Related papers: A Method for Constructing Wavelet Functions on the…
The purpose of this paper is to represent the integral Hankel transform as a series. If one uses B-spline wavelet this series is a linear combination of the hypergeometrical functions. Numerical evaluation of the test function with known…
We call $i$ a fixed point of a given sequence if the value of that sequence at the $i$-th position coincides with $i$. Here, we enumerate fixed points in the class of restricted growth sequences. The counting process is conducted by…
The main objective of this paper is to define the mother wavelet on local fields and study the continuous wavelet transform (CWT) and some of their basic properties. its inversion formula, the Parseval relation and associated convolution…
Time series foundation models (TSFMs) have recently achieved remarkable success in universal forecasting by leveraging large-scale pretraining on diverse time series data. Complementing this progress, incorporating frequency-domain…
In this paper we consider the continuous wavelet transform using Gaussian wavelets multiplied by an appropriate rational term. The zeros and poles of this rational modifier act as free parameters and their choice highly influences the shape…
The selection of grouped variables using the random forest algorithm is considered. First a new importance measure adapted for groups of variables is proposed. Theoretical insights into this criterion are given for additive regression…
An invex function generalizes a convex function in the sense that every stationary point is a global minimizer. Recently, invex functions and their subclasses have attracted attention in signal processing and machine learning. However,…
Continuous wavelet design is the endeavor to construct mother wavelets with desirable properties for the continuous wavelet transform (CWT). One class of methods for choosing a mother wavelet involves minimizing a functional, called the…
Let Y be a response variable related with a set of explanatory variables and let f1, f2, ..., fk be a set of the parametric forms representing a set of candidate's model. Let f* be the true model among the set of k plausible models. We…
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…
This paper provides central limit theorems for the wavelet packet decomposition of stationary band-limited random processes. The asymptotic analysis is performed for the sequences of the wavelet packet coefficients returned at the nodes of…
A complex-valued convolutional network (convnet) implements the repeated application of the following composition of three operations, recursively applying the composition to an input vector of nonnegative real numbers: (1) convolution with…
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…
In this paper, the frequency-domain sound field is regarded as an element of some band-limited function space, and a representation of the field as a linear combination of the reproducing kernel in that space is proposed. This model has the…
It is the main goal of this article to address the bipartite ranking issue from the perspective of functional data analysis (FDA). Given a training set of independent realizations of a (possibly sampled) second-order random function with a…
In this paper we study the general reconstruction of a compactly supported function from its Fourier coefficients using compactly supported shearlet systems. We assume that only finitely many Fourier samples of the function are accessible…
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…
An extremely simple single-trace transmission example shows how an extended source formulation of full waveform inversion can produce an optimization problem without spurious local minima ("cycle skipping"). The data consist of a single…
We introduce a definition of a quasiconvex function on an infinite directed regular tree that depends on what we understood by a segment on the tree. Our definition is based on thinking on segments as sub-trees with the root as the midpoint…
This paper introduces WaveNet, a deep neural network for generating raw audio waveforms. The model is fully probabilistic and autoregressive, with the predictive distribution for each audio sample conditioned on all previous ones;…