Related papers: Continuous empirical wavelets systems
The use of orthonormal wavelet basis functions for solving singular integral scattering equations is investigated. It is shown that these basis functions lead to sparse matrix equations which can be solved by iterative techniques. The…
In this paper we explore generalizations of metric structures of the gravitational wave type to geometries containing an independent connection. The aim is simply to establish a new category of connections compatible, according to some…
Natural and engineered media usually involve combinations of solid, fluid and porous layers, and accurate and stable modelling of wave propagation in such complex multilayered media is fundamental to evaluating their properties with…
Here we present a method of constructing steerable wavelet frames in $L_2(\mathbb{R}^d)$ that generalizes and unifies previous approaches, including Simoncelli's pyramid and Riesz wavelets. The motivation for steerable wavelets is the need…
In order to reconstruct the initial conditions of the universe it is important to devise a method that can efficiently constrain the shape of the power spectrum of primordial matter density fluctuations in a model-independent way from data.…
For an arbitrary matrix dilation, any integer n and any integer/semi-integer c, we describe all masks that are symmetric with respect to the point c and have sum rule of order n. For each such mask, we give explicit formulas for wavelet…
Using continuous wavelet transform it is possible to construct a regularization procedure for scale-dependent quantum field theory models, which is complementary to functional renormalization group method in the sense that it sums up the…
A statistical inference method is developed and tested for pairwise interacting systems whose degrees of freedom are continuous angular variables, such as planar spins in magnetic systems or wave phases in optics and acoustics. We…
With the recent success of representation learning methods, which includes deep learning as a special case, there has been considerable interest in developing techniques that incorporate known physical constraints into the learned…
Random Wavelet Series form a class of random processes with multifractal properties. We give three applications of this construction. First, we synthesize a random function having any given spectrum of singularities satisfying some…
Given an inverse problem with a normalizing flow prior, we wish to estimate the distribution of the underlying signal conditioned on the observations. We approach this problem as a task of conditional inference on the pre-trained…
We report numerical investigations of wave turbulence in a vibrating plate. The possibility to implement advanced measurement techniques and long time numerical simulations makes this system extremely valuable for wave turbulence studies.…
In this paper we study the problem of computing wavelet coefficients of compactly supported functions from their Fourier samples. For this, we use the recently introduced framework of generalized sampling. Our first result demonstrates that…
In this short report it is argued that by the use of wavelets formalism it is possible to describe the q-bit state. The wavelet formalism address the real-valued physical signals, for example, obtained during typical physical measurements.
We consider an approach to the analysis of nonstationary processes based on the application of wavelet basis sets constructed using segments of the analyzed time series. The proposed method is applied to the analysis of time series…
This paper outlines a general formal framework for reasoning systems, intended to support future analysis of inference architectures across domains. We model reasoning systems as structured tuples comprising phenomena, explanation space,…
In this paper, we derive a practical, general framework for creating adaptive iterative (linearization or splitting) algorithms to solve multi-physics problems. This means that, given an iterative method, we derive \textit{a posteriori}…
This paper examines the wavelet multiplicity function. An explicit formula for the multiplicity function is derived. An application to operator interpolation is then presented. We conclude with several remarks regarding the wavelet…
We introduce layer systems for proving generalizations of the modularity of confluence for first-order rewrite systems. Layer systems specify how terms can be divided into layers. We establish structural conditions on those systems that…
It is an open problem whether any pair of Bessel sequences with wavelet structure can be extended to a pair of dual frames by adding a pair of singly generated wavelet systems. We consider the particular case where the given wavelet systems…