Related papers: Rational Gaussian wavelets and corresponding model…
Graph-based models require aggregating information in the graph from neighbourhoods of different sizes. In particular, when the data exhibit varying levels of smoothness on the graph, a multi-scale approach is required to capture the…
The wavelet analysis technique is a powerful tool and is widely used in broad disciplines of engineering, technology, and sciences. In this work, we present a novel scheme of constructing continuous wavelet functions, in which the wavelet…
We suggest an adaptive sampling rule for obtaining information from noisy signals using wavelet methods. The technique involves increasing the sampling rate when relatively high-frequency terms are incorporated into the wavelet estimator,…
Wavelet (Besov) priors are a promising way of reconstructing indirectly measured fields in a regularized manner. We demonstrate how wavelets can be used as a localized basis for reconstructing permeability fields with sharp interfaces from…
Wavelets have proven to be highly successful in several signal and image processing applications. Wavelet design has been an active field of research for over two decades, with the problem often being approached from an analytical…
In this paper we develop an adaptive transform-domain technique based on rational function systems. It is of general importance in several areas of signal theory, including filter design, transfer function approximation, system…
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…
We use Daubechies' orthonormal compact wavelets as a variational basis for the $XY$ model in two and three dimensions. Assuming that the fluctuations of the wavelet coefficients are Gaussian and uncorrelated, minimization of the free energy…
We introduce a variational Bayesian neural network where the parameters are governed via a probability distribution on random matrices. Specifically, we employ a matrix variate Gaussian \cite{gupta1999matrix} parameter posterior…
Wavelet based algorithms in numerical analysis are similar to other transform methods in that vectors and operators are expanded into a basis and the computations take place in this new system of coordinates. However, due to the recursive…
Wavelets are well known for data compression, yet have rarely been applied to the compression of neural networks. This paper shows how the fast wavelet transform can be used to compress linear layers in neural networks. Linear layers still…
The representation of solutions of Maxwell's equations as superpositions of scalar wavelets with vector coefficients developed earlier is generalized to wavelets with polarization, which are matrix-valued. The construction proceeds in four…
Artificial neural networks (NNs) have become the de facto standard in machine learning. They allow learning highly nonlinear transformations in a plethora of applications. However, NNs usually only provide point estimates without…
Spectral graph convolution, an important tool of data filtering on graphs, relies on two essential decisions: selecting spectral bases for signal transformation and parameterizing the kernel for frequency analysis. While recent techniques…
This work introduces a wavelet neural network to learn a filter-bank specialized to fit non-stationary signals and improve interpretability and performance for digital signal processing. The network uses a wavelet transform as the first…
Graph Signal Processing has become a very useful framework for signal operations and representations defined on irregular domains. Exploiting transformations that are defined on graph models can be highly beneficial when the graph encodes…
A novel method for learning optimal, orthonormal wavelet bases for representing 1- and 2D signals, based on parallels between the wavelet transform and fully connected artificial neural networks, is described. The structural similarities…
This work shows the use of a two-dimensional Gabor wavelets in image processing. Convolution with such a two-dimensional wavelet can be separated into two series of one-dimensional ones. The key idea of this work is to utilize a Gabor…
Variational Bayes (VB) has become a widely-used tool for Bayesian inference in statistics and machine learning. Nonetheless, the development of the existing VB algorithms is so far generally restricted to the case where the variational…
Spatial concurrent linear models, in which the model coefficients are spatial processes varying at a local level, are flexible and useful tools for analyzing spatial data. One approach places stationary Gaussian process priors on the…