formula is derived which inverts this transform. A special…
There are many cases in collider physics and elsewhere where a calibration dataset is used to predict the known physics and / or noise of a target region of phase space. This calibration dataset usually cannot be used out-of-the-box but…
This article introduces the class of continuous time locally stationary wavelet processes. Continuous time models enable us to properly provide scale-based time series models for irregularly-spaced observations for the first time, while…
(Bi)orthogonal (multi)wavelets on the real line have been extensively studied and employed in applications with success. A lot of problems in applications are defined on bounded intervals or domains. Therefore, it is important in both…
In this series of eight papers we present the applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. In this part we consider application of FWT to metaplectic…
We construct a multiresolution theory for spaces bigger then L^2(R). For a good choice of the dilation and translation operators on these larger spaces, it is possible to build singly generated wavelet bases, thus obtaining examples of…
A recently developed new approach, called ``Empirical Wavelet Transform'', aims to build 1D adaptive wavelet frames accordingly to the analyzed signal. In this paper, we present several extensions of this approach to 2D signals (images). We…
A simple inverse problem for the wave equation requires determination of both the wave velocity in a homogenous acoustic material and the transient waveform of an isotropic point radiator, given the time history of the wavefield at a remote…
A program WWZ is introduced, which realizes the wavelet analysis using an improved modification of the algorithm of the Morlet wavelet for a general case of irregularly spaced data, which is typical for the databases available in virtual…
We construct spherical wavelets based on approximate identities that are directional, i.e. not rotation-invariant, and have an adaptive angular selectivity. The problem of how to find a proper representation of distinct kinds of details of…
All wavelets can be associated to a multiresolution like structure, i.e. an incr easing sequence of subspaces of L^2(R). We consider the interaction of a wavel et and the translation operator in terms of which of the subspaces in this multi…
Wavelet basis functions are a natural tool for analyzing turbulent flows containing localized coherent structures of different spatial scales. Here, wavelets are used to study the onset and subsequent transition to fully developed…
Compressed sensing (CS) using overcomplete wavelet dictionaries has been a well-investigated topic in the recent times for image and vision applications. In this paper, different overcomplete wavelet transforms have been studied to estimate…
We consider a random process $Y(t)=\exp\{X(t)\}$, where $X(t)$ is a centered second-order process which correlation function $R(t,s)$ can be represented as $\int_{\mathbb{R}} u(t,y)\overline{u(s,y)} dy.$ A multiplicative wavelet-based…